How U-Monkey is tested

No standards body publishes a test suite for U-value calculations, so U-Monkey publishes its own: each reference case with the expected answer, where that answer comes from, and what the calculator's current engine gives. The page is generated from that engine every time the site is built.

engine.js v4.4 (version header dated 17 October 2026) · page built 19 October 2026

  • 20 of 20 reference cases pass
  • 46 of 46 comparisons within tolerance
  • 3 published worked examples, 16 hand calculations, 1 closed-form limit

SHA-256 of the engine file: 994af3813cad496f…

Why we publish this

Thermal-bridge software can be checked against the test reference cases in BS EN ISO 10211, and ΨMonkey's results against them are published. There is no equivalent for U-values: no standards body publishes a test suite for BS EN ISO 6946 or BR 443 calculations. BRE's own book of worked examples, FB 42, U-value conventions in practice, is listed in the BRE bookshop as “recently archived”, with the note that it “is not consistent with the current (2019) edition of BR443”.

So we publish our own checks: three published worked examples we can cite, and hand calculations written out in full so that anyone can repeat them with a calculator. Every number in the U-Monkey column below was calculated by the engine the calculator runs, when this page was built.

How to read the results

ISO 6946 combined method / BR 443

Layer resistances, air layers, bridging and ventilated cavities: the calculation behind every wall, pitched roof, flat roof and exposed floor.

ISO 6946 combined method / BR 443: expected values, U-Monkey's results and tolerances
Compared Expected U-Monkey Difference Tolerance Result
1. Timber-frame wall with brick cladding, studs at 15% Published example gov.scot U-values guidance, worked example 6.B.2
Upper limit R′Tm²K/W 3.435±0.005 3.435 0.0000 ±0.005 PASS
Lower limit R″Tm²K/W 3.304±0.005 3.304 0.0000 ±0.005 PASS
Total resistance RTm²K/W 3.369±0.005 3.3693 +0.00026 ±0.005 PASS
Air-gap correction ΔUW/m²K 0.006±0.0005 0.0064 +0.00039 ±0.0005 PASS
U-valueW/m²K 0.30±0.005 0.3032 +0.00319 ±0.005 PASS
2. Unfilled cavity wall, no bridging Hand-worked Working written out below
U-valueW/m²K 0.8528±0.0001 0.8528 +0.00001 ±0.0001 PASS
3. Cavity wall with a 25 mm low-emissivity cavity Hand-worked Working written out below
U-valueW/m²K 0.6980±0.0001 0.6980 +0.00004 ±0.0001 PASS
4. Partial-fill cavity wall: a 50 mm cavity beside a board certified at ε 0.05 Published example BBA 14/5133 Product Sheet 2 (Kingspan Thermawall TW50)
Cavity resistancem²K/W 0.665±0.0005 0.6651 +0.00007 ±0.0005 PASS
5. Empty timber-stud wall: an air layer bridged by studs Hand-worked Working written out below
Upper limit R′Tm²K/W 0.4961±0.0005 0.496 −0.0001 ±0.0005 PASS
Lower limit R″Tm²K/W 0.4879±0.0005 0.488 +0.0001 ±0.0005 PASS
U-valueW/m²K 2.0325±0.0001 2.0325 −0.00002 ±0.0001 PASS
6. Plasterboard on dabs: the dabs bridge the air gap (BR 443 §4.6.1) Hand-worked Working written out below
U-valueW/m²K 0.8716±0.0001 0.8716 −0.00003 ±0.0001 PASS
7. Loft insulated at ceiling level: joists at BR 443’s 12.8% and the roof space above (BR 443 §8) Hand-worked Working written out below
Roof space R_um²K/W 0.20±0 0.200 0.0000 ±0 PASS
Upper limit R′Tm²K/W 6.869±0.0005 6.869 0.0000 ±0.0005 PASS
Lower limit R″Tm²K/W 6.591±0.0005 6.591 0.0000 ±0.0005 PASS
U-valueW/m²K 0.1486±0.0001 0.1486 0.00000 ±0.0001 PASS
8. Wall to an integral garage: the unheated space added as SAP 10.2 formula (3) Hand-worked Working written out below
Total resistance RT (the wall as if it faced outside air)m²K/W 3.727±0.0005 3.727 0.0000 ±0.0005 PASS
U0, as if it faced outside airW/m²K 0.2683±0.0001 0.2683 0.00000 ±0.0001 PASS
Garage R_um²K/W 0.35±0 0.35 0.000 ±0 PASS
U-valueW/m²K 0.2453±0.0001 0.2453 −0.00003 ±0.0001 PASS
9. Rainscreen wall: well-ventilated cavity Hand-worked Working written out below
U-valueW/m²K 1.0532±0.0001 1.0532 +0.00002 ±0.0001 PASS
10. Slightly ventilated cavity, openings 1,000 mm² per metre Hand-worked Working written out below
U-valueW/m²K 0.9425±0.0001 0.9425 −0.00002 ±0.0001 PASS
11. Exposed floor over a well-ventilated void Hand-worked Working written out below
U-valueW/m²K 2.0900±0.0001 2.0900 +0.00003 ±0.0001 PASS
12. Light steel frame wall, cold frame: the BRE Digest 465 weighting Hand-worked Working written out below
Upper limit R′Tm²K/W 3.1982±0.0005 3.198 −0.0002 ±0.0005 PASS
Lower limit R″Tm²K/W 1.3199±0.0005 1.320 +0.0001 ±0.0005 PASS
Digest 465 weighting p– 0.4051±0.0001 0.4051 +0.00005 ±0.0001 PASS
Total resistance RTm²K/W 2.0809±0.0001 2.0809 −0.00004 ±0.0001 PASS
Air-gap correction ΔUW/m²K 0.0012±0.0001 0.0012 +0.00001 ±0.0001 PASS
U-valueW/m²K 0.4818±0.0001 0.4818 −0.00002 ±0.0001 PASS

