How U-Monkey is tested

1. Timber-frame wall with brick cladding, studs at 15% Published example

Build-up, outside to inside: Brick 102 mm (λ 0.77) · unventilated cavity 50 mm · timber sheathing 9 mm (λ 0.13) · mineral wool 140 mm (λ 0.040) between timber studs (15% of the area, λ 0.12) · plasterboard 12.5 mm (λ 0.21). Air-gap correction level 1.

Source: Scottish Government, “U Values: guidance” (published 11 February 2020), document 6.B “Worked examples of U-value calculations using the combined method”, example 6.B.2: timber-framed wall. First issued in 2007 by the Scottish Building Standards Agency.

Figures in the source

1. Layer resistances in the example: brick 0.132, cavity 0.18, sheathing 0.069, plasterboard 0.060 m²K/W; mineral wool 140 mm at λ 0.040 bridged by timber studs at λ 0.12 over 15% of the area; Rsi 0.13, Rse 0.04.
2. Published results: R′T 3.435, R″T 3.304, RT 3.369 m²K/W; air-gap correction ΔU = 0.01 × (2.692 / 3.369)² = 0.006 W/m²K, where 2.692 is the bridged insulation layer; U = 0.30 W/m²K.

The example leaves the 0.006 correction out because it is under 3% of U, which ISO 6946 allows; U-Monkey always adds it, so its unrounded U is a little higher. Both round to 0.30. The resistances are checked to ±0.005 because the example gives each layer’s resistance to three decimal places, so its totals carry that rounding. It dates from 2007, but every input is stated in it, so it checks the combined-method arithmetic rather than any choice of convention.

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2. Cavity wall with an aircrete inner leaf and an insulated dry-lining: two bridged layers Published example

Build-up, outside to inside: Brick 102 mm (λ 0.77) · unventilated cavity 50 mm · aircrete (AAC) blocks 125 mm (λ 0.11) bridged by mortar joints over 6.7% of the area (λ 0.88) · mineral wool 89 mm (λ 0.038) between 38 × 89 mm timber studs and noggings, 11.8% of the area (λ 0.13) · plasterboard 12.5 mm (λ 0.21). Air-gap correction level 1.

Source: Scottish Government, “U Values: guidance” (published 11 February 2020), document 6.B “Worked examples of U-value calculations using the combined method”, example 6.B.3: cavity wall with lightweight masonry leaf and insulated dry-lining.

Figures in the source

1. Layer resistances in the example: brick 0.132 and cavity 0.180; AAC blocks 1.136 over 93.3% of the area and mortar 0.142 over 6.7%; mineral wool 2.342 over 88.2% and timber 0.685 over 11.8%; plasterboard 0.060 m²K/W; Rse 0.04, Rsi 0.13.
2. Upper limit from the four paths: blocks and wool 4.020 m²K/W over 0.823 of the area, mortar and wool 3.026 over 0.059, blocks and timber 2.363 over 0.110, mortar and timber 1.369 over 0.008, so R′T = 3.617 m²K/W.
3. Lower limit: the two bridged layers come to 0.773 and 1.821 m²K/W, so R″T = 3.136 m²K/W, and RT = 3.376 m²K/W.
4. Air-gap correction at level 1: ΔUg = 0.01 × (1.820 / 3.386)² = 0.003 W/m²K. That is under 3% of 1/RT (0.296), so the example leaves it out: U = 1 / 3.376 = 0.30 W/m²K.

Two slips in the example leave its answer unchanged: the averaging step prints 3.636 for R′T, though the 3.617 it has just worked out is what gives its RT of 3.376, and the air-gap step carries the resulting 3.386 (0.003 either way). Its drawing labels the plasterboard λ 0.25 and the studs at 400 mm centres; the calculation uses 0.21 and 11.8%. U-Monkey adds the 0.003 the example leaves out, as it always does; both round to 0.30.

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3. Unfilled cavity wall, no bridging Hand-worked

Build-up, outside to inside: Brick 102.5 mm (λ 0.77) · unventilated cavity 50 mm · aircrete block 100 mm (λ 0.15) · plaster 13 mm (λ 0.57).

Source: hand calculation from the published method, below.

Working

1. RT = Rsi + brick + cavity + block + plaster + Rse = 0.13 + 0.1025/0.77 + 0.18 + 0.100/0.15 + 0.013/0.57 + 0.04
2. = 0.13 + 0.1331 + 0.18 + 0.6667 + 0.0228 + 0.04 = 1.1726 m²K/W
3. U = 1 ÷ RT = 0.8528 W/m²K. There is no insulation layer, so no air-gap correction applies.
4. Basis: Rsi 0.13 and Rse 0.04 for horizontal heat flow; unventilated cavity R 0.18 (BR 443 §4.7.1).

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4. Cavity wall with a 25 mm low-emissivity cavity Hand-worked

Build-up, outside to inside: Brick 102.5 mm (λ 0.77) · 25 mm unventilated cavity faced on one side with a low-emissivity surface · aircrete block 100 mm (λ 0.15) · plaster 13 mm (λ 0.57).

Source: hand calculation from the published method, below.

Working

1. RT = 0.13 + 0.1025/0.77 + 0.44 + 0.100/0.15 + 0.013/0.57 + 0.04 = 0.13 + 0.1331 + 0.44 + 0.6667 + 0.0228 + 0.04 = 1.4326 m²K/W
2. U = 1 ÷ RT = 0.6980 W/m²K
3. Basis: an unventilated cavity of 25 mm or more with one low-emissivity surface (ε 0.2) has R 0.44 in a wall (BR 443 §4.7.2), against 0.18 for an ordinary cavity.

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5. Partial-fill cavity wall: a 50 mm cavity beside a board certified at ε 0.05 Published example

Build-up, outside to inside: Brick 102.5 mm (λ 0.77) · 50 mm unventilated cavity · foil-faced PIR 50 mm (λ 0.022) whose foil is certified at ε 0.05 · aircrete block 100 mm (λ 0.15) · plaster 13 mm (λ 0.57).

Source: BBA Agrément Certificate 14/5133, Product Sheet 2: Kingspan Thermawall TW50 (Issue 2, 28 February 2024). It declares the composite foil facing’s emissivity as 0.05 (BS EN 15976:2011), and its example U-value calculations take a “50 mm low emissivity clear cavity (R = 0.665 m²·K·W⁻¹)”. The certificate for EcoTherm Eco-Cavity (BBA 24/7114, Product Sheet 2, Issue 2, 16 February 2026) uses the same 0.665.

