How to use the roof pitch calculator
- Choose what you already know: a rise and run you measured, a pitch such as 6/12, or an angle in degrees.
- Enter the numbers. Rise and run can be any matching unit, such as inches or centimetres.
- Enter the horizontal run of the rafter to get its sloped length and the height gained.
- Read the pitch, angle, percent slope and multiplier together, and note the roof type, which affects which roofing materials can be used.
The formulas behind the conversions
Angle = arctan(rise ÷ run) × 180 ÷ π
Percent slope = 100 × rise ÷ run
Pitch multiplier = 1 ÷ cos(angle) = √(1 + (rise ÷ run)²)
Rafter length = horizontal run × multiplier
The multiplier is the most useful number for estimating: multiply any flat plan area by it to get the sloped roof area. The rafter length here is the line from wall plate to ridge; real rafters also need the overhang added and the ridge board allowed for, so this is not a cutting guide.
Worked example
A roof that rises 6 in for every 12 in of run, with a 12 ft horizontal run from the wall to the ridge:
- Pitch: 12 × 6 ÷ 12 = 6/12, a slope of 50%.
- Angle: arctan(6 ÷ 12) = 26.57°.
- Multiplier: 1 ÷ cos(26.57°) = 1.118.
- Rafter length: 12 ft × 1.118 = 13.42 ft, and the ridge sits 6 ft above the top of the wall.
Tips and common mistakes
- Measure from inside where possible. In the attic, hold a level against a rafter, mark 12 in along it and measure straight up to the rafter.
- Percent and degrees are not the same. A slope that rises one foot for every foot of run is 45°, yet as a percentage it is written as one hundred per cent. Mixing them up is a common source of wrong quotes.
- Use the multiplier for any sloped surface. The same factor turns the flat plan area of a vaulted ceiling, an attic slope or a solar array into its true surface area, which helps when ordering drywall or insulation.
- Check the material’s minimum pitch. Asphalt shingles need extra underlayment on low slopes and are not used below 2/12; low slopes usually need a membrane roof.
- Steep roofs need extra safety. Above about 8/12, roofers need harnesses and roof jacks, which raises labour costs.
US, UK and Canada differences
In the US and Canada, pitch is spoken as rise in 12, such as “a six-twelve roof”, and building codes give minimum slopes for each material that way. In the UK and Europe, roof pitch is given in degrees, and tile and slate makers state a minimum angle for each product. Both describe the same slope, so this tool shows them side by side.
Metric units and other countries
In metric mode, rise and run are in centimetres and the rafter run in metres, while the pitch is still shown as x/12 for anyone comparing North American products. Ramps and drainage slopes are often given as a percentage or a ratio, and the same formulas apply: a 1:12 ramp rises one unit for every twelve along, which is a pitch of 1/12, about 4.76° or 8.3%.