Roof geometry
Hipped roof (rectangular, equal pitches): area, ridge, hips and eaves
- where
- rise (m)
- plan width, shorter side (m)
- roof pitch (°)
- length of one hip (m)
- roof area, all slopes (m²)
- plan length, longer side (m)
- ridge length (m)
- total hip length, four hips (m)
- eaves length (m)
Explain this equation
Quantities for a rectangular hipped roof with all four slopes at the same pitch: area, ridge, total hip length and eaves. Use it to price tiles, hip and ridge tiles, and fascia and gutter.
R is the rise from the half width W/2. Each hip runs diagonally on plan across a square of side W/2, so its plan length is √2 × W/2; adding the rise by Pythagoras gives L_h. With equal pitches every slope has the same factor 1/cos p, so the whole roof area is the plan area L W scaled up. The hips eat half the width off each end, leaving a ridge of L − W.
The roof is four planes at one pitch, so area scales with 1/cos p, and the hips are the diagonals of the corner squares lifted by the rise.
Sense check: a 10 × 8 m plan at 35° gives about 97.7 m² of roof, a 2 m ridge and four hips of about 6.31 m each.
Watch out: a square plan gives a ridge of zero, a pyramid roof. Include the overhang in L and W for areas, but remember the eaves line is then the outer edge.
A rectangular roof hipped at both ends with every slope at the same pitch: covered area, ridge length, total hip length and eaves run.
Enter your values to see the result.
Good to know
With equal pitches the hips run at 45° in plan, so the ridge is the length less the width. A square plan gives a pyramid roof with no ridge. The area follows the plan ÷ cos θ rule. Use the hip length to order hip tiles or a dry hip roll, and one hip iron per hip where mortar-bedded hips are used.
Common mistake
Taking the hip length as the common rafter length. Hips are about 1.3 to 1.6 times the common run, depending on pitch.
Limits
Rectangular plan, all four slopes at one pitch, hips over 90° corners. Lengths are to the eaves corner at the plan size entered.
Sources
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.