How the result is calculated
- 01
Roof angle = arctangent(rise / 12) - 02
Slope multiplier = square root of (12 squared + rise squared) / 12 - 03
Rafter slope length = horizontal run x slope multiplier
ROOFING
Roof Pitch Calculator
Calculate roof pitch in degrees, slope multiplier and rafter length from rise per 12. Enter your measurements below and the estimate updates instantly.
Formula, validation and worked example reviewed November 12, 2026. See our calculation methodology.
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ROOFING
US UNITSRoof Pitch
YOUR ESTIMATE
26.57°6:12 pitchMultiplier 1.118 · Slope length 16.77 ft
Geometric slope length, not a rafter cut length.
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Slope geometry
Convert rise-per-12 into angle and rafter length.
To calculate roof pitch, use a right triangle with 12 inches of horizontal run, the entered vertical rise, and a sloped hypotenuse used to find degrees and the slope multiplier.
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:
θ=arctan(Rise12)
(Roof angle in degrees)M=√(12² + Rise²)12
(Pythagorean pitch factor)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.
6:12 pitch with a 15 ft horizontal run
- The slope ratio is 6 / 12 = 0.5.
- Arctangent of 0.5 gives 26.57 degrees.
- The 6:12 slope multiplier is about 1.118.
- 15 x 1.118 = 16.77 ft of simple slope length.
Quick reference chart
Roof Pitch to Degrees, Grade % & Rafter Multiplier Lookup Chart
Exact right-triangle conversions for standard US framing pitches (rise per 12 inches of horizontal run).
| Pitch (Rise:12) | Angle (Degrees) | Slope Grade (%) | Rafter Multiplier |
|---|---|---|---|
| 2:12 | 9.46° | 16.7% | 1.014× |
| 4:12 | 18.43° | 33.3% | 1.054× |
| 5:12 | 22.62° | 41.7% | 1.083× |
| 6:12 | 26.57° | 50.0% | 1.118× |
| 8:12 | 33.69° | 66.7% | 1.202× |
| 10:12 | 39.81° | 83.3% | 1.302× |
| 12:12 | 45.00° | 100.0% | 1.414× |
Common mistakes to avoid
- Entering total roof span when the field expects horizontal run from ridge to wall.
- Confusing rise-per-12 slope with total rise over the full building span.
- Adding overhang to horizontal run without confirming where the rafter measurement begins and ends.
- Using simple triangle length as a cut length without ridge, seat, tail, or connection details.
- Assuming the same pitch applies to every plane, dormer, or addition.
Questions answered
Calculator FAQ
How do I calculate roof pitch in degrees?+
Divide the rise by 12 and take the arctangent of that ratio. For example, a 6:12 pitch is arctangent of 0.5, or about 26.57 degrees.
How do I convert a 6:12 or 8:12 roof pitch to degrees?+
A 6:12 pitch equals 26.57° (slope ratio 0.50). An 8:12 pitch equals 33.69° (slope ratio 0.67). A 4:12 pitch equals 18.43° and a 12:12 pitch equals 45.00°.
What does a 6:12 roof pitch mean?+
The roof rises 6 inches for every 12 inches of horizontal run.
What are 4:12, 8:12 and 12:12 roof pitches in degrees?+
Using arctangent of rise divided by 12, 4:12 is about 18.43 degrees, 8:12 is about 33.69 degrees and 12:12 is 45 degrees.
Is horizontal run the same as building width?+
Usually not. On a simple centered gable, run is approximately half the span before overhang and construction details.
What does the slope multiplier do?+
It converts horizontal run or projected area into a corresponding sloped length or area for a simple plane.
Is the rafter result a cut length?+
No. It is basic slope geometry and does not include ridge, birdsmouth, tail, overhang, connectors, or engineered adjustments.
Can I use it for multiple roof pitches?+
Calculate each distinct roof plane with its own pitch and run, then combine the appropriate results.
Practical selection guide
Common roof pitch conversions at a glance.
These values use the exact rise-per-12 right-triangle formula. The rafter result is geometric slope length, not a finished cut length.
4:12 roof pitch
18.43 degrees with a 1.054 slope multiplier.
6:12 roof pitch
26.57 degrees with a 1.118 slope multiplier.
8:12 roof pitch
33.69 degrees with a 1.202 slope multiplier.
12:12 roof pitch
45.00 degrees with a 1.414 slope multiplier.
Method references: GAF explanation of roof slope and squares · GAF steep-slope field guide