Roof pitch calculator
Convert a roof pitch between degrees, percent and rise over run, then work out rafter length and roof area in metres.
Slope in percent
- Slope in percent
- 41.4%
- Pitch in degrees
- 22.5°
- Pitch as x/12 (US plans)
- 4.97/12
- Rise to run
- 1 : 2.41
- Slope factor
- 1.0824Rafter length per metre of run
Rafter length and roof area
Half the span for a simple gable roof.
The roof seen from above, including the eaves.
Rafter length and roof area
- Rafter length before eaves overhang
- 4.33 m
- Roof surface area
- 216.5 m²
Estimate only. Check product labels and the building rules in your state or territory before you buy or build.
Quick answer
Roof pitch is the angle of the roof above horizontal, and its tangent is the rise divided by the run. A 22.5° roof rises tan(22.5°) = 0.414 m for every metre of run, a 41.4% slope. Multiply the run by the slope factor √(1 + (rise ÷ run)²), 1.0824 at 22.5°, to get the rafter length: a 4 m run needs a 4.33 m rafter.
How to use the roof pitch calculator
- Choose how you know the pitch: in degrees from the plans or a digital angle finder, as a percent, as a rise and run you measured yourself, or as x/12 from American plans.
- Type the value. The pitch in degrees, the percent slope, the rise-to-run ratio and the slope factor update as you type.
- For rafter length, enter the horizontal run from the outside of the wall to the centre of the ridge. For roof area, enter the plan area of the roof seen from above, eaves included.
How do you work out roof pitch in degrees?
Take the inverse tangent of the rise divided by the run. Degrees, percent and rise over run all describe the same ratio: how far the roof climbs for each metre it covers horizontally. A roof that rises 1.2 m over a 4 m run has a ratio of 0.3, a 30% slope and a pitch of 16.70°.
The slope factor is the length of the sloped side of a right-angled triangle whose run is 1. Multiply any horizontal measurement by it to get the matching measurement along the slope, which is how you get rafter length from the run and roof area from the plan area.
pitch (degrees) = arctan(rise ÷ run)slope % = rise ÷ run × 100rise per metre of run = tan(pitch) × 1,000 mmslope factor = √(1 + (rise ÷ run)²)rafter length = run × slope factorroof area = plan area × slope factorRoof pitch chart: degrees to percent and rise per metre
Every value below comes from the formulas above, rounded to one decimal for the percent, the nearest millimetre for the rise and four decimals for the slope factor.
| Pitch | Slope | Rise per metre of run | Slope factor |
|---|---|---|---|
| 1° | 1.7% | 17 mm | 1.0002 |
| 2° | 3.5% | 35 mm | 1.0006 |
| 3° | 5.2% | 52 mm | 1.0014 |
| 5° | 8.7% | 87 mm | 1.0038 |
| 7.5° | 13.2% | 132 mm | 1.0086 |
| 10° | 17.6% | 176 mm | 1.0154 |
| 12.5° | 22.2% | 222 mm | 1.0243 |
| 15° | 26.8% | 268 mm | 1.0353 |
| 17.5° | 31.5% | 315 mm | 1.0485 |
| 20° | 36.4% | 364 mm | 1.0642 |
| 22.5° | 41.4% | 414 mm | 1.0824 |
| 25° | 46.6% | 466 mm | 1.1034 |
| 27.5° | 52.1% | 521 mm | 1.1274 |
| 30° | 57.7% | 577 mm | 1.1547 |
| 35° | 70.0% | 700 mm | 1.2208 |
| 40° | 83.9% | 839 mm | 1.3054 |
| 45° | 100.0% | 1,000 mm | 1.4142 |
Worked examples
Rafters and roof area for a 22.5° roof
A house is 8 m wide between the outside faces of the walls, with a roof pitched at 22.5°. The run of each rafter is half the width, 4 m. The slope factor for 22.5° is 1.0824, so each rafter is 4 × 1.0824 = 4.33 m before you add the eaves overhang.
Seen from above, the roof covers 200 m² including the eaves. The sloped surface is 200 × 1.0824 = 216.5 m². Order roof tiles or sheeting for the sloped area, not the plan area. If every face of a hip roof has the same pitch, the same multiplication gives the whole hip roof surface.
Checking a skillion roof for corrugated sheeting
A skillion roof over a rear extension falls 300 mm over a 4.5 m run. Enter a rise of 300 and a run of 4500: the pitch is 3.81°, a 6.7% slope, or 1 : 15. That is below the 5° minimum the NCC Housing Provisions set for corrugated metal sheeting, but above the 2° minimum for trapezoidal profiles.
