Roof pitch calculator: degrees and rafter length
The calculator needs JavaScript. The worked example, formula and figures below show exactly how it works, so you can do the sum yourself. A guide, not advice. Check your supplier's or maker's figures before ordering.
Short answer
Worked example
| You enter | Value |
|---|---|
| I know the | Rise |
| Roof | Two slopes (run = half the width) |
| Building width, wall plate to wall plate | 6 m |
| Rise | 2.1 m |
| Eaves overhang | 0.3 m |
| Roof length | 8 m |
| Rafter spacing, centre to centre | 400 mm |
Pitch 35.0°, rafter length 4.03 m
- Out of scope Rafter size and span Rafter sizes and spans are a structural design: ask a structural engineer or building control, or use timber span tables. UK-wide: Approved Document A (structure). Check with the source.
| Result | Value |
|---|---|
| Pitch | 35 ° |
| Pitch as rise : run | 0.7 : 1 (1 in 1.43) |
| Pitch as a percentage | 70 % |
| Rise | 2.1 m |
| Run (each slope) | 3 m |
| Rafter length (including overhang) | 4.03 m |
| Plumb cut angle (set on a roofing square) | 35 ° |
| Seat cut angle | 55 ° |
| Roof slope area | 64.45 m² |
| Rafters | 42 |
Show the working
- Run: (6 m − 0 mm ridge) ÷ 2 = 3 m
- Pitch: atan(2.1 ÷ 3) = 35°
- Rafter: √(3² + 2.1²) = 3.662 m + 0.3 m ÷ cos(35°) = 4.028 m
- Cuts: plumb 35°, seat 90° − 35° = 55°
- Slope area: 4.028 m × 8 m × 2 = 64.45 m²
- Rafters: 8 m ÷ 400 mm, rounded up, + 1 = 21 per slope × 2 = 42
How it works
- Run = half the building width less half the ridge board (two slopes), or the full width (one slope)
- Pitch = atan(rise ÷ run); or rise = run × tan(pitch)
- Rafter length = √(run² + rise²) + overhang ÷ cos(pitch)
- Plumb cut = the pitch; seat cut = 90° − pitch
- Slope area = rafter length × roof length × slopes; rafters = (roof length ÷ spacing, rounded up, + 1) × slopes
This gives geometry only. Rafter sizes, grades and how far they can reach are a structural design: use a structural engineer, timber span tables or building control.
Rafter length is measured along the top edge from the ridge cut to the tail, before any trimming on site.
Our default (adjustable)
These are typical planning figures and our own allowances, not facts about your product. Change any of them in the calculator to match your bag, pack or tin.
This calculator has no built-in defaults: every figure comes from you or your product's data.
Regulations and standards
- Approved Document A (structure): rafter sizes and spans are for a structural engineer, timber span tables or building control
Explained: Approved Document A (structure).
Our checks use the guidance for England unless a badge says otherwise. Wales, Scotland and Northern Ireland have their own rules: check the source for where you live.