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. 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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3. 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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4. 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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5. 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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6. 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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7. 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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8. 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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9. 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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10. 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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11. 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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12. 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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ISO 6946 Annex F corrections

The corrections added to U after the combined method: gaps in the insulation, metal fixings through it, and rain water under an inverted roof (BR 443 §4.8).

ISO 6946 Annex F corrections: expected values, U-Monkey's results and tolerances
Compared Expected U-Monkey Difference Tolerance Result
13. Air-gap correction, level 1 Hand-worked Working written out below
Air-gap correction ΔUW/m²K 0.0069±0.0001 0.0069 +0.00002 ±0.0001 PASS
U-valueW/m²K 0.1899±0.0001 0.1899 +0.00001 ±0.0001 PASS
14. Stainless-steel wall ties through partial-fill PIR Hand-worked Working written out below
Fixings correction ΔUfW/m²K 0.00268±0.00001 0.00268 +0.000003 ±0.00001 PASS
U-valueW/m²K 0.1775±0.0001 0.1775 −0.00003 ±0.0001 PASS
15. Inverted flat roof: rain-water correction Hand-worked Working written out below
Rain-water correction ΔUrW/m²K 0.0982±0.0001 0.0982 +0.00002 ±0.0001 PASS
U-valueW/m²K 0.3546±0.0001 0.3546 −0.00004 ±0.0001 PASS

13. 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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14. 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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15. 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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ISO 13370 ground floors

A ground floor loses heat into the ground, so its U-value depends on the floor’s size and shape (B′ = A ÷ ½P) as well as on its layers.

ISO 13370 ground floors: expected values, U-Monkey's results and tolerances
Compared Expected U-Monkey Difference Tolerance Result
16. Uninsulated suspended timber floor (published field-study model) Published example Pelsmakers et al., Building Research & Information, Tables 1 and 4
U-value, wind 5 m/sW/m²K 0.57±0.005 0.5696 −0.00037 ±0.005 PASS
U-value, wind 1 m/sW/m²K 0.51±0.005 0.5074 −0.00264 ±0.005 PASS
17. Ground-bearing floor with 150 mm PIR Hand-worked Working written out below
U-valueW/m²K 0.1259±0.0001 0.1259 +0.00005 ±0.0001 PASS
18. Uninsulated ground-bearing floor, larger plan Hand-worked Working written out below
U-valueW/m²K 0.6285±0.0001 0.6285 +0.00004 ±0.0001 PASS
19. Ground-bearing floor with edge insulation, horizontal or vertical Hand-worked Working written out below
U₀, no edge insulationW/m²K 0.52330±0.00002 0.52330 +0.000003 ±0.00002 PASS
Extra thickness d′m 2.95000±0.00002 2.95000 0.000000 ±0.00002 PASS
Ψ, horizontal, D 1.0 mW/mK -0.24276±0.00002 -0.24276 −0.000004 ±0.00002 PASS
U-value, horizontalW/m²K 0.42620±0.00002 0.42620 −0.000002 ±0.00002 PASS
Ψ, vertical, D 0.5 mW/mK -0.24276±0.00002 -0.24276 −0.000004 ±0.00002 PASS
U-value, verticalW/m²K 0.42620±0.00002 0.42620 −0.000002 ±0.00002 PASS

16. 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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17. 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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18. 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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19. 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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ISO 13786 dynamic properties

The 24-hour heat-transfer-matrix method behind the areal heat capacity κ, the decrement factor and the time lag.

ISO 13786 dynamic properties: expected values, U-Monkey's results and tolerances
Compared Expected U-Monkey Difference Tolerance Result
20. Very thick dense concrete: areal heat capacity tends to ρcδ/√2 Closed-form Working written out below
Areal heat capacity κ (inside face)kJ/m²K 210.4±0.1 210.4 0.00 ±0.1 PASS

20. 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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