Figures in the source

1. Cavity, BS EN ISO 6946:2017 Annex D (unventilated, horizontal heat flow, d = 0.050 m): hₐ = max(1.25, 0.025/d) = 1.25 W/m²K. E = 1 ÷ (1/0.9 + 1/0.05 − 1) = 0.04972, so hᵣ = E × 5.1 = 0.2536 W/m²K. R = 1 ÷ (hₐ + hᵣ) = 1 ÷ 1.5036 = 0.6651 m²K/W: the certificate’s 0.665.
2. Basis: the foil faces the cavity at its certified 0.05 and the brick face is taken at 0.9. BR 443 §4.7.2 allows a value below 0.2 only where a certificate gives it; at BR 443’s 0.2 the same cavity is 0.44.
3. In this wall that is worth 0.015 W/m²K: RT = 0.13 + 0.1025/0.77 + 0.665 + 0.050/0.022 + 0.100/0.15 + 0.013/0.57 + 0.04 = 3.9303 m²K/W and U = 0.2544, against 0.2699 with the 0.44 cavity.

The certificate gives the cavity resistance to three decimal places, so it is checked to ±0.0005. In the calculator the board in the link carries its certified emissivity, and the cavity beside it picks that up automatically and names the certificate.

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6. Empty timber-stud wall: an air layer bridged by studs Hand-worked

Build-up, outside to inside: OSB 9 mm (λ 0.13) · 100 mm unventilated cavity crossed by 38 mm timber studs at 600 mm centres (λ 0.13) · plasterboard 12.5 mm (λ 0.21).

Source: hand calculation from the published method, below.

Working

1. Stud fraction f = 38/600 = 0.0633. Air path: R 0.18 (100 mm cavity). Stud path: 0.100/0.13 = 0.7692.
2. Other layers and both surfaces: 0.13 + 0.009/0.13 + 0.0125/0.21 + 0.04 = 0.2988.
3. Upper limit: 1/R′T = 0.9367/(0.2988 + 0.18) + 0.0633/(0.2988 + 0.7692), so R′T = 0.4961.
4. Lower limit: R″T = 0.2988 + 1/(0.0633/0.7692 + 0.9367/0.18) = 0.4879.
5. RT = (R′T + R″T)/2 = 0.4920 m²K/W; U = 1 ÷ RT = 2.0325 W/m²K. U-Monkey reports the two limits to 3 d.p.

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7. Plasterboard on dabs: the dabs bridge the air gap (BR 443 §4.6.1) Hand-worked

Build-up, outside to inside: Brick 102.5 mm (λ 0.77) · aircrete block 100 mm (λ 0.15) · 15 mm dot-and-dab gap: air R 0.17 with plaster dabs over 20% of it (λ 0.43) · plasterboard 12.5 mm (λ 0.21).

Source: hand calculation from the published method, below.

Working

1. BR 443 (2019) §4.6.1, plasterboard on dabs: dabs 20% of the area, λ 0.43, 15 mm thick; the 15 mm air space R 0.17. §1 counts "plaster dabs of wall drylining systems" among the repeating thermal bridges included in U.
2. Air path: 0.13 + 0.1025/0.77 + 0.100/0.15 + 0.17 + 0.0125/0.21 + 0.04 = 0.13 + 0.1331 + 0.6667 + 0.17 + 0.0595 + 0.04 = 1.1993. Dab path: the 0.17 replaced by 0.015/0.43 = 0.0349, so 1.0642.
3. Upper limit: 1/R′T = 0.8/1.1993 + 0.2/1.0642, so R′T = 1.1696. Lower limit: the gap as one layer, 1/(0.8/0.17 + 0.2/0.0349) = 0.0958, so R″T = 1.1993 − 0.17 + 0.0958 = 1.1251.
4. RT = (1.1696 + 1.1251)/2 = 1.1474 m²K/W; U = 1 ÷ RT = 0.8716 W/m²K. With the gap left unbridged at 0.17 it would be 0.8338.

Until 11 Oct 2026 U-Monkey took the dab gap as a plain 0.17 air layer; it now adds the dabs as this bridge automatically, as BBA certificates for insulated plasterboards on dabs also do.

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8. Loft insulated at ceiling level: joists at BR 443’s 12.8% and the roof space above (BR 443 §8) Hand-worked

Build-up, outside to inside: Mineral wool 170 mm (λ 0.040) over the joists · mineral wool 100 mm (λ 0.040) between them, softwood joists 12.8% of the area (λ 0.13) · plasterboard 12.5 mm (λ 0.21). Above the insulation: the roof space, R_u 0.2 (tiles on felt, boards or an underlay); Rsi 0.10, Rse 0.04. Air-gap correction level 0 (a second layer covers the joists).

Source: hand calculation from the published method, below.

Working

1. BR 443 (2019) §8, insulation at ceiling level: “All construction elements above insulation layer are collectively assigned a single thermal resistance given in Table 9 of BS EN ISO 6946.” §4.7.6: those values exclude Rse, which is taken as 0.04; they run from 0.06 (tiles with no felt, boards or similar) to 0.3 (roofs lined with boards and felt), and 0.2 is the row for tiles with felt or boards beneath them. §4.5.1: ceiling joists, in the absence of specific information, 47 mm at 400 mm centres plus 1% for other timbers, 0.128.
2. Insulation path: 0.10 + 0.170/0.040 + 0.100/0.040 + 0.0125/0.21 + 0.2 + 0.04 = 0.10 + 4.25 + 2.5 + 0.0595 + 0.2 + 0.04 = 7.1495. Joist path: 2.5 replaced by 0.100/0.13 = 0.7692, so 5.4188.
3. Upper limit: 1/R′T = 0.872/7.1495 + 0.128/5.4188, so R′T = 6.869. Lower limit: the joist layer as one, 1/(0.872/2.5 + 0.128/0.7692) = 1.9410, so R″T = 0.10 + 4.25 + 1.9410 + 0.0595 + 0.2 + 0.04 = 6.591.
4. RT = (6.869 + 6.591)/2 = 6.730 m²K/W; U = 1 ÷ RT = 0.1486 W/m²K. Without the roof space it would be 0.1532; with the joists at 9% and no roof space, as U-Monkey had it before, 0.1506.

Until 11 Oct 2026 U-Monkey treated the roof space as outside (Rse 0.04 alone) and started ceiling joists at 9%. The roof space is now added for every loft, from the roof type chosen in the app (0.2 unless changed), and joists start at BR 443’s 12.8%.

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9. Wall to an integral garage: the unheated space added as SAP 10.2 formula (3) Hand-worked

Build-up, outside to inside: Dense concrete block 100 mm (λ 1.13) on the garage side · PIR board 75 mm (λ 0.022) · plasterboard 12.5 mm (λ 0.21). Beyond it a single integral garage, fully integral, its walls outside the insulation: R_u 0.35 (SAP 10.2 Table 3.1). Rsi 0.13, Rse 0.04; air-gap correction level 0, so the arithmetic stays in the open.

Source: hand calculation from the published method, below.

