Roof geometry
Roof pitch from rise and run (degrees, percentage, 1 in n)
- where
- roof pitch (°)
- rise, wall plate to ridge (mm)
- run, horizontal half span (mm)
- slope as a percentage (%)
- slope expressed as 1 in n
- sloping length over the run (mm)
Explain this equation
Turns a measured rise and run into the roof pitch, in degrees, as a percentage and as 1 in n. Use it when you have a tape on an existing roof and need the pitch to check a tile's minimum, or to order rafters.
R is how far the roof climbs from the wall plate to the ridge and G is the level distance it covers to get there, normally half the span. Their ratio R/G is the slope; arctan turns it into an angle. Multiplying by 100 gives the percentage slope, and flipping it gives the 1 in n figure used for low pitches.
Rise, run and rafter form a right-angled triangle, so Pythagoras gives the sloping length L_s and basic trigonometry gives the angle.
Sense check: a rise of 1200 over a 2000 run is a 60% slope, about 31°, with a sloping length of about 2.33 m. Equal rise and run is always 45°.
Watch out: measure the run level and the rise plumb. Measuring along the slope by mistake gives a pitch that is too low.
Turns a measured rise and run into the roof pitch in degrees, the slope as a percentage and as 1 in n, and the sloping length.
Enter your values to see the result.
Good to know
Measure rise and run between the same two points: for example from the top of the wall plate to the top of the ridge, and from the wall plate line to the centre of the ridge in plan. On an existing roof, a digital level on the rafter gives pitch directly; rise and run are better from drawings. Manufacturer minimum pitches (for example 22.5° for Marley Modern at 75 mm headlap, 35° for plain tiles) are in degrees, so check against the degrees figure.
Common mistake
Using the full span as the run. The run is half the span on a symmetrical duo-pitch roof, so using the full span roughly halves the pitch.
Limits
Plane, straight slopes only. Sprocketed eaves, bellcast and mansard roofs have more than one pitch: work each part separately.
Sources
- Colchester Institute: Traditional cut roof with hip and valley (common rafter geometry: span, rise, run, overhang)
- BS 5534:2014+A2:2018 Slating and tiling for pitched roofs and vertical cladding. Code of practice (BSI)
- Marley Modern concrete interlocking tile: technical data (420 × 330 mm, 292 mm cover width, 345 mm max gauge, 9.9 tiles/m², 2.9 m battens/m², 50 kg/m²)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the roof covering manufacturer’s fixing specification, BS 5534, BS 8000-6, BS 6229, the Lead Sheet Training Academy guidance and Building Regulations. Wind uplift and structural design need a competent designer.