Roof Pitch to Degrees Converter
Convert roof pitch (X:12), degrees from horizontal, slope %, or 1:N ratio — change any field to update all four.
Angle from horizontal: 26.57°
Conversion results
Degrees are measured from the horizontal plane, not from vertical, and not a complementary cutting angle. Complementary / miter cut (90° − θ): 63.43°.
Quick Presets
Roof slope diagram
Mathematical conversion only. Degrees are measured from horizontal. Actual roof angles may vary due to construction tolerances.
Is that degree from horizontal, or the cutting angle?
The converter reports the roof angle from a level line, not the complementary cutting angle on a speed square.
A 6:12 pitch is 26.57° from horizontal. The complementary cut is 90° minus 26.57°, which is 63.43°.
Pitch, Degrees, Slope %, and 1:N Conversion Table (1/12 to 24/12)
Standard roof pitches from 1/12 to 24/12 with their exact angle from horizontal, complementary speed-square cut angle (90° − θ), slope percentage, and 1:N ratio. Click any row to load it directly into the converter above.
| Pitch | Degrees (from horizontal) | Complementary Cut (90° − θ) | Slope % | 1:N ratio | Action |
|---|---|---|---|---|---|
| 1/12 | 4.76° | 85.24° | 8.3% | 1:12 | |
| 2/12 | 9.46° | 80.54° | 16.7% | 1:6 | |
| 3/12 | 14.04° | 75.96° | 25.0% | 1:4 | |
| 4/12 | 18.43° | 71.57° | 33.3% | 1:3 | |
| 5/12 | 22.62° | 67.38° | 41.7% | 1:2.4 | |
| 6/12 | 26.57° | 63.43° | 50.0% | 1:2 | |
| 7/12 | 30.26° | 59.74° | 58.3% | 1:1.714 | |
| 8/12 | 33.69° | 56.31° | 66.7% | 1:1.5 | |
| 9/12 | 36.87° | 53.13° | 75.0% | 1:1.333 | |
| 10/12 | 39.81° | 50.19° | 83.3% | 1:1.2 | |
| 11/12 | 42.51° | 47.49° | 91.7% | 1:1.091 | |
| 12/12 | 45.00° | 45.00° | 100.0% | 1:1 | |
| 13/12 | 47.29° | 42.71° | 108.3% | 1:0.923 | |
| 14/12 | 49.40° | 40.60° | 116.7% | 1:0.857 | |
| 15/12 | 51.34° | 38.66° | 125.0% | 1:0.8 | |
| 16/12 | 53.13° | 36.87° | 133.3% | 1:0.75 | |
| 17/12 | 54.78° | 35.22° | 141.7% | 1:0.706 | |
| 18/12 | 56.31° | 33.69° | 150.0% | 1:0.667 | |
| 19/12 | 57.72° | 32.28° | 158.3% | 1:0.632 | |
| 20/12 | 59.04° | 30.96° | 166.7% | 1:0.6 | |
| 21/12 | 60.26° | 29.74° | 175.0% | 1:0.571 | |
| 22/12 | 61.39° | 28.61° | 183.3% | 1:0.545 | |
| 23/12 | 62.45° | 27.55° | 191.7% | 1:0.522 | |
| 24/12 | 63.43° | 26.57° | 200.0% | 1:0.5 |
Common Half-Pitches & Low Slopes in Degrees (0.5/12 to 6.5/12)
Half-inch rises per foot of run (0.5/12, 1.5/12, 2.5/12, 3.5/12, 4.5/12, 5.5/12, and 6.5/12) are frequently used on porch roofs, shed additions, and low-slope transitions. Click any row to load its exact angle and 1:N ratio.