Working

1. SAP 10.2 §3.3: “U = 1 / (1/Uo + Ru)” (formula 3), where Uo is “the U-value of the element between heated and unheated spaces calculated as if the element was fully exposed to external conditions”. Table 3.1 gives Ru for integral single garages: 0.35 m²K/W for a fully integral garage (side wall, end wall and floor) whose walls separating it from the dwelling are the external walls. BR 443 (2019) §5: “the effect of the unheated space can be incorporated into the U-value of the element”.
2. The wall as if it faced outside air: RT = 0.13 + 0.100/1.13 + 0.075/0.022 + 0.0125/0.21 + 0.04 = 0.13 + 0.0885 + 3.4091 + 0.0595 + 0.04 = 3.7271 m²K/W, so U0 = 1 ÷ 3.7271 = 0.2683 W/m²K.
3. With the garage: U = 1 / (1/0.2683 + 0.35) = 1 / (3.7271 + 0.35) = 1 / 4.0771 = 0.2453 W/m²K. Facing outside air the same wall would need about 8 mm more PIR (R 0.35 × λ 0.022) to reach the same figure.

Added 12 Oct 2026 with U-Monkey’s “On the other side” option, which offers every row of SAP 10.2 Tables 3.1-3.4 (integral garages, unheated stairwells and access corridors, the loft void beside a room in roof) or an Ru of your own.

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10. Rainscreen wall: well-ventilated cavity Hand-worked

Build-up, outside to inside: Timber cladding 20 mm (λ 0.13) · well-ventilated cavity 38 mm · aircrete block 100 mm (λ 0.15) · plaster 13 mm (λ 0.57).

Source: hand calculation from the published method, below.

Working

1. A well-ventilated cavity and everything outside it are disregarded, and the external surface resistance becomes 0.13, equal to Rsi (ISO 6946 §6.9.4; BR 443 §4.7.3).
2. RT = 0.13 + 0.100/0.15 + 0.013/0.57 + 0.13 = 0.13 + 0.6667 + 0.0228 + 0.13 = 0.9495 m²K/W
3. U = 1 ÷ RT = 1.0532 W/m²K

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11. Slightly ventilated cavity, openings 1,000 mm² per metre Hand-worked

Build-up, outside to inside: Brick 102.5 mm (λ 0.77) · 50 mm cavity with 1,000 mm² of openings per metre · aircrete block 100 mm (λ 0.15) · plaster 13 mm (λ 0.57).

Source: hand calculation from the published method, below.

Working

1. Openings between 500 and 1,500 mm² per metre make the cavity slightly ventilated. ISO 6946 §6.9.3: RT = (1500 − Av)/1000 × RT (unventilated) + (Av − 500)/1000 × RT (well-ventilated).
2. Unventilated: 1.1726 m²K/W, as for the unfilled cavity wall above. Well-ventilated: brick and cavity disregarded, Rse 0.13: 0.13 + 0.6667 + 0.0228 + 0.13 = 0.9495 m²K/W.
3. Av = 1,000: RT = 0.5 × 1.1726 + 0.5 × 0.9495 = 1.0610 m²K/W; U = 1 ÷ RT = 0.9425 W/m²K

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12. Exposed floor over a well-ventilated void Hand-worked

Build-up, outside to inside: Soffit board 10 mm (λ 0.25) · well-ventilated void 150 mm · timber deck 18 mm (λ 0.13); heat flow downwards.

Source: hand calculation from the published method, below.

Working

1. The ventilated void and the soffit below it are disregarded. The external surface resistance becomes 0.17, the internal value for downward heat flow (ISO 6946 §6.9.4), not 0.13.
2. RT = 0.17 + 0.018/0.13 + 0.17 = 0.17 + 0.1385 + 0.17 = 0.4785 m²K/W
3. U = 1 ÷ RT = 2.0900 W/m²K. Floors carry no air-gap correction (BR 443 §4.8.1).

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13. Light steel frame wall, cold frame: the BRE Digest 465 weighting Hand-worked

Build-up, outside to inside: Brick 102.5 mm (λ 0.77) · unventilated cavity 50 mm · cement particle board 12 mm (λ 0.23) · mineral wool slab 100 mm (λ 0.038) between steel C-studs 100 mm deep with 50 mm flanges and a 1.2 mm web at 600 mm centres (steel λ 50) · plasterboard 12.5 mm (λ 0.21). Cold frame: all the insulation is between the studs. Air-gap correction level 1.

Source: hand calculation from the published method, below.

Working

1. Layer resistances: brick 0.1025/0.77 = 0.1331; cavity 0.18 (50 mm, unventilated); cement particle board 0.012/0.23 = 0.0522; plasterboard 0.0125/0.21 = 0.0595; with Rsi 0.13 and Rse 0.04 these sum to 0.5948 m²K/W. The λ values are those in U-Monkey’s materials list (steel 50, BR 443 §3.9).
2. The studs are a bridged layer, the fraction taken from the central web (BR 443 §4.10): f = 1.2/600 = 0.002, with no noggings. Through the 100 mm layer the wool path is 0.100/0.038 = 2.6316 m²K/W and the steel path 0.100/50 = 0.0020 m²K/W.
3. Upper limit: 1/R′T = 0.998/(0.5948 + 2.6316) + 0.002/(0.5948 + 0.0020) = 0.30932 + 0.00335 = 0.31267, so R′T = 3.1982 m²K/W.
4. Lower limit: the bridged layer is 1/(0.002/0.0020 + 0.998/2.6316) = 1/(1.0000 + 0.3792) = 0.7250, so R″T = 0.5948 + 0.7250 = 1.3199 m²K/W.
5. Digest 465 weighting for a cold frame with flange w = 50 mm, centres s = 600 mm and depth d = 100 mm: p = 0.8 × (R″T/R′T) + 0.44 − 0.1 × (w/40) − 0.2 × (600/s) − 0.04 × (d/100) = 0.8 × 0.41268 + 0.44 − 0.125 − 0.2 − 0.04 = 0.4051.
6. RT = p × R′T + (1 − p) × R″T = 0.4051 × 3.1982 + 0.5949 × 1.3199 = 2.0809 m²K/W, so U₀ = 1 ÷ RT = 0.4806 W/m²K. The plain ISO 6946 average (p = 0.5) would give RT 2.2590 m²K/W and U 0.4427 W/m²K.
7. Air gaps, level 1 (BR 443 §4.8.1), with R₁ the bridged insulation layer as in the timber-frame example: ΔU = 0.01 × (0.7250/2.0809)² = 0.0012 W/m²K. U = 0.4806 + 0.0012 = 0.4818 W/m²K.
8. Basis: BR 443 (2019) §4.10: a warm frame takes the normal ISO 6946 calculation, while a cold frame or hybrid uses “the basis in Digest 465”. The p equation is as reproduced in Santos, Lemes and Mateus, Energies 13 (2020) 840, Eq. 10, and in SCI P312, Eq. [3].

BRE Digest 465 itself (2002) is not freely available and was not read. The p equation is taken from two independent reproductions, which agree, and SCI P312’s worked example (p = 0.9670) fixes the sign of every term. U-Monkey also notes that this wall is outside the 0.20–0.45 W/m²K range the equation was derived from: a cold frame with 100 mm of wool between the studs is a poor wall.

