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
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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.
- Roof Angle Calculator Guide: Degrees, Pitch and Percent ExplainedPitch, angle and percent are three languages for the same slope. Here is the trigonometry that connects them, a full conversion chart, and how to measure a roof's real angle with tools you already own.
- Roof Gradient and Slope Percent: Converting Between Global NotationsGradient, fall ratio and slope percent are the same rise-over-run relationship dressed in three regional conventions. Here is how to convert between them accurately, plus the drainage fall minimums that actually matter on a low-slope roof.
- Rafter Length and Cuts: The Complete Layout and Calculation GuideRafter math has three layers most guides skip: the difference between line length and true length, the half-ridge deduction, and the geometry of the birdsmouth. Get all three right and the framing square step-off method will put you within a sixteenth of an inch every time.
- Gambrel and Mansard Roof Guide: Dual-Pitch Angles and AreaGambrel and mansard roofs both use two pitches per side instead of one, trading a simple triangle for a broken-line profile that buys usable attic space. Here is the classic layout method, the angle math, the area formula and where mansard rules diverge under building codes.
- Roof Height and Ridge Calculation: Rise, Peak Height and Zoning LimitsRidge height is not just a rise calculation — it depends on where you measure from, how the ridge board and heel height shift the number, and whether your jurisdiction measures height to the ridge or to the mean of the roof. Here is the full worked math.
- Flat and Low-Slope Roofs: Minimum Slope, Drainage and Tapered Insulation'Flat' roofs still need slope. Here is the IRC minimum, why ponding water fails membranes, how tapered insulation and crickets create fall, and how to size drains, scuppers and gutters for a low-slope roof.
- Roof Overhang and Eaves: How Far Should a Roof Overhang, and WhyAn overhang is one of the cheapest design levers on a house, protecting walls, shading windows and shaping how the roof reads from the street. Get the horizontal-vs-slope math, the shading geometry and the wind limits right, and it works quietly for decades.
- Best Roof Pitch for Solar Panels: Tilt, Latitude and ProductionSolar output depends on tilt and orientation together, not pitch alone. Here is the latitude rule, a real production-loss table by pitch and azimuth, and how to convert tilt degrees into the X:12 pitch language roofers use.
Last updated 2026-08-05. Results are estimates for planning and are not a substitute for a licensed engineer or local code review.