Degrees to Pitch Calculator
Reviewed by the My Roof Pitch editorial team · Updated · Free, no sign-up, works offline after first load
To convert degrees to roof pitch, take the tangent of the angle and multiply by 12. The result is the rise in inches per 12 inches of run. A 30 degree roof is tan(30°) × 12 = 6.93, so it is roughly a 7:12 pitch with a 57.7 percent slope.
Key takeaways
- Pitch = tan(angle) × 12, written as X:12.
- 30° ≈ 7:12, 45° = 12:12, 18.43° = 4:12, 26.57° = 6:12.
- Percent slope = tan(angle) × 100 — it is not the same as the angle.
- Round to the nearest half-inch of rise for framing; keep decimals for area.
Your measurements
Enter the values you know — results update live.
Angle from horizontal, as read on an angle finder or a European drawing.
Analysis
Live results from your measurements.
Show the working
- Tangent:
tan(30°)= 0.5774 - Rise per 12:
0.5774 × 12= 6.93:12 - Percent slope:
0.5774 × 100= 57.7% - Multiplier:
√(6.93² + 144) ÷ 12= 1.1547
What this calculator does
A degrees to pitch calculator converts the angle of a roof, measured from the horizontal, into the rise-over-run pitch used on North American framing plans and material labels. Angle finders, phone inclinometers, European and Australian drawings and solar mounting specs all speak in degrees, while shingle wrappers, building codes such as the IRC and most US rafter tables speak in X:12. The conversion is a single tangent, but it is non-linear: every degree is worth a little more rise as the roof gets steeper, so mental shortcuts drift badly above about 30 degrees. This tool gives the exact rise per 12, the percent grade, the nearest whole framing pitch and the area multiplier you need for a material take-off.
How to use it
- Measure the roof angle with a digital angle finder on the top of a rafter or on the roofing itself.
- Enter the angle in degrees from horizontal.
- Read the exact rise per 12 inches and the nearest whole-number pitch.
- Use the area multiplier to convert footprint area into sloped roof area.
- Check the pitch against the minimum slope for your roofing material.
The formula
Degrees to pitch
rise per 12 = tan(angle) × 12
Tangent is rise over run. Multiplying by 12 scales the run to one foot.
Percent slope
slope % = tan(angle) × 100
The same ratio expressed per 100 units of run, as used in drainage and civil work.
Area multiplier
multiplier = 1 ÷ cos(angle)
Multiply plan-view area by this to get the true sloped surface.
Worked example
A solar installer reads 22.5° on an existing roof and needs the pitch for the shingle warranty check.
- tan(22.5°) = 0.4142
- 0.4142 × 12 = 4.97, so the roof is a 5:12 pitch
- Slope = 41.4 percent; multiplier = 1 ÷ cos(22.5°) = 1.0824
22.5 degrees is a 5:12 pitch (4.97:12), comfortably above the 4:12 standard minimum for asphalt shingles.
Common angles converted to pitch
| Angle | Pitch (X:12) | Slope % | Multiplier |
|---|---|---|---|
| 5° | 1.05:12 | 8.7% | 1.0038 |
| 10° | 2.12:12 | 17.6% | 1.0154 |
| 15° | 3.22:12 | 26.8% | 1.0353 |
| 20° | 4.37:12 | 36.4% | 1.0642 |
| 22.5° | 4.97:12 | 41.4% | 1.0824 |
| 25° | 5.60:12 | 46.6% | 1.1034 |
| 30° | 6.93:12 | 57.7% | 1.1547 |
| 35° | 8.40:12 | 70.0% | 1.2208 |
| 40° | 10.07:12 | 83.9% | 1.3054 |
| 45° | 12:12 | 100% | 1.4142 |
| 50° | 14.30:12 | 119.2% | 1.5557 |
| 60° | 20.78:12 | 173.2% | 2.0000 |
Common mistakes
- Treating percent slope as degrees — a 30 percent slope is only 16.7 degrees.
- Measuring on the underside of a sagging rafter instead of along the roof plane.
- Dividing the angle by a constant: pitch is not proportional to degrees.
- Rounding to the nearest whole pitch before calculating area, which can hide 2–3 percent of material.
- Forgetting that a phone held on shingles reads the shingle surface, slightly flatter than the deck at the butt edges.
Assumptions and limits
- Angle is measured from horizontal, not from vertical.
- The roof plane is flat (no bellcast or curve).
- Results are geometric; material minimums follow 2021 IRC Chapter 9.
Frequently asked questions
What pitch is a 30 degree roof?
tan(30°) × 12 = 6.93, so a 30 degree roof is almost exactly 7:12. It is a 57.7 percent slope.
What pitch is a 45 degree roof?
12:12. Rise equals run, so the slope is 100 percent and the area multiplier is 1.414.
What pitch is 20 degrees?
tan(20°) × 12 = 4.37, so about 4 3/8 in 12. It is a 36.4 percent slope.
What pitch is 22.5 degrees?
4.97:12 — effectively a 5:12 roof. 22.5° is a common angle on metric drawings and solar specs.
What pitch is 15 degrees?
3.22:12. That is above the 3:12 minimum for many metal panels but below the 4:12 standard for shingles.
How do I convert degrees to pitch without a calculator?
Use the table: 18.4° is 4:12, 26.6° is 6:12, 33.7° is 8:12 and 45° is 12:12. Interpolate between neighbours for a close estimate.
Is degrees or pitch more accurate?
Both are exact descriptions of the same slope. Pitch is easier to lay out with a framing square; degrees are easier to read with a digital finder.
What is 10 degrees as a roof pitch?
2.12:12, about 2 1/8 in 12. That is low slope; asphalt shingles need double underlayment at this pitch and many systems require membrane roofing.
Related guides
Last updated 2026-10-08. Results are estimates for planning and are not a substitute for a licensed engineer or local code review.