Roof Pitch to Angle Converter
Reviewed by the My Roof Pitch editorial team · Updated · Free, no sign-up, works offline after first load
To convert roof pitch to degrees, divide the rise by 12 and take the arctangent. A 6:12 pitch is arctan(0.5) = 26.57°. To reverse it, take the tangent of the angle and multiply by 12: a 30° roof is a 6.93:12 pitch.
Your measurements
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The first number in an X:12 pitch. Enter 6 for a 6:12 roof.
Analysis
Live results from your measurements.
Show the working
- Ratio:
6 ÷ 12= 0.5 - Pitch to degrees:
arctan(0.5)= 26.57° - Degrees to pitch:
tan(30°) × 12= 6.93:12 - Multiplier:
√(6² + 144) ÷ 12= 1.118
What this calculator does
Pitch and angle are two notations for the same roof geometry. The X:12 ratio is a carpenter's shorthand that maps directly onto a framing square, while degrees are what a digital inclinometer, a CAD drawing or a European specification will give you. Converting between them is a single trigonometric step, but getting it wrong by mixing up tangent and sine is one of the most common framing errors — the sine relationship uses the rafter length, not the run.
How to use it
- Take the first number of the pitch — the rise over a 12-unit run.
- Divide that rise by 12 to get the slope ratio.
- Take the arctangent of the ratio to get the angle in radians.
- Multiply by 180 ÷ π to convert radians to degrees.
- To reverse, take the tangent of the angle in degrees and multiply the result by 12.
The formula
Pitch to degrees
angle = arctan(rise / 12) × (180 / pi)
Arctangent because rise and run are the two legs of a right triangle.
Degrees to pitch
rise = tan(angle in radians) × 12
The reverse conversion. Convert degrees to radians first by multiplying by π ÷ 180.
Worked example
An inclinometer on a roof plane reads 22.5 degrees.
- Radians: 22.5 × π ÷ 180 = 0.3927
- Tangent: tan(0.3927) = 0.4142
- Pitch: 0.4142 × 12 = 4.97
22.5° is a 4.97:12 pitch — for practical framing purposes, a 5:12 roof.
Reference chart
| Pitch (rise:12) | Angle (degrees) | Slope (%) | Pitch multiplier |
|---|---|---|---|
| 1:12 | 4.76 | 8.3 | 1.0035 |
| 2:12 | 9.46 | 16.7 | 1.0138 |
| 3:12 | 14.04 | 25 | 1.0308 |
| 4:12 | 18.43 | 33.3 | 1.0541 |
| 5:12 | 22.62 | 41.7 | 1.0833 |
| 6:12 | 26.57 | 50 | 1.118 |
| 7:12 | 30.26 | 58.3 | 1.1577 |
| 8:12 | 33.69 | 66.7 | 1.2019 |
| 9:12 | 36.87 | 75 | 1.25 |
| 10:12 | 39.81 | 83.3 | 1.3017 |
| 11:12 | 42.51 | 91.7 | 1.3566 |
| 12:12 | 45 | 100 | 1.4142 |
| 14:12 | 49.4 | 116.7 | 1.5366 |
| 16:12 | 53.13 | 133.3 | 1.6667 |
| 18:12 | 56.31 | 150 | 1.8028 |
| 24:12 | 63.43 | 200 | 2.2361 |
Common angles and their nearest standard pitch
| Angle | Exact pitch | Nearest standard pitch |
|---|---|---|
| 10° | 2.12:12 | 2:12 |
| 15° | 3.22:12 | 3:12 |
| 18.43° | 4:12 | 4:12 |
| 20° | 4.37:12 | 4:12 |
| 25° | 5.6:12 | 6:12 |
| 26.57° | 6:12 | 6:12 |
| 30° | 6.93:12 | 7:12 |
| 33.69° | 8:12 | 8:12 |
| 35° | 8.4:12 | 8:12 |
| 40° | 10.07:12 | 10:12 |
| 45° | 12:12 | 12:12 |
Common mistakes
- Using sine instead of tangent. Sine relates rise to the rafter length, not to the run.
- Forgetting to convert radians to degrees — most programming and spreadsheet trig functions return radians.
- Rounding the pitch to a whole number before converting. Convert first, round last.
- Assuming a 45° roof is a 45:12 pitch. It is 12:12.
- Reading an inclinometer on the shingle surface rather than the deck plane on a thick tile or shake roof.
Assumptions and limits
- Angles are measured from horizontal, not from vertical.
- The run is a true horizontal distance.
- Conversions are exact; only the displayed result is rounded.
Frequently asked questions
What angle is a 6/12 pitch?
A 6/12 pitch is 26.57 degrees. Divide 6 by 12 to get 0.5, then take the arctangent of 0.5. The same roof is a 50% slope with a 1.1180 pitch multiplier.
What pitch is 30 degrees?
A 30-degree roof is a 6.93:12 pitch. The tangent of 30 degrees is 0.5774, multiplied by 12. In practice that gets framed as a 7:12 roof, which is 30.26 degrees.
What angle is a 12/12 pitch?
Exactly 45 degrees. Rise equals run, so the tangent is 1 and the arctangent of 1 is 45 degrees. It is the only whole-number pitch with an exact whole-degree angle.
Why do Americans use X:12 instead of degrees?
The 12-unit run matches the inch markings on a framing square, so a carpenter can lay out a rafter cut directly from the ratio without any trigonometry or a calculator.
What angle is a 4/12 pitch?
18.43 degrees. That is arctan(4 ÷ 12) = arctan(0.3333). A 4/12 roof is a 33.3% slope and the lowest pitch at which standard single-layer shingle underlayment is approved.
How do I set a saw for a roof pitch?
The plumb cut angle equals the roof angle measured from vertical, so set the saw to 90 minus the roof angle for a plumb cut, or to the roof angle itself for the seat cut.
Related guides
- How to Calculate Roof Pitch: 6 Methods That Actually WorkSix field-tested ways to find the pitch of a roof — from the ladder, from the attic, from a photo — plus the arithmetic that turns any measurement into X:12, degrees and percent.
- Roof Pitch to Degrees: Full Conversion Chart and FormulaThe complete pitch-to-degree conversion table, the trigonometry behind it, and why 6:12 is 26.57° rather than the 30° people expect.
Last updated 2026-08-05. Results are estimates for planning and are not a substitute for a licensed engineer or local code review.