Roof Pitch Calculator: Angle, Slope and Pitch Multiplier
Roof pitch, angle, slope percent and the rafter multiplier from rise and run, with roof area and the IRC shingle rule.
Inputs
- Working
- 4 ÷ 12 = 0.3333; angle = arctan(0.3333) = 18.43°; multiplier = √(1 + 0.3333²) = 1.054
- Angle
- 18.43°
- Slope percent
- 33.33%
- Pitch multiplier (rafter ÷ run)
- 1.054
- Pitch in 12
- 4 in 12
- Asphalt shingles
- Shingles allowed with ordinary underlayment (4:12 and steeper)
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What each Roof Pitch input means
- Rise
- How far the roof climbs over the run, in any unit — inches for a US pitch such as 6 in 12, or millimetres or metres.
- Run
- The horizontal distance for that rise, in the same unit: 12 for a US pitch, or the measured run.
- Footprint (plan) area, optional
- Optional: the roof's footprint measured flat, overhangs included, in m² or sq ft. The page multiplies it by the pitch multiplier to give the sloped area to cover.
- Convention
- Sets the unit for the footprint and the roof area. Rise and run only need to match each other.
Roof Pitch formula
pitch = rise : run · angle = arctan(rise ÷ run) · slope % = rise ÷ run × 100 · multiplier = √(1 + (rise ÷ run)²)
Pitch is how far the roof rises for a horizontal distance — in the US, inches of rise per 12 inches of run, so a 6-in-12 roof climbs 6 inches every foot. The ratio rise ÷ run is all that matters: it gives the slope as a percentage, the angle as its arctangent, and the pitch multiplier, √(1 + ratio²), which is the length of the sloped rafter for every unit of run. That multiplier is how roofers turn plan measurements into real ones: a rafter is run × multiplier long, and the roof's surface area is the footprint's area × multiplier. Enter the footprint to get the area here. The International Residential Code then sets the floor for asphalt shingles: not below 2:12, and with double underlayment up to 4:12.
Roof Pitch worked example
A 4-in-12 roof: 4 ÷ 12 = 0.333, an angle of arctan(0.333) = 18.43° and a slope of 33.3%. The multiplier √(1 + 0.333²) = 1.054 turns flat measurements into sloped ones: a rafter over 14 ft of run is 14 × 1.054 = 14.76 ft long, and a 1,500 sq ft footprint carries 1,581 sq ft of roof. Under the IRC, 4:12 is the lowest pitch where asphalt shingles need only ordinary underlayment.
More Roof Pitch examples
A 6-in-12 roof over a 1,500 sq ft footprint: the ratio is 0.5, the angle 26.57° and the multiplier 1.118, so there are 1,677.1 sq ft of roof to sheathe and shingle. The headline reads 6.0-in-12.
A metric roof that rises 30 cm for every metre: the page shows the pitch as 30:100, an angle of 16.70° and a multiplier of 1.044 — about 3.6-in-12, so asphalt shingles would need double underlayment under the IRC.
Where the Roof Pitch calculator can give the wrong answer
- Rise and run can be in any unit as long as both are the same — inches, feet, metres or millimetres.
- The footprint must include the overhangs, measured flat, or the roof area will come out short.
- Hips and valleys do not change the area of a simple hip roof of one pitch, but they do change the waste and the length of ridge and hip capping, which this does not count.
- Shingle manufacturers can be stricter than the IRC, and other roofing — metal, tile, membrane — has its own minimum slopes.
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Roof Pitch reference table
| Pitch | Angle | Slope | Multiplier |
|---|---|---|---|
| 2 in 12 | 9.46° | 16.7% | 1.014 |
| 3 in 12 | 14.04° | 25% | 1.031 |
| 4 in 12 | 18.43° | 33.3% | 1.054 |
| 5 in 12 | 22.62° | 41.7% | 1.083 |
| 6 in 12 | 26.57° | 50% | 1.118 |
| 7 in 12 | 30.26° | 58.3% | 1.158 |
| 8 in 12 | 33.69° | 66.7% | 1.202 |
| 9 in 12 | 36.87° | 75% | 1.250 |
| 10 in 12 | 39.81° | 83.3% | 1.302 |
| 12 in 12 | 45° | 100% | 1.414 |
Roof Pitch FAQ
- The length of the sloped roof for every unit of horizontal run: √(1 + (rise ÷ run)²). 4:12 is 1.054, 6:12 is 1.118, 8:12 is 1.202, 12:12 is 1.414. Multiply the footprint by it for the roof's area, or a rafter's run by it for its length.
- Divide rise by run and multiply by 12 to get inches in 12: a roof that rises 5 ft over 15 ft of run is 5 ÷ 15 × 12 = 4-in-12. The angle is arctan(5 ÷ 15) = 18.43°.
- 26.57°: arctan(6 ÷ 12) = arctan(0.5). Its slope is 50% and its multiplier 1.118.
- 2:12 under the International Residential Code (R905.2.2), and between 2:12 and 4:12 the code requires double underlayment. Below 2:12 a low-slope membrane or metal system is used instead.
- Pitch in 12 = 12 × tan(angle). 30° gives 12 × 0.577 = 6.9-in-12; 45° gives 12-in-12.
- 12 in 12: the rise equals the run, so the slope is 100% and the multiplier 1.414.