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14. Air-gap correction, level 1 Hand-worked

Build-up, outside to inside: Render 20 mm (λ 0.87) · aircrete block 100 mm (λ 0.15) · PIR 100 mm (λ 0.022) · plasterboard 12.5 mm (λ 0.21). One insulation layer, so level 1.

Source: hand calculation from the published method, below.

Working

1. RT = 0.13 + 0.020/0.87 + 0.100/0.15 + 0.100/0.022 + 0.0125/0.21 + 0.04 = 0.13 + 0.0230 + 0.6667 + 4.5455 + 0.0595 + 0.04 = 5.4646 m²K/W; U₀ = 1 ÷ RT = 0.1830 W/m²K
2. Level 1 (BR 443 §4.8.1): ΔU″ = 0.01, so ΔU = 0.01 × (R₁/RT)² = 0.01 × (4.5455/5.4646)² = 0.0069 W/m²K, where R₁ is the PIR layer.
3. U = U₀ + ΔU = 0.1899 W/m²K

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15. Stainless-steel wall ties through partial-fill PIR Hand-worked

Build-up, outside to inside: Brick 102.5 mm (λ 0.77) · unventilated cavity 50 mm · PIR 100 mm (λ 0.022) crossed by stainless ties · aircrete block 100 mm (λ 0.15) · plaster 13 mm (λ 0.5). Air-gap level 0.

Source: hand calculation from the published method, below.

Working

1. RT = 0.13 + 0.1025/0.77 + 0.18 + 0.100/0.022 + 0.100/0.15 + 0.013/0.5 + 0.04 = 5.7212 m²K/W; U₀ = 1 ÷ RT = 0.1748 W/m²K. With no bridging, the upper-limit resistance RT,h is the same 5.7212.
2. Ties: stainless steel λ 17 W/mK, 12.5 mm² cross-section, 2.5 per m² (the typical figures in BR 443 §4.8.2), passing right through the 100 mm PIR, so α = 0.8.
3. ΔUf = α × λf × nf × Af ÷ d₀ × (R₁/RT,h)² = 0.8 × 17 × 2.5 × 0.0000125 ÷ 0.100 × (4.5455/5.7212)² = 0.00425 × 0.6312 = 0.00268 W/m²K (ISO 6946 Annex F)
4. U = U₀ + ΔUf = 0.1775 W/m²K

Next to a foil-faced board U-Monkey would normally treat the cavity as low-emissivity; this case uses the ordinary 0.18 cavity to keep the arithmetic short, and the link opens it with that automatic setting switched off.

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16. Inverted flat roof: rain-water correction Hand-worked

Build-up, outside to inside: Gravel ballast 50 mm (λ 2.0) · XPS 120 mm (λ 0.034), butt-jointed · waterproofing 2 mm (λ 0.23) · timber deck 18 mm (λ 0.13) · plasterboard 12.5 mm (λ 0.21). Rain p = 3 mm/day.

Source: hand calculation from the published method, below.

Working

1. Upward heat flow: Rsi 0.10, Rse 0.04. RT = 0.10 + 0.050/2.0 + 0.120/0.034 + 0.002/0.23 + 0.018/0.13 + 0.0125/0.21 + 0.04 = 3.9011 m²K/W; U₀ = 1 ÷ RT = 0.2563 W/m²K
2. Rain water running between the boards and over the membrane: ΔUr = p × f·x × (R₁/RT)², with p = 3 mm/day and f·x = 0.04 for butt-jointed boards (BR 443 §4.8.6). R₁ = 0.120/0.034 = 3.5294, the insulation above the waterproofing.
3. ΔUr = 3 × 0.04 × (3.5294/3.9011)² = 0.12 × 0.8185 = 0.0982 W/m²K
4. U = U₀ + ΔUr = 0.3546 W/m²K

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17. Uninsulated suspended timber floor (published field-study model) Published example

Build-up, outside to inside: 19 mm softwood floorboards (λ 0.13) over a ventilated void. Exposed perimeter 9.1 m, floor area 27.7 m², foundation wall 220 mm, clay (λ 1.5), floor 0.17 m above ground, void walls U 1.7, vents 0.0024 m² per metre of perimeter, shielding factor 0.05.

Source: Pelsmakers, S., Croxford, B. and Elwell, C. A., “Suspended timber ground floors: measured heat loss compared with models”, Building Research & Information 47(2), 127–140 (published online 2017), doi:10.1080/09613218.2017.1331315. Inputs from Table 1; ISO 13370 result from Table 4 (open-access accepted manuscript, White Rose eprint 116433).

Figures in the source

1. Inputs as published in Table 1: perimeter 9.1 m, area 27.7 m² (B′ 6.09 m), foundation wall 0.22 m, clay λ 1.5 W/mK, floor 0.17 m above ground, foundation wall U 1.7 W/m²K, ventilation 0.0024 m² per metre, wind 5 m/s, shielding 0.05, 19 mm softwood boards λ 0.13; Rsi 0.17, Rse 0.04.
2. Published ISO 13370 result in Table 4: 0.57 W/m²K, and 0.51 W/m²K with the wind speed at 1 m/s.

U-Monkey’s intermediate figures at 5 m/s: B′ 6.088 m, ground Ug 0.5499, ventilation Ux 0.2378 W/m²K, deck with both surface resistances 0.486 m²K/W.

The same paper measured this floor on site at 1.04 ± 0.12 W/m²K, nearly double every model’s figure. This case shows that U-Monkey applies ISO 13370 as published, not that ISO 13370 predicts that floor. The link opens the 5 m/s case.

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18. Scotland’s table of solid ground floor U-values: all 170 cells Published example

Build-up, outside to inside: Ground-bearing floors with perimeter/area 0.05 to 1.00 and all-over insulation of R 0 to 4.0 m²K/W, the insulation counted alone, as the table’s own worked example does. Clay ground (λ 1.5 W/mK), as the table states; wall thickness 0.3 m (not stated).

Source: Scottish Government, “U Values: guidance” (published 11 February 2020), document 6.C “U-values of ground floors and basements”, Table 1: U-values for solid ground floors. Its tables are “derived from BS EN ISO 13370” and refer to clay soil, which 6.C.0 says to assume where the soil type is unknown, “as this is the most typical soil type in the UK”.

Figures in the source

1. Table 1 gives U to two decimal places for P/A 0.05 to 1.00 in steps of 0.05 and all-over insulation R 0 to 4.0 m²K/W in steps of 0.5. The uninsulated column is “N/A” above P/A 0.50, which leaves 170 printed cells. For example, P/A 0.50: 0.70, 0.50, 0.40, 0.33, 0.28, 0.24, 0.22, 0.19, 0.18 W/m²K for R 0 to 4.0.
2. Its worked example (6.C.1), a 150 mm slab with 80 mm of insulation at λ 0.025 and a 65 mm screed, says “Only the insulation layer is included in the calculation of the thermal resistance”: R 3.2, read from the P/A 0.50 row. U-Monkey is given the insulation alone in the same way, at λ 0.025.
3. Ground: clay, λ 1.5 W/mK, as stated in 6.C.0. The wall thickness is not stated; 0.3 m reproduces every cell, where 0.2 m reproduces 83 of the 170.

