Roof pitch calculator
Enter a pitch in degrees or a rise over a run. It gives you the other one, plus the multipliers for every sloping length on the roof — with the formulas, so you can check it.
A sloping length equals its plan length times 1 / cos(pitch).
A hip or valley on a square corner uses a different, smaller factor —
√(1 + tan²(pitch) ⁄ 2) — because it is already running diagonally across the
plan. Roof area uses the rafter factor. Ridges and gutters are level and use neither.
Ridge and gutter lengths are level — no factor applies to them.
The worked example, by hand
Those default numbers are a 25° roof, and here is the whole calculation without the calculator:
| What | Formula | At 25° |
|---|---|---|
| Rise per metre of run | tan θ | 0.466 m |
| As a ratio | 1 : 1 / tan θ | 1 : 2.14 |
| Rafter / sheet run / barge / area factor | 1 / cos θ | 1.103 |
| Hip or valley factor, square corner | √(1 + tan²θ ⁄ 2) | 1.053 |
| A 4.000 m plan rafter | 4.000 × 1.103 | 4.414 m |
Which factor goes where
Getting this wrong is the most common estimating error there is, so it is worth being explicit about every line on a roof:
| Measurement | Factor |
|---|---|
| Sheet run, ridge to gutter | 1 / cos θ |
| Rafter length | 1 / cos θ |
| Barge, along a gable rake | 1 / cos θ |
| Roof area from footprint area | 1 / cos θ |
| Hip, from its plan length | √(1 + tan²θ ⁄ 2) |
| Valley, from its plan length | √(1 + tan²θ ⁄ 2) |
| Ridge | none — level |
| Gutter, fascia, eave | none — level |
| Face width, for counting sheets | none — level |
The hip and valley formula assumes the two planes meet at a square corner and share a pitch. An odd-angled corner, or two roofs at different pitches meeting in a valley, needs the geometry worked properly — the table is not a substitute for that.
Why the hip factor is smaller
A hip runs diagonally in plan as well as sloping. On a square corner its plan length is already √2 times the run, so it has picked up most of its extra distance horizontally before pitch is applied. At 25° a rafter gains 10.3 per cent and a hip gains 5.3 per cent.
Multiply a hip by the rafter factor and you over-order the longest, most expensive flashing on the roof by about five per cent. The full explanation is in roof pitch explained.
Measuring the pitch to put in
A pitch gauge or a phone level on a rafter or a sheet, taken in more than one place — old roofs sag, and a lean-to is usually not the same pitch as the roof it hangs off. Or rise over run with a level and a tape: hold the level horizontal against the slope, measure 1 m along it, drop to the roof, and that vertical is the rise.
An aerial photo cannot give you pitch. It gives you the plan shape, which is everything else.
Using this calculator.
How do I convert roof pitch from degrees to a ratio?
The rise per unit of run is tan(pitch), so the ratio is 1 : 1/tan(pitch). At 25°, tan is 0.466, so the ratio is 1 : 2.14 — the roof rises 466 mm for every metre it runs.
Going the other way, pitch = atan(rise ÷ run).
What multiplier do I use for a hip or a valley?
√(1 + tan²θ ⁄ 2) applied to the hip’s plan length, for two equally-pitched planes meeting at a square corner. At 25° that is 1.053.
Not the rafter factor. The hip is already diagonal in plan, so the rafter factor over-states it — by about five per cent at 25°.
Does the pitch factor apply to roof area?
Yes, the rafter factor does. The roof is stretched in one direction only, so area scales by the same 1 / cos θ.
A 120 m² footprint at 30° is 138.6 m² of roof — 18.6 m² of steel and underlay that a footprint estimate does not buy.
Is this calculator accurate enough to order from?
The arithmetic is exact. What decides whether the order is right is the pitch and the plan lengths you put in, and both come off the roof.
Take the pitch in more than one place, measure critical lengths on site before anything is cut, and treat any single number as something to sanity-check rather than trust.
Next
Try it on one of your own roofs.
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