| Pitch | Degrees (from horizontal) | Complementary Cut (90° − θ) | Slope % | 1:N ratio | Action |
|---|---|---|---|---|---|
| 0.5/12 | 2.39° | 87.61° | 4.17% | 1:24 | |
| 1.5/12 | 7.13° | 82.87° | 12.50% | 1:8 | |
| 2.5/12 | 11.77° | 78.23° | 20.83% | 1:4.8 | |
| 3.5/12 | 16.26° | 73.74° | 29.17% | 1:3.429 | |
| 4.5/12 | 20.56° | 69.44° | 37.50% | 1:2.667 | |
| 5.5/12 | 24.62° | 65.38° | 45.83% | 1:2.182 | |
| 6.5/12 | 28.44° | 61.56° | 54.17% | 1:1.846 |
degrees = arctan(rise ÷ 12) × (180 ÷ π). Complementary cut = 90° − degrees. Slope % = (rise ÷ 12) × 100. 1:N = 1 unit of rise per N units of horizontal run.
4/12 Pitch in Degrees (4/12 Roof Pitch Angle)
A 4/12 roof pitch equals 18.43° from horizontal (71.57° complementary cut), 33.3% slope, and a 1:3 ratio.
Pitch
4/12
Angle (Horizontal)
18.43°
Complementary (90° − θ)
71.57°
Slope
33.3%
1:N
1:3
Angle is measured from horizontal; complementary cut (90° − θ) matches the degree scale on a rafter speed square.
4 inches of vertical rise over 12 inches of horizontal run (sometimes searched as a 12 4 pitch roof angle) gives rise ÷ run = 1/3. The roof pitch angle is arctan(4 ÷ 12) = 18.43° from horizontal, and the complementary miter/speed-square angle is 90° − 18.43° = 71.57°. The slope percentage is (4 ÷ 12) × 100 = 33.3%.
Click 'Load 4/12 in converter' or enter 4 in the pitch field above to reproduce 18.43°, 33.3%, and 1:3.
5/12 Pitch in Degrees (5/12 Roof Pitch Angle)
A 5/12 roof pitch equals 22.62° from horizontal (67.38° complementary cut), 41.7% slope, and a 1:2.4 ratio.
Pitch
5/12
Angle (Horizontal)
22.62°
Complementary (90° − θ)
67.38°
Slope
41.7%
1:N
1:2.4
Angle is measured from horizontal; complementary cut (90° − θ) matches the degree scale on a rafter speed square.
5 inches of rise over 12 inches of run gives arctan(5 ÷ 12) = 22.62° from horizontal — the standard whole roof pitch closest to 22.5°. Its complementary cut angle is 67.38°, the slope percentage is (5 ÷ 12) × 100 = 41.7%, and the 1:N ratio is 12 ÷ 5 = 1:2.4.
Click 'Load 5/12 in converter' or enter 5 in the pitch field above to reproduce 22.62°, 41.7%, and 1:2.4.
6/12 Pitch in Degrees (6/12 Roof Pitch Angle)
A 6/12 roof pitch equals 26.57° from horizontal (63.43° complementary cut), 50% slope, and a 1:2 ratio. It is not 22.5°.
Pitch
6/12
Angle (Horizontal)
26.57°
Complementary (90° − θ)
63.43°
Slope
50.0%
1:N
1:2
Angle is measured from horizontal; complementary cut (90° − θ) matches the degree scale on a rafter speed square.
Half of a 12:12 pitch is not half of 45°. Because roof angle follows arctangent, a 6/12 pitch is arctan(6 ÷ 12) = 26.57° from horizontal (with a 63.43° complementary cut angle). The slope percentage is exactly 50%, and the 1:N ratio is 1:2. The pitch nearest 22.5° is 5/12 (22.62°).
Click 'Load 6/12 in converter' or enter 6 in the pitch field above to reproduce 26.57°, 50%, and 1:2.
Common Roof Pitch Angles (1/12 to 12/12 in Degrees)
Direct angle lookup for other frequently searched roof pitches — from a 1:12 slope in degrees (1/12 = 4.76°) up to a 12/12 45-degree roof.