U-Monkey’s largest difference from a printed cell is +0.004982 W/m²K (P/A 0.50, R 3.5: table 0.19, U-Monkey 0.194982, which still rounds to the printed figure); the mean difference over all 170 cells is −0.0002 W/m²K.

U-Monkey’s own default ground is sand or gravel (λ 2.0); this case sets clay, as the table does. With λ 2.0 only one of the 170 cells would be within ±0.005: sand or gravel gives a higher U-value in every cell, by 6% at P/A 0.50 with R 3.0 (0.234 against 0.22) and by 25% with no insulation (0.878 against 0.70). The link opens the P/A 0.50 floor with R 3.0, the cell the worked example reads.

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19. Scotland’s table of uninsulated basement floors: all 50 cells Published example

Build-up, outside to inside: Uninsulated basement floors 0.5 to 2.5 m below ground, perimeter/area 0.1 to 1.0, with no floor layers. Clay ground (λ 1.5 W/mK), as stated; wall thickness 0.3 m (not stated).

Source: Scottish Government, “U Values: guidance” (published 11 February 2020), document 6.C “U-values of ground floors and basements”, Table 5: U-values of uninsulated basement floors. Its tables are “derived from BS EN ISO 13370” and refer to clay soil, which 6.C.0 says to assume where the soil type is unknown, “as this is the most typical soil type in the UK”.

Figures in the source

1. Table 5 gives U to two decimal places for P/A 0.1 to 1.0 in steps of 0.1 and basement depths of 0.5, 1, 1.5, 2 and 2.5 m: 50 cells. For example, P/A 0.5: 0.61, 0.55, 0.50, 0.46, 0.43 W/m²K from 0.5 to 2.5 m deep.
2. Ground: clay, λ 1.5 W/mK, as stated in 6.C.0. The wall thickness is not stated; 0.3 m reproduces every cell, where 0.2 m reproduces 3 of the 50.

U-Monkey’s largest difference from a printed cell is +0.004999 W/m²K (P/A 0.8, depth 0.5 m: table 0.79, U-Monkey 0.794999, which still rounds to the printed figure); the mean difference over all 50 cells is +0.0005 W/m²K.

The guidance adds insulation to these floors as U = 1 / (1/U₀ + R_ins), a simplification of ISO 13370 that U-Monkey does not use, so only the uninsulated table is compared. Its Table 6, basement walls, is not here: it does not state the floor it assumes, and U-Monkey reproduces 18 of its 25 cells with an uninsulated one. The link opens the P/A 0.5 floor 1.0 m deep.

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20. Ground-bearing floor with 150 mm PIR Hand-worked

Build-up, outside to inside: PIR 150 mm (λ 0.022) as the floor’s thermal layer. Exposed perimeter 30 m, area 50 m², wall 300 mm, ground λ 2.0 W/mK.

Source: hand calculation from the published method, below.

Working

1. B′ = A ÷ (½P) = 50 ÷ 15 = 3.3333 m
2. dt = w + λ(Rsi + Rf + Rse) = 0.3 + 2.0 × (0.17 + 0.150/0.022 + 0.04) = 0.3 + 2.0 × 7.0282 = 14.3564 m
3. dt ≥ B′ (a well-insulated floor), so U = λ ÷ (0.457B′ + dt) = 2.0 ÷ (1.5233 + 14.3564) = 0.1259 W/m²K
4. Basis: BS EN ISO 13370 slab-on-ground equations (BR 443 §9.1); Rsi 0.17, Rse 0.04.

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21. Uninsulated ground-bearing floor, larger plan Hand-worked

Build-up, outside to inside: No insulation and no other floor layers. Exposed perimeter 60 m, area 200 m², wall 300 mm, ground λ 2.0 W/mK.

Source: hand calculation from the published method, below.

Working

1. B′ = 200 ÷ 30 = 6.6667 m; dt = 0.3 + 2.0 × (0.17 + 0 + 0.04) = 0.72 m
2. dt < B′, so U = 2λ ÷ (πB′ + dt) × ln(πB′/dt + 1) = 4.0 ÷ (20.944 + 0.72) × ln(20.944/0.72 + 1) = 0.184639 × 3.404157 = 0.6285 W/m²K
3. Basis: BS EN ISO 13370 slab-on-ground equations (BR 443 §9.1); Rsi 0.17, Rse 0.04.

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22. Ground-bearing floor with edge insulation, horizontal or vertical Hand-worked

Build-up, outside to inside: Softwood floor 26 mm (λ 0.13, so R_f = 0.20 m²K/W) on the slab. Exposed perimeter 20 m, area 50 m², wall 300 mm, clay ground λ 1.5 W/mK. Edge insulation 50 mm thick, R 2.0 m²K/W: either a horizontal strip 1.0 m wide or vertical insulation 0.5 m deep.

Source: hand calculation from the published method, below.

Working

1. B′ = A ÷ (½P) = 50 ÷ 10 = 5.0000 m; R_f = 0.026/0.13 = 0.2000 m²K/W.
2. d_t = w + λ(Rsi + R_f + Rse) = 0.3 + 1.5 × (0.17 + 0.20 + 0.04) = 0.9150 m. That is less than B′, so U₀ = 2λ ÷ (πB′ + d_t) × ln(πB′/d_t + 1) = 3.0 ÷ 16.62296 × ln(18.16717) = 0.180473 × 2.899616 = 0.52330 W/m²K.
3. Edge insulation: R′ = R_n − d_n/λ = 2.0 − 0.050/1.5 = 1.96667 m²K/W, the resistance it adds over the ground it replaces; d′ = R′ × λ = 1.96667 × 1.5 = 2.95000 m.
4. Horizontal strip, D = 1.0 m: Ψ = −(λ/π) × [ln(D/d_t + 1) − ln(D/(d_t + d′) + 1)] = −0.477465 × [ln(2.092896) − ln(1.258732)] = −0.477465 × 0.508444 = −0.24276 W/mK.
5. Vertical insulation, D = 0.5 m: the vertical form takes 2D in place of D, and 2D = 1.0 m, so Ψ = −0.24276 W/mK as well.
6. U = U₀ + 2Ψ/B′ = 0.52330 + 2 × (−0.24276) ÷ 5.0 = 0.52330 − 0.09711 = 0.42620 W/m²K, for either.
7. Basis: BS EN ISO 13370:2017 Annex D, as reproduced in G. Schilf’s TalTech MSc thesis (2025), §2.4.1, eqs 2.42–2.46; Rsi 0.17 and Rse 0.04 (BR 443 §9.1).

The standard itself was not read; the equations are those reproduced in the thesis. Where a floor has both kinds of edge insulation, U-Monkey counts only the more effective one rather than adding them; the thesis gives no rule for that case.

