Know which measurement is horizontal run
A 6:12 pitch rises 6 inches for every 12 inches of horizontal run. Run is level. On a centered gable roof, one horizontal run equals half the building span after you subtract half the ridge board thickness, whereas total rafter length follows the sloped diagonal.
Find the pitch angle by taking the arctangent of rise divided by 12. Find the slope multiplier by taking the square root of 12 squared plus rise squared, then dividing by 12.
How do you calculate roof pitch, angle, and rafter factor?
In US framing, roof pitch is written as rise : 12—the number of vertical inches the roof rises for every 12 inches of horizontal level run. Treating the roof profile as a right triangle, we derive the roof angle and the framing-square slope multiplier:
where:
- Rise – Vertical rise in inches per 12 inches of horizontal run (for example, 6 in a 6:12 pitch);
- θ – Roof slope angle measured in degrees above horizontal;
- M – Slope multiplier (rafter factor) used to convert flat horizontal area or run into sloped surface length (see the roofing calculator); and
- L_slope – Geometric rafter slope length (L_slope = Run × M). For ridge deduction and overhang tails, open the rafter length calculator.
Common roof pitch to degrees chart
| Pitch | Degrees | Slope multiplier |
|---|---|---|
| 2:12 | 9.46° | 1.014 |
| 3:12 | 14.04° | 1.031 |
| 4:12 | 18.43° | 1.054 |
| 5:12 | 22.62° | 1.083 |
| 6:12 | 26.57° | 1.118 |
| 7:12 | 30.26° | 1.158 |
| 8:12 | 33.69° | 1.202 |
| 9:12 | 36.87° | 1.250 |
| 10:12 | 39.81° | 1.302 |
| 12:12 | 45.00° | 1.414 |
Three outputs, three uses
- 01
Pitch ratio
Use rise-per-12 to describe the roof slope consistently.
- 02
Degrees
Use the angle as a geometry check or to compare slope ranges, not as a complete roof-system specification.
- 03
Slope multiplier
Multiply horizontal run by the factor to estimate the simple diagonal length, or horizontal area by the factor for a simple roof plane.
- 04
Rafter slope length
Treat the result as the hypotenuse only. It excludes ridge adjustments, seat cut, tail, overhang and connection details.
Worked example: 6:12 pitch and 15 ft run
The ratio is 6 / 12, or 0.5. The arctangent of 0.5 is approximately 26.57 degrees. The slope multiplier is approximately 1.118.
Multiplying a 15 ft horizontal run by 1.118 gives a simple slope length of about 16.77 ft. That number is useful for checking geometry, but it is not a finished rafter cut length.
Mistakes that change the answer
- Entering the total span when the field expects one horizontal run.
- Including overhang in one input but not in the estimate sketch.
- Using one pitch for additions, dormers or planes with different slopes.
- Treating slope length as a cut length without ridge, seat and tail details.
- Measuring from an unsafe roof position when drawings or a qualified professional should be used.
Use the multiplier consistently
For a simple plane, the same multiplier can connect horizontal projection to sloped length or area. It should not be applied once to a footprint that mixes multiple pitches. Break a complex roof into verified planes, document each pitch and combine the separate results.
Roof access can involve serious fall hazards. Do not climb solely to obtain a calculator input. Use safe records, ground-based methods or a qualified roofing professional.
Frequently asked questions
How do I convert roof pitch to degrees?
Divide the rise by 12 and take the arctangent. A 6:12 pitch is arctangent of 0.5, which is about 26.57 degrees.
How do I calculate rafter slope length?
Multiply verified horizontal run by the slope multiplier for the pitch. The result is only the right-triangle hypotenuse, not a finished rafter cut length.
Is roof run the same as total roof span?
Run and span are different measurements: on a centered gable, one horizontal run is roughly half the building span before overhang and ridge adjustments.
Can one multiplier be used for a roof with mixed pitches?
Each slope needs its own multiplier: calculate each roof plane with its own pitch and horizontal dimensions, then combine the verified results.