Convert between roof pitch, angle and rafter length — pitch as rise over 12, the angle in degrees and the multiplier that turns a horizontal run into a rafter. Runs entirely in your browser — your numbers never leave this device.
Rafter length is the theoretical line length before overhang, birdsmouth and ridge deductions. The slope multiplier converts flat (plan) roof area to true sloped area: sloped area = plan area × multiplier.
| Pitch | Angle | Multiplier |
|---|---|---|
| 1/12 | 4.76° | 1.0035 |
| 2/12 | 9.46° | 1.0138 |
| 3/12 | 14.04° | 1.0308 |
| 4/12 | 18.43° | 1.0541 |
| 5/12 | 22.62° | 1.0833 |
| 6/12 | 26.57° | 1.1180 |
| 7/12 | 30.26° | 1.1577 |
| 8/12 | 33.69° | 1.2019 |
| 9/12 | 36.87° | 1.2500 |
| 10/12 | 39.81° | 1.3017 |
| 11/12 | 42.51° | 1.3566 |
| 12/12 | 45.00° | 1.4142 |
Roof pitch in the imperial convention is stated as rise over a standard 12 units of run: a roof that climbs 6 units for every 12 across is a 6/12 pitch. The same slope exists in two other forms that other trades prefer. As an angle it is the arctangent of rise over run — 26.57° for 6/12 — and as a multiplier it is the square root of one plus the squared slope, the factor that converts a horizontal distance into the sloping rafter length over it. This calculator moves between all three forms, and the table prints the full standard range so any pitch can be read off without calculating.
The multiplier is the working number on site. A building whose horizontal run from wall plate to ridge is 15 ft needs rafters of 15 times the multiplier at the roof's pitch: 16.77 ft at 6/12. Note what the multiplier is not — at 4/12 it is already 1.0541, so estimating rafter length from the horizontal run without it under-orders material on every roof, steeply on steep ones, where 12/12 multiplies by 1.4142.
Pitch is measured from any two of its forms: enter a measured rise and run, a known x/12, or an angle read by a level or phone inclinometer, and the remaining forms follow. Figures here are geometric lengths along the slope; cutting allowances, overhangs and ridge thickness are carpentry additions made on top of the geometric rafter length.
The roof rises 6 units for every 12 units of horizontal run. The 12 is a fixed convention, not a measurement of the building — any slope can be expressed in the form by scaling its rise and run until the run is 12.
They describe the same slope in different forms. Pitch is the ratio x/12; the angle is its arctangent in degrees. A 12/12 pitch is a 45° angle, and the table on this page pairs every standard pitch with its angle.
Converting horizontal distance to sloping length. Rafter length, roofing area and shingle quantities all live on the slope, while plans and tape measures on the ground read horizontally — multiplying the horizontal run by the pitch's multiplier gives the true sloping figure.
No. The lengths here are the geometric slope length over the horizontal run entered. An eaves overhang extends the rafter beyond the wall; add the overhang's horizontal length to the run before calculating if the full rafter including overhang is the figure needed.
No. The calculation runs entirely in the browser and nothing entered is uploaded, stored or tracked.
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