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23. Very thick dense concrete: areal heat capacity tends to ρcδ/√2 Closed-form

Build-up, outside to inside: One layer of dense concrete 1,000 mm thick: λ 1.4 W/mK, ρ 2,300 kg/m³, c 1,000 J/kgK. 24-hour period.

Source: closed-form calculation, below.

Working

1. Periodic penetration depth for a 24-hour cycle: δ = √(λT/(πρc)) = √(1.4 × 86,400 ÷ (π × 2,300 × 1,000)) = 0.12938 m. The slab is 1,000 mm thick, so d/δ = 7.7.
2. At that depth cosh and sinh in the ISO 13786 layer matrix both tend to eˣ/2, so |(Z₂₂ − 1)/Z₁₂| → √2·λ/δ and κ = (T/2π) × √2·λ/δ = ρcδ/√2.
3. κ = 2,300 × 1,000 × 0.12938 ÷ √2 = 210,424 J/m²K = 210.4 kJ/m²K. At 1,000 mm the exact matrix value is 0.02 kJ/m²K below the limit; U-Monkey reports κ to 0.1 kJ/m²K.

This checks the matrix arithmetic against a closed-form result. It does not test a published example, and it does not settle conventions such as whether surface films are counted in κ (U-Monkey leaves them out).

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24. External wall insulation, EPS on brick or dense block, galvanised or stainless fixings (36 cells) Published example

Build-up, outside to inside: Render 7.5 mm (λ 1.0) · webertherm EPS 70 grey, λD 0.032, 30 to 200 mm in 10 mm steps, with 7 fixings per m² at χp 0.004 W/K each (galvanised, Table 10) or 0.002 W/K (stainless, Table 11) · 5 mm adhesive bed, adhesive (λ 1.0) over 50% of it · 215 mm protected brickwork (λ 0.56) with 17.1% mortar, or 200 mm dense blockwork (λ 1.75) with 6.7% mortar (λ 0.88) · plaster 13 mm (λ 0.57). No air-gap correction.

Source: BBA Agrément Certificate 91/2691, Product Sheet 1 (Issue 4, 27 March 2025): webertherm XM External Wall Insulation System (low rise, mechanically fixed EPS). Tables 10 and 11, “Insulation thickness required to achieve U value”, with galvanised and with stainless steel fixings, and their footnotes (1) to (3).

Figures in the source

1. Table 10, galvanised fixings, thickness in mm on brickwork | dense blockwork, by target U: 0.13 – | –; 0.15 – | –; 0.17 200 | –; 0.18 190 | 200; 0.21 160 | 160; 0.26 120 | 130; 0.28 110 | 120; 0.30 100 | 110; 0.35 80 | 90. A dash is a target the 200 mm maximum does not reach.
2. Table 11, stainless fixings: 0.13 – | –; 0.15 – | –; 0.17 180 | 190; 0.18 170 | 180; 0.21 150 | 150; 0.26 110 | 120; 0.28 100 | 110; 0.30 100 | 100; 0.35 80 | 90.
3. Footnotes: 13 mm plaster (λ 0.57); brickwork (protected) with 17.1% mortar or dense blockwork with 6.7% mortar (λ 0.88); λD 0.032 (Table 9: 30 to 200 mm); a 5 mm adhesive layer (λ 1) covering 50% of the area; board emissivity 0.9; 7.5 mm render (λ 1); 7 fixings per m² at χp 0.004 W/K (galvanised) or 0.002 W/K (stainless); gap correction zero; 10 mm increments. Brick λ 0.56 and block λ 1.75 are in the column headings.

Table 10, closest calls in U-Monkey’s figures: dense blockwork for 0.21, where 160 mm gives U 0.2148 (to count it must round to 0.21); and dense blockwork for 0.18, where one step thinner (190 mm) gives 0.1870, just too much, so 200 mm is needed.

U-Monkey is given the construction in the footnotes and, for each target, takes the least thickness in the certificate’s own steps whose U-value, rounded to two decimal places as U-values are quoted, meets the target; a dash in the table means the thickest board cannot reach it. The certificates do not say how they compare a U-value with its target; compared unrounded, 61 of the 157 cells on this page would come out differently (60 a step thicker, one out of reach). Surface resistances are the standard ones (not stated). The adhesive bed is an unventilated 5 mm air layer, emissivity 0.9 on both faces, bridged by the adhesive. The two tables differ only in the fixings, so together they check the point-fixing correction (ISO 6946 Annex F): 7 × 0.004 = 0.028 W/m²K against 0.014. The link opens the brick wall with 190 mm and galvanised fixings.

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25. External wall insulation, two grey EPS boards on brick or dense block (28 cells) Published example

Build-up, outside to inside: Render 9 mm (λ 1.0) · grey EPS 100 030 (λD 0.030, 60 to 250 mm) or grey EPS 70 032 (λD 0.032, 60 to 260 mm) in 10 mm steps, 7 fixings per m² at χp 0.002 W/K · 6 mm adhesive bed, adhesive (λ 0.43) over 40% · 215 mm protected brickwork (λ 0.56, 17.1% mortar) or 200 mm dense blockwork (λ 1.75, 6.7% mortar; mortar λ 0.88) · plaster 13 mm (λ 0.57). No air-gap correction.

Source: BBA Agrément Certificate 20/5744, Product Sheet 3 (first issued 22 April 2020, amended 4 May 2020): K Systems E External Wall Insulation System. Table 4, “Insulation thickness required to achieve design U values”, its footnotes (1) to (4), and Table 3 (declared thermal conductivity and thicknesses).

Figures in the source

1. Table 4, thickness in mm on brickwork (EPS 100 030 | EPS 70 032) and dense blockwork (EPS 100 030 | EPS 70 032), by target U: 0.18 160 | 170 | 170 | 180; 0.19 150 | 160 | 160 | 170; 0.25 110 | 120 | 120 | 130; 0.26 110 | 110 | 110 | 120; 0.28 100 | 100 | 100 | 110; 0.30 90 | 100 | 100 | 100; 0.35 70 | 80 | 80 | 90.
2. Footnotes: 13 mm plaster (λ 0.57); brickwork (protected) with 17.1% mortar or dense blockwork with 6.7% mortar (λ 0.88); a 6 mm adhesive layer (λ 0.43) covering 40% of the area; board emissivity 0.9; 9 mm render (λ 1.0); 7 fixings per m² at χp 0.002 W/K; gap correction zero; 10 mm increments. Table 3: EPS 100 030 from 60 to 250 mm, EPS 70 032 from 60 to 260 mm.
3. Footnote (4): with the maximum available insulation thickness these walls can achieve 0.13 W/m²K, for both insulations and both wall types. The two extremes are checked: the least insulating (EPS 70 032 at 260 mm on block) and the most (EPS 100 030 at 250 mm on brick).

