Equivalent area calculator
The same opening part at every angle in Appendix D
| Angle | Equivalent area (each) | Method |
|---|
Approved Document O (2021), Appendix D: Tables D1–D9 where the size and angle are on the table grid (D2b), the discharge-coefficient calculation behind them otherwise (D2a; MHCLG FAQ 8), D3 for which dimension is which, para 3.9a and FAQ 15 for the handle, paras 3.8–3.9 for guarding. The same engine as O-Monkey.
A worked example
One side-hung casement, 600 mm wide and 1200 mm high — 0.72 m² of opening part:
- Fully open, 90°: 0.62 m² (86% of the opening part). The size is not on the table grid, so the discharge-coefficient calculation gives it.
- With the frame 150 mm back from the inside face: the 650 mm handle rule caps it at 56.4°, giving 0.56 m².
- On a 100 mm restrictor: 9.6°, giving 0.19 m² — under 10°, so an extrapolation, and only 35% of what the same window counts for at 56.4°.
- As a tilt-and-turn opening inward, the 650 mm rule does not apply: 0.62 m².
That is the difference between a design that passes and one that does not: the same hole in the wall counts for anything from 0.19 to 0.62 m² depending on how it opens.
How Appendix D treats each type
| Type | Assessed as |
|---|---|
| Side-hung casement, French door | h = the hinged side (its height), w = the width from hinge to handle, at the opening angle. |
| Top- and bottom-hung | h and w reversed (D3a): the hinge runs along the window's width. |
| Centre-pivot | Two hung sections, each half the size, at the same angle (D3b). |
| Vertical sliding sash | Table D9 at 90° on the clear opening when fully open (D3c). One sash only. |
| Sliding and bifold doors | Not mentioned in Appendix D; O-Monkey assesses the clear opening like a sash, one pane of a slider only (Future Homes Hub guidance). |
| Top-hung roof window | Counted in its centre-pivot position at 90°, which most have and which is used for ventilation — an O-Monkey reading, stated in its report. |
| Tested windows | A test to BS EN 13141-1 can be used instead of the tables (D1). |
Table D9 — fully open (90°)
Equivalent area in m² of a hinged opening part fully open, by the length of its hinged side (h) and its width (w):
| h \ w | 0.50 m | 0.75 m | 1.00 m | 1.25 m | 1.50 m |
|---|---|---|---|---|---|
| 0.50 m | 0.22 | 0.35 | 0.47 | 0.61 | 0.74 |
| 0.75 m | 0.33 | 0.50 | 0.70 | 0.88 | 1.05 |
| 1.00 m | 0.43 | 0.66 | 0.88 | 1.17 | 1.40 |
| 1.25 m | 0.53 | 0.83 | 1.10 | 1.38 | 1.76 |
| 1.50 m | 0.64 | 0.96 | 1.33 | 1.66 | 1.99 |
| 1.75 m | 0.75 | 1.12 | 1.55 | 1.93 | 2.32 |
| 2.00 m | 0.86 | 1.28 | 1.71 | 2.21 | 2.65 |
| 2.25 m | 0.96 | 1.44 | 1.93 | 2.48 | 2.98 |
| 2.50 m | 1.07 | 1.60 | 2.14 | 2.67 | 3.31 |
| 2.75 m | 1.18 | 1.76 | 2.35 | 2.94 | 3.64 |
| 3.00 m | 1.28 | 1.93 | 2.57 | 3.21 | 3.85 |
From Approved Document O (2021), Appendix D, Table D9. Contains public sector information licensed under the Open Government Licence v3.0. Tables D1 to D8 give the same grid at 10° to 80°; the calculator above reads all nine.
The calculation behind the tables
Tables D1–D9 come from a discharge-coefficient model for hinged windows: the discharge coefficient Cd rises with the opening angle towards a maximum that depends on the window's proportions (the hinged length over the opening width), and the equivalent area is Cd × the opening part's area ÷ 0.62. Run across the tables' grid it reproduces all 495 of their values to two decimal places, which is how O-Monkey and this calculator know it is the right model. MHCLG's FAQ points to it for sizes the tables do not cover. Where your size and angle are on the grid, the table value itself is used, and the result says which.
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Every window at once, against the Part O minimums
O-Monkey works out the equivalent area of every window and door in the home this way, adds them up against Tables 1.3 and 1.4 and checks every bedroom — then ranks the window swaps that would add the most if it falls short.
Free to check. Building Control-ready PDF with the Appendix B checklist £25 +VAT (£30 inc VAT) per house type, every plot included.
Frequently asked questions
What is equivalent area?
How much air an opening actually lets through, expressed as the area of an ideal sharp-edged hole that would pass the same flow. A window open at 30° passes much less air than its frame size suggests, so Approved Document O compares its minimum free areas with each opening’s equivalent area, not the size of the frame (para 1.12).
How does Approved Document O work out equivalent area?
Appendix D gives two ways: a test to BS EN 13141-1, or Tables D1–D9, which give the equivalent area of hinged windows by height, width and opening angle from 10° to 90°. The tables come from a discharge-coefficient calculation, Aeq = Cd × A ÷ 0.62, where Cd rises with the opening angle and depends on the window's proportions. That calculation reproduces all 495 tabulated values to two decimal places, and MHCLG's FAQ says to use it for sizes the tables do not cover.
Which way round do height and width go?
In Appendix D, h is the length of the hinged side and w is the width of the opening part, from the hinge to the handle side. For a side-hung casement that is the window’s height and width. For top- and bottom-hung windows they are reversed (D3a): the hinge runs along the width. This calculator asks for the size of the opening part as you see it and turns it round for you.
How are centre-pivot windows and sashes counted?
A centre-pivot window is assessed as two hung sections, each half the size, opening the same angle (D3b). A vertical sliding sash is assessed on Table D9 at 90°, using the clear opening when it is fully open (D3c); only one sash counts, because only one can be fully open at a time. O-Monkey treats sliding and bifold doors the same way, on their clear opening — Approved Document O does not mention them, so confirm that with Building Control.
What if the window has a restrictor?
Use the restricted position, as MHCLG’s FAQ says: enter the gap at the opening edge and the calculator works out the angle it allows. A 100 mm restrictor on a 600 mm casement allows under 10°, below the range the discharge-coefficient model was tested over, so the result is an extrapolation and is flagged as one.
Does the 650 mm handle rule change the answer?
For outward-opening windows, yes. Paragraph 3.9a says the handle should be no more than 650 mm from the inside face of the wall, and MHCLG FAQ 15 says to count the window at the angle where that happens. Enter the reveal depth and the calculator caps the angle accordingly; inward-opening windows, doors and roof windows are not affected.
Next: the 650 mm handle rule · is my site high risk? · how to use O-Monkey.
Sources: Approved Document O (2021 edition), para 1.12, Section 3 and Appendix D · Approved Document O frequently asked questions (MHCLG), FAQ 8 and 15.