Roof Pitch to Degrees: Measure Rise and Run, Then Check the Angle
To convert roof pitch to degrees, calculate angle = arctan(vertical rise ÷ horizontal run). For an 18 in rise over a 120 in horizontal run, the angle is 8.5308°. Check it independently by calculating 120 × tan(8.5308°), which returns 18 in.
Use a measured triangle, not an angle by itself
Record vertical rise and horizontal run from the same roof plane and in the same unit. Divide rise by run, take the inverse tangent, and convert the result to degrees. An angle on its own is not enough to independently reproduce the geometry; the paired measurements are the audit trail.
- Measure vertical rise over a known horizontal run on one plane.
- Calculate
degrees = arctan(rise ÷ run) × 180 ÷ π. - Reverse-check with
rise = run × tan(degrees).
For the matching ratio, percent, and degree views, compare the same two inputs in the roof pitch chart.
Roof pitch to degrees reverse-check table
Each displayed degree below was calculated from the rise and 12-inch horizontal run. The last column recalculates the rise from the displayed angle; small differences after you round an angle are normal.
| Rise | Horizontal run | Pitch ratio | Angle | Reverse check |
|---|---|---|---|---|
| 1 in | 12 in | 1:12 (0.083333) | 4.7636° | 12 × tan(4.7636°) ≈ 1 in |
| 3 in | 12 in | 3:12 (0.250000) | 14.0362° | 12 × tan(14.0362°) ≈ 3 in |
| 4 in | 12 in | 4:12 (0.333333) | 18.4349° | 12 × tan(18.4349°) ≈ 4 in |
| 6 in | 12 in | 6:12 (0.500000) | 26.5651° | 12 × tan(26.5651°) ≈ 6 in |
| 11 in | 12 in | 11:12 (0.916667) | 42.5104° | 12 × tan(42.5104°) ≈ 11 in |
| 12 in | 12 in | 12:12 (1.000000) | 45.0000° | 12 × tan(45.0000°) ≈ 12 in |
A low-pitch field check with the measurements visible
Use a measured rise and horizontal run from the same roof plane, then keep both numbers beside the angle. In this inch-based example: 18 ÷ 120 = 0.15; arctan(0.15) = 8.5308°; and 120 × tan(8.5308°) = 18 in. It is a geometry check, not a roof-system recommendation.
| Record | Calculation | Independent return check | What it does not decide |
|---|---|---|---|
| 18 in vertical rise; 120 in horizontal run | arctan(18 ÷ 120) = 8.5308° | 120 × tan(8.5308°) = 18 in | Whether a named covering, underlayment, or local requirement applies. |
This is the extra check a bare degree converter leaves out: preserve the two measurements and show whether the angle can return the same rise. A geometry result does not select a roofing assembly. For that separate product-specific question, see the minimum slope for metal roof guide.
Questions a pitch-to-degree conversion can answer
What is the angle of a 4:12 roof pitch?
A 4:12 pitch is 18.4349° when the ratio is computed as 4 ÷ 12 and the inverse tangent is converted to degrees. The reverse check is 12 × tan(18.4349°), which returns approximately 4.
Can I calculate degrees from a decimal roof slope?
Yes. If the decimal is rise divided by horizontal run, calculate arctan(decimal) and convert to degrees. Keep the original rise and run if you need to check the result later.
Does a roof angle approve a material choice?
No. An angle is geometry only. Product suitability needs the named system’s current instructions and the applicable project requirements.
Method and source notes
- Calculation method:
degrees = arctan(rise ÷ horizontal run) × 180 ÷ π; reverse check:rise = horizontal run × tan(degrees). Every displayed numeric row is independently calculated in the accompanying verification record. - The 18 in / 120 in low-pitch row is a self-calculated geometry example. It is illustrative only, not a construction specification or a product instruction.