Closest calls in U-Monkey’s figures: brickwork, EPS 100 030 for 0.35, where 70 mm gives U 0.3538 (to count it must round to 0.35); and brickwork, EPS 70 032 for 0.30, where one step thinner (90 mm) gives 0.3062, just too much, so 100 mm is needed.

U-Monkey is given the construction in the footnotes and, for each target, takes the least thickness in the certificate’s own steps whose U-value, rounded to two decimal places as U-values are quoted, meets the target; a dash in the table means the thickest board cannot reach it. The certificates do not say how they compare a U-value with its target; compared unrounded, 61 of the 157 cells on this page would come out differently (60 a step thicker, one out of reach). Surface resistances are the standard ones (not stated). The adhesive bed is an unventilated 6 mm air layer, emissivity 0.9 on both faces, bridged by the adhesive. The link opens the block wall with 180 mm of EPS 70 032.

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26. External wall insulation, phenolic board on brick or dense block (14 cells) Published example

Build-up, outside to inside: Render 9 mm (λ 1.0) · phenolic 020 (λD 0.020, 45 to 120 mm) in 10 mm steps, 7 fixings per m² at χp 0.002 W/K · 6 mm adhesive bed, adhesive (λ 0.43) over 40% · 215 mm protected brickwork (λ 0.56, 17.1% mortar) or 200 mm dense blockwork (λ 1.75, 6.7% mortar; mortar λ 0.88) · plaster 13 mm (λ 0.57). No air-gap correction.

Source: BBA Agrément Certificate 20/5744, Product Sheet 1 (first issued 22 April 2020, amended 4 May 2020): K Systems P External Wall Insulation System. Table 4, “Insulation thickness required to achieve design U values”, its footnotes (1) to (3), and Table 3 (declared thermal conductivity and thicknesses).

Figures in the source

1. Table 4, thickness in mm on brickwork | dense blockwork, by target U: 0.18 105 | 115; 0.19 105 | 105; 0.25 75 | 85; 0.26 75 | 75; 0.28 65 | 75; 0.30 65 | 65; 0.35 55 | 55.
2. Footnotes as for the K Systems E sheet: 13 mm plaster (λ 0.57); protected brickwork with 17.1% or dense blockwork with 6.7% mortar (λ 0.88); 6 mm adhesive (λ 0.43) over 40%; board emissivity 0.9; 9 mm render (λ 1.0); 7 fixings per m² at χp 0.002 W/K; gap correction zero; 10 mm increments. Table 3: phenolic 020 from 45 to 120 mm (thinner boards are λD 0.021), so the steps run 45, 55, 65 mm and so on.

Closest calls in U-Monkey’s figures: brickwork for 0.18, where 105 mm gives U 0.1847 (to count it must round to 0.18); and dense blockwork for 0.25, where one step thinner (75 mm) gives 0.2564, just too much, so 85 mm is needed.

U-Monkey is given the construction in the footnotes and, for each target, takes the least thickness in the certificate’s own steps whose U-value, rounded to two decimal places as U-values are quoted, meets the target; a dash in the table means the thickest board cannot reach it. The certificates do not say how they compare a U-value with its target; compared unrounded, 61 of the 157 cells on this page would come out differently (60 a step thicker, one out of reach). Surface resistances are the standard ones (not stated). This sheet’s footnote (4) says the walls reach 0.13 to 0.15 W/m²K at the maximum thickness, which its own table contradicts: 0.18 already needs 105 to 115 mm of the 120 mm board. U-Monkey gives 0.165 and 0.171 at 120 mm, so the footnote is not compared. The link opens the brick wall with 75 mm.

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27. External wall insulation, mineral wool on brick or dense block (28 cells) Published example

Build-up, outside to inside: Render 9 mm (λ 1.0) · MW Dual Density 036 (100 to 250 mm) or MW EWI Slab 036 (100 to 260 mm), λD 0.036, in 10 mm steps, 7 fixings per m² at χp 0.002 W/K · 6 mm adhesive bed, adhesive (λ 0.43) over 40% · 215 mm protected brickwork (λ 0.56, 17.1% mortar) or 200 mm dense blockwork (λ 1.75, 6.7% mortar; mortar λ 0.88) · plaster 13 mm (λ 0.57). No air-gap correction.

Source: BBA Agrément Certificate 20/5744, Product Sheet 2 (first issued 3 April 2020, amended 4 May 2020): K Systems M External Wall Insulation System. Table 4, “Insulation thickness required to achieve design U values”, its footnotes (1) to (3), and Table 3 (declared thermal conductivity and thicknesses).

Figures in the source

1. Table 4, thickness in mm on brickwork (Dual Density | EWI Slab) and dense blockwork (Dual Density | EWI Slab), by target U: 0.18 190 | 190 | 200 | 200; 0.19 180 | 180 | 190 | 190; 0.25 130 | 130 | 140 | 140; 0.26 130 | 130 | 130 | 130; 0.28 120 | 120 | 120 | 120; 0.30 110 | 110 | 120 | 120; 0.35 100 | 100 | 100 | 100.
2. Footnotes as for the other K Systems sheets: 13 mm plaster (λ 0.57); protected brickwork with 17.1% or dense blockwork with 6.7% mortar (λ 0.88); 6 mm adhesive (λ 0.43) over 40%; board emissivity 0.9; 9 mm render (λ 1.0); 7 fixings per m² at χp 0.002 W/K; gap correction zero; 10 mm increments. Table 3: both products λD 0.036, Dual Density 100 to 250 mm, EWI Slab 100 to 260 mm.

Closest calls in U-Monkey’s figures: dense blockwork, Dual Density for 0.26, where 130 mm gives U 0.2649 (to count it must round to 0.26); and dense blockwork, Dual Density for 0.30, where one step thinner (110 mm) gives 0.3055, just too much, so 120 mm is needed.

U-Monkey is given the construction in the footnotes and, for each target, takes the least thickness in the certificate’s own steps whose U-value, rounded to two decimal places as U-values are quoted, meets the target; a dash in the table means the thickest board cannot reach it. The certificates do not say how they compare a U-value with its target; compared unrounded, 61 of the 157 cells on this page would come out differently (60 a step thicker, one out of reach). Surface resistances are the standard ones (not stated). The two mineral wools share a λD, so their columns differ only in the thickest board available. The link opens the brick wall with 180 mm of Dual Density.

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28. External wall insulation, white or grey EPS on brick or dense block (28 of 32 cells) Published example

Build-up, outside to inside: Render 9 mm (λ 1.0) · Mapetherm EPS 70 038 white (λD 0.038) or EPS 70 031 grey (λD 0.031), 40 to 300 mm in 10 mm steps, 7 fixings per m² at χp 0.001 W/K · 6 mm adhesive bed, adhesive (λ 0.43) over 40% · 215 mm protected brickwork (λ 0.56, 17.1% mortar) or 200 mm dense blockwork (λ 1.75, 6.7% mortar; mortar λ 0.88) · plaster 13 mm (λ 0.57). No air-gap correction.

