Work out the roof pitch
Pitch = tan⁻¹(rise ÷ run). Rafter length = √(rise² + run²). Roof area = plan area × pitch factor (1 ÷ cos pitch).
A geometry guide. Rafter sizes, birdsmouth cuts and minimum pitch come from the structural design and the tile or slate manufacturer.
Roof pitch factor table, 15° to 60°
The pitch factor turns a plan (flat) area into the sloping area you actually cover. It is also the rafter length per metre of run.
| Pitch | Rise per 1 m run | Pitch factor | 50 m² plan → |
|---|---|---|---|
| 15° | 268 mm | 1.035 | 51.8 m² |
| 17.5° | 315 mm | 1.049 | 52.4 m² |
| 20° | 364 mm | 1.064 | 53.2 m² |
| 22.5° | 414 mm | 1.082 | 54.1 m² |
| 25° | 466 mm | 1.103 | 55.2 m² |
| 27.5° | 521 mm | 1.127 | 56.4 m² |
| 30° | 577 mm | 1.155 | 57.7 m² |
| 32.5° | 637 mm | 1.186 | 59.3 m² |
| 35° | 700 mm | 1.221 | 61.0 m² |
| 37.5° | 767 mm | 1.260 | 63.0 m² |
| 40° | 839 mm | 1.305 | 65.3 m² |
| 42.5° | 916 mm | 1.356 | 67.8 m² |
| 45° | 1,000 mm | 1.414 | 70.7 m² |
| 47.5° | 1,091 mm | 1.480 | 74.0 m² |
| 50° | 1,192 mm | 1.556 | 77.8 m² |
| 52.5° | 1,303 mm | 1.643 | 82.1 m² |
| 55° | 1,428 mm | 1.743 | 87.2 m² |
| 57.5° | 1,570 mm | 1.861 | 93.1 m² |
| 60° | 1,732 mm | 2.000 | 100.0 m² |
Rise, run, span and pitch
- Run — the level distance from the wall plate to below the ridge. On a symmetrical duo-pitch roof it is half the span.
- Rise — the height of the ridge above the wall plate.
- Pitch — the angle of the rafter from level: tan⁻¹(rise ÷ run). A 2 m rise over a 4 m run is 26.6°.
- Rafter length — √(rise² + run²), here 4.47 m, plus the overhang measured along the slope.
Roof area from the plan
Measure the roof on plan (including overhangs), then multiply by the pitch factor 1 ÷ cos(pitch). At 35° the factor is 1.221, so 50 m² on plan is about 61 m² of roof slope. This is what you price tiles, membrane and battens from.
Minimum pitch depends on the product
Every tile and slate has a minimum pitch set by the manufacturer, and it changes with the headlap and exposure. Clay plain tiles are typically 35° minimum, while large-format interlocking concrete tiles can go down to about 17.5°–22.5° depending on headlap. Always check the manufacturer's data before you quote.
Questions roofers ask
How do I calculate roof pitch?
Divide the rise by the run and take the inverse tangent. For a 2,000 mm rise over a 4,000 mm run, tan⁻¹(0.5) = 26.6°. On a symmetrical roof the run is half the span.
What is a pitch factor?
It is 1 ÷ cos(pitch), the number you multiply a plan area by to get the sloping roof area. It is 1.155 at 30°, 1.221 at 35° and 1.414 at 45°.
How do I work out rafter length?
Rafter length = √(rise² + run²). A 2 m rise and 4 m run gives 4.47 m from wall plate to ridge. Add the overhang: a level overhang of 300 mm adds 300 ÷ cos(pitch) along the slope.
What is the minimum pitch for roof tiles?
It depends on the tile and headlap: clay plain tiles are typically 35°, while some large interlocking concrete tiles are rated down to 17.5° with a 100 mm headlap. Use the manufacturer's figure for the exact product and exposure.
More free tools for roofers
Roof tile calculator — tiles, slates, battens and ridge› All free calculators for the trades›Every roof documented, every extra paid
Dated photo evidence per job, quotes from the scaffold, signed extras, scaffold inspections and live job costing.
See Graftum for roofersA geometry guide; minimum pitch and structure come from the manufacturer and the design.