How to calculate a hip roof
A regular hip roof has the same pitch on every slope. The run is half the building's width, and the rise is the run × tan(pitch). From those three numbers everything else follows.
- Common rafter: run ÷ cos(pitch).
- Hip rafter: the square root of run² + run² + rise², because on plan it runs diagonally across a square.
- Ridge: the building length minus its width.
A worked example. A 10m by 6m building at 30°: the run is 3m and the rise 1.73m. The common rafter is 3.464m, the hip rafter 4.583m at a pitch of 22.21°, and the ridge 4m. The roof area is 69.3m², and at 600mm centres the jacks step up by 0.693m, 4 to each side of every hip.
How to calculate the area of a hipped roof
Take the plan area inside the eaves, including any overhang, and divide by cos(pitch). At 30° that multiplier is 1.155. Because every slope has the same pitch, a hipped roof has exactly the same sloped area as a gable roof on the same plan at the same pitch: the hip ends just take it from the gables.
Hip rafter angle formula
The hip pitch is the inverse tangent of rise ÷ (run × √2). The hip is longer on plan than a common rafter by √2, so it always rises at a shallower angle than the roof itself.
The hip runs at 45° on plan for a regular hip. That is where its 45° side cut comes from, not its angle in elevation.
Does a hip rafter have to be 45 degrees?
On plan, yes, for a regular hip where both slopes have the same pitch. If one slope is steeper than the other, the hip is irregular and does not run at 45°. This calculator handles regular hips only.
Jack rafters and the common difference
Jack rafters run from the wall plate up to the hip. On plan, each jack's run is its distance from the corner, so each one is longer than the last by the same amount, the common difference: the rafter centres ÷ cos(pitch). Each has a 45° side cut on plan where it meets the hip, and a plumb cut at the roof pitch.
Hip roof angle chart
| Roof pitch | Hip pitch | Common rafter multiplier | Hip multiplier (per plan length) |
|---|---|---|---|
| 10° | 7.1° | 1.015 | 1.008 |
| 15° | 10.7° | 1.035 | 1.018 |
| 20° | 14.4° | 1.064 | 1.033 |
| 25° | 18.2° | 1.103 | 1.053 |
| 30° | 22.2° | 1.155 | 1.08 |
| 35° | 26.3° | 1.221 | 1.116 |
| 40° | 30.7° | 1.305 | 1.163 |
| 45° | 35.3° | 1.414 | 1.225 |
| 50° | 40.1° | 1.556 | 1.308 |
| 55° | 45.3° | 1.743 | 1.421 |
| 60° | 50.8° | 2 | 1.581 |
Frequently asked questions
How do you calculate a hip roof?
Find the run (half the width) and the rise (run × tan pitch). The common rafter is run ÷ cos(pitch), the hip is the square root of run² + run² + rise², and the ridge is the length minus the width. The calculator does all of it and draws the plan.
How do I calculate the area of a hipped roof?
Plan area ÷ cos(pitch), including any overhang. A 10m × 6m roof at 30° is 60m² on plan and 69.3m² on the slope. It is the same as a gable roof of the same plan and pitch.
How to calculate the hip?
The hip rafter length is the square root of run² + run² + rise². For a 6m wide building at 30°, the run is 3m and the rise 1.73m, so the hip is 4.583m to the centre line.
What is the formula for calculating the hip rafter angle?
Hip pitch = inverse tan of rise ÷ (run × √2). At a 30° roof pitch, that is 22.2°. The hip is always shallower than the roof itself.
Does a hip rafter have to be 45 degrees?
On plan, for a regular hip with the same pitch both sides, yes. In elevation it is shallower than the roof pitch. Irregular hips, with different pitches on each side, are not at 45°.
How do I calculate the angle of a roof?
Divide the rise by the run and take the inverse tangent. For a hip, use the rise over the run × √2 instead. The roof pitch calculator converts any pitch between degrees, x:12, percent and 1 in N.
What is a pyramid hip roof?
A hip roof on a square plan, where the four hips meet at a point and there is no ridge. Choose "Pyramid" in the calculator.
Can I use this for an irregular hip?
No. It assumes the same pitch on every slope, so the hips run at 45° on plan. Irregular hips need their own geometry for each side.
How many jack rafters do I need?
One at every rafter centre along each side of each hip, stopping short of the hip's top. A 10m × 6m roof at 600mm centres has 4 per side, 32 in all.
Sources
- Marley: low pitch tiles and minimum pitches (opens in a new tab)
- Cupa Pizarras: minimum pitch for a slate roof (NHBC and BS 5534) (opens in a new tab)
- Maguire Brothers: roof pitches (opens in a new tab)
- Bauder: BS 6229:2025, the key changes for flat roofs (opens in a new tab)
- Marley: how to calculate roof pitch (opens in a new tab)
Rafter sizes, spans and fixings are for your engineer or Building Control. This tool works out the geometry and quantities only.
By Janusz Wozniak, Founder & Lead Developer
Built so a hip roof can be set out from three measurements, with the plan drawn as you type.
Last updated .
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