Source: BBA Agrément Certificate 13/4977, Product Sheet 1 (Issue 4, 22 May 2025): Mapetherm EPS Standard and Plus External Wall Insulation Systems. Table 9, “Insulation thickness required to achieve the design U values”, its footnotes (1) to (3), and Table 8 (thermal conductivity of the insulations).

Figures in the source

1. Table 9, thickness in mm on brickwork (white 038 | grey 031) and dense blockwork (white 038 | grey 031), by target U: 0.13 280 | 230 | 290 | 240; 0.15 240 | 200 | 250 | 200; 0.17 210 | 170 | 220 | 180; 0.18 200 | 160 | 200 | 170; 0.21 160 | 140 | 170 | 140; 0.26 130 | 100 | 130 | 110; 0.28 120 | 90 | 120 | 100; 0.30 110 | 90 | 120 | 100.
2. Footnotes: 13 mm plaster (λ 0.57); protected brickwork with 17.1% or dense blockwork with 6.7% mortar (λ 0.88); a 6 mm adhesive layer (λ 0.43) covering 40% of the area; 9 mm render (λ 1.0); 7 fixings (galvanised steel pin) per m² at χp 0.001 W/K; gap correction zero; 10 mm increments. Table 8: white 038 from 40 to 300 mm; the grey board’s range is blank, so the same is assumed.

Closest calls in U-Monkey’s figures: dense blockwork, grey 031 for 0.28, where 100 mm gives U 0.2847 (to count it must round to 0.28); and brickwork, grey 031 for 0.21, where one step thinner (130 mm) gives 0.2152, just too much, so 140 mm is needed.

U-Monkey is given the construction in the footnotes and, for each target, takes the least thickness in the certificate’s own steps whose U-value, rounded to two decimal places as U-values are quoted, meets the target; a dash in the table means the thickest board cannot reach it. The certificates do not say how they compare a U-value with its target; compared unrounded, 61 of the 157 cells on this page would come out differently (60 a step thicker, one out of reach). Surface resistances are the standard ones (not stated). The board emissivity is not stated here; 0.9 is taken, as in the K Systems sheets on the same basis. Four cells are left out of the count: the 0.26 and 0.28 rows for grey board on brick (printed 100 and 90 mm) and for white board on block (130 and 120 mm). At those thicknesses U-Monkey gives 0.268, 0.292, 0.270 and 0.290, and needs 10 mm more for each; the rest of the table agrees with it to the step. Two of the printed figures sit oddly together: 120 mm of white board for 0.28 on brick, so 110 mm (R 2.89 m²K/W) falls short, yet 90 mm of grey (R 2.90, with the same fixings) is enough. That holds only if the cut-off for 0.28 falls in the 0.008 m²K/W between them; U-Monkey gives 0.292 for both. The link opens the brick wall with 280 mm of white EPS.

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29. Phenolic board over rafters, dwarf wall and dormer cheek linings (23 cells) Published example

Build-up, outside to inside: Over rafters (Table 7): concrete tiles on 25 mm well-ventilated battens, low-resistance breather membrane · Unilin Safe-R SR/PR (λD 0.021 below 100 mm, 0.020 from 100 mm; foil ε 0.05), 50 to 150 mm, searched in 5 mm steps, 11 stainless fixings per m² (λ 17, 9 mm²) · 47 × 150 mm rafters (11.75%, λ 0.13) with a low-emissivity air cavity between them · AVCL · plasterboard 15 mm (λ 0.25). Dwarf wall (Table 9) and dormer cheek (Table 10): a 100 mm timber frame (15%) filled with the board, then a lining of it with 4.4 stainless fixings per m² (6.6 mm²), AVCL and 15 mm plasterboard; outside, a roof space of R 0.2 or ventilated tile cladding on OSB.

Source: BBA Agrément Certificate 23/6884, Product Sheet 1 (Issue 1, 21 June 2024): Unilin Safe-R Pitched Roof Board (SR/PR). Tables 7, 9 and 10, “Example U values” for a pitched roof, a dwarf wall and a dormer cheek, their footnotes, and Tables 5 and 6 (declared thermal conductivity and foil emissivity).

Figures in the source

1. Table 7, over rafters, thickness in mm by target U: 0.09 –; 0.11 –; 0.12 –; 0.13 145; 0.15 125; 0.16 115; 0.18 100; 0.20 95; 0.25 75 (a dash: footnote (5), only the between-rafter systems reach it). Its footnote (1): concrete tiles on 25 mm battens (well-ventilated) on a low-resistance breather membrane; 11 stainless steel fixings per m² (λ 17, 9 mm² cross-section); 47 × 150 mm rafters (11.75%, λ 0.13) with a low-e (ε 0.05) air cavity between them; AVCL; 15 mm plasterboard (λ 0.25).
2. Tables 9 and 10, lining thickness in mm by target U, the same in both: 0.13 80; 0.15 60; 0.17 50; 0.18 50; 0.21 50; 0.26 50; 0.28 50 (50 mm is the thinnest lining). Dwarf wall: an uninsulated tiled roof with felt (R 0.2) outside a 100 mm frame (λ 0.13, 15%) filled with the board. Dormer cheek: 10 mm tile cladding, a 25 mm ventilated cavity, breather membrane and 9 mm OSB (λ 0.13) outside the same frame. Both: a lining with 4.4 stainless fixings per m² (6.6 mm²), AVCL, 15 mm plasterboard (λ 0.25).
3. Table 5: λD 0.021 from 50 to 99 mm and 0.020 from 100 to 150 mm. Table 6: foil facing emissivity 0.05. The certificate states the range but not a step; every thickness it prints is a multiple of 5 mm, so U-Monkey searches in 5 mm steps.

Table 7, closest calls in U-Monkey’s figures: over rafters for 0.18, where 100 mm gives U 0.1833 (to count it must round to 0.18); and over rafters for 0.25, where one step thinner (70 mm) gives 0.2563, just too much, so 75 mm is needed.

U-Monkey is given the construction in the footnotes and, for each target, takes the least thickness in the certificate’s own steps whose U-value, rounded to two decimal places as U-values are quoted, meets the target; a dash in the table means the thickest board cannot reach it. The certificates do not say how they compare a U-value with its target; compared unrounded, 61 of the 157 cells on this page would come out differently (60 a step thicker, one out of reach). Surface resistances are the standard ones (not stated). Heat flows upward through a pitched roof, so the rafter cavity is about 0.45 m²K/W rather than the 0.67 a wall’s would be. The 0.30 rows of Tables 9 and 10, which need no lining, are not compared. Nor are Table 7’s two between-rafter columns or Table 8, a ceiling: their footnotes leave the order or position of the boards open, and with the fixings they state, U-Monkey needs more board than printed in some of their cells (70 mm between and 70 mm over the rafters gives 0.158 for a target of 0.15, and 0.153 with the fixings left out). The link opens the roof with 100 mm over the rafters.

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