To use corrugated sheeting on the same run, the roof needs a fall of at least tan(5°) × 4,500 mm = 394 mm.
What is the minimum pitch for a metal roof in Australia?
The NCC Housing Provisions set the minimum pitch by sheet profile: 5° for corrugated, 2° for trapezoidal and close-pitched trapezoidal, and 1° for concealed-fastened sheeting (Part 7.2, Figure 7.2.3, the same in NCC 2022 and NCC 2025). The figure notes add that the drainage capacity of the sheeting should be considered when choosing the pitch and the length of the sheets, so check the manufacturer’s installation guide for long runs.
Building rules come from the National Construction Code, which each state and territory adopts and may vary. Check with your council or a building surveyor or certifier before you build, and use a qualified tradesperson for structural roof work.
Does a tiled roof need sarking?
Under the NCC Housing Provisions, every tiled roof pitched below 18° needs sarking. From 18° up, Table 7.3.4 of Part 7.3 allows a rafter or truss top chord of up to 4,500 mm (18° to under 20°), 5,500 mm (20° to under 22°) or 6,000 mm (22° and steeper) without sarking, measured from the apex down. Beyond that length, sarking must be installed over the rest of the rafter towards the eaves.
Use the rafter length from the calculator, plus the sloped length of the eaves overhang, to compare with these limits. Where sarking is installed on a roof pitched below 20°, or on any roof without an eaves overhang, Part 7.3 also requires an anti-ponding device or board.
Common questions
What is a 22.5° roof pitch as a ratio?
A 22.5° roof rises about 414 mm for every metre of run, a rise-to-run ratio of 1 : 2.41 and a slope of 41.4%. The tangent of 22.5° is 0.4142, which gives all three figures. The slope factor is 1.0824, so each metre of horizontal run needs 1.08 m of rafter, and the roof surface is about 8% larger than its plan area.
How do I convert rise and run to degrees?
Divide the rise by the run and take the inverse tangent of the result. A rise of 1.2 m over a run of 4 m gives 1.2 ÷ 4 = 0.3, and arctan(0.3) = 16.70°. On most phone calculators the key is labelled tan⁻¹. To go the other way, multiply the run by the tangent of the pitch: a 25° roof over a 4 m run rises 4 × 0.4663 = 1.87 m.
How many millimetres per metre is a 5° fall?
A 5° roof falls 87 mm for every metre of run, because tan(5°) = 0.0875. Over a 4.5 m run that is 394 mm. A 2° roof falls 35 mm per metre and a 1° roof 17 mm per metre. These three are the NCC minimum pitches for corrugated, trapezoidal and concealed-fastened metal sheeting, so they are useful checks for low-pitched skillion roofs.
How much larger is the roof than the plan area?
Multiply the plan area by the slope factor for your pitch. A 15° roof is 3.5% larger than its plan area (factor 1.0353), a 22.5° roof is 8.2% larger (1.0824), a 30° roof is 15.5% larger (1.1547) and a 45° roof is 41.4% larger (1.4142). Include the eaves in the plan area, because the roof covering runs out over them too.
Does a hip roof change the roof area calculation?
No, as long as every face has the same pitch: the roof area is still the plan area multiplied by the slope factor. Each face is tilted by the same angle, so each one is larger than its plan by the same factor. What does change is the length of the hips and valleys, which run diagonally and are longer than the common rafters.
Sources
- Australian Building Codes Board, NCC 2025 Housing Provisions, Part 7.2 Sheet roofing (checked 19 October 2026)Figure 7.2.3: minimum pitch 5° corrugated, 2° trapezoidal and close-pitched trapezoidal, 1° concealed fastened.
- Australian Building Codes Board, NCC 2022 Housing Provisions, Part 7.2 Sheet roofing (checked 19 October 2026)Same minimum pitches in Figure 7.2.3.
- Australian Building Codes Board, NCC 2025 Housing Provisions, Part 7.3 Roof tiles and shingles (checked 19 October 2026)Table 7.3.4 sarking limits by pitch and rafter length; 7.3.5 anti-ponding device below 20°. NCC 2022 Part 7.3 has the same table.
- Australian Building Codes Board, General NCC FAQ (checked 19 October 2026)The NCC is given legal effect through adoption by each state and territory.
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