1/12 (1:12 Slope)
4.76°- 90° − θ
- 85.24°
- Slope
- 8.3%
- 1:N
- 1:12
1/12 pitch (1:12 slope) is 4.76° from horizontal (85.24° complement, 8.3% grade). Common on low-slope metal and porch roofs.
2/12 Pitch
9.46°- 90° − θ
- 80.54°
- Slope
- 16.7%
- 1:N
- 1:6
2/12 roof pitch equals 9.46° from horizontal (80.54° complement, 16.7% grade, 1:6 ratio) — a common low-slope residential threshold.
3/12 Pitch
14.04°- 90° − θ
- 75.96°
- Slope
- 25.0%
- 1:N
- 1:4
3/12 roof pitch equals 14.04° from horizontal (75.96° complement, exactly 25.0% slope and 1:4 ratio). Popular for porch overhangs and ranch homes.
7/12 Pitch
30.26°- 90° − θ
- 59.74°
- Slope
- 58.3%
- 1:N
- 1:1.714
7/12 roof pitch equals 30.26° from horizontal (59.74° complement, 58.3% grade) — the closest standard whole pitch to a 30-degree roof.
8/12 Pitch
33.69°- 90° − θ
- 56.31°
- Slope
- 66.7%
- 1:N
- 1:1.5
8/12 roof pitch equals 33.69° from horizontal (56.31° complement, 66.7% grade, 1:1.5 ratio). Classic steep residential gable pitch.
9/12 Pitch
36.87°- 90° − θ
- 53.13°
- Slope
- 75.0%
- 1:N
- 1:1.333
9/12 roof pitch equals 36.87° from horizontal (53.13° complement, 75.0% grade, 3:4:5 triangle geometry).
10/12 Pitch
39.81°- 90° − θ
- 50.19°
- Slope
- 83.3%
- 1:N
- 1:1.2
10/12 roof pitch equals 39.81° from horizontal (50.19° complement, 83.3% grade) — closest whole pitch to a 40-degree roof.
12/12 Pitch
45.00°- 90° − θ
- 45.00°
- Slope
- 100.0%
- 1:N
- 1:1
12/12 roof pitch equals exactly 45.00° from horizontal (45.00° complement, 100% slope, 1:1 ratio) where rise equals run.
How to Calculate Roof Pitch in Degrees (and Degree to Roof Pitch)
The converter links four ways to express the same roof slope: X:12 pitch, angle from horizontal (°), slope percent (%), and 1:N ratio.
Pitch to Degrees Formula
degrees = arctan(rise ÷ run) × (180 ÷ π)
For a 6/12 pitch: arctan(6 ÷ 12) × 57.2958 = 26.57° from horizontal
Degrees to Roof Pitch Formula
pitch = tan(degrees × π ÷ 180) × 12
For 30° from horizontal: tan(30 × 0.01745) × 12 = 6.93:12 ≈ 7/12 pitch
For 15° from horizontal: tan(15°) × 12 = 3.22:12 (and 22° = 4.85:12)
Degrees to Roof Pitch Reference Table (5° to 60°)
Have an angle in degrees from a solar panel spec, architectural drawing, or digital angle finder? Use this reverse lookup table to convert degrees to exact X:12 roof pitch and nearest standard whole pitch.
| Angle (°) | Exact Roof Pitch (X:12) | Nearest Whole Pitch | Slope % | 1:N Ratio | Action |
|---|---|---|---|---|---|
| 5° | 1.05:12 | 1/12 | 8.7% | 1:11.43 | |
| 10° | 2.12:12 | 2/12 | 17.6% | 1:5.671 | |
| 15° | 3.22:12 | 3/12 | 26.8% | 1:3.732 | |
| 20° | 4.37:12 | 4/12 | 36.4% | 1:2.747 | |
| 22° | 4.85:12 | 5/12 | 40.4% | 1:2.475 | |
| 22.5° | 4.97:12 | 5/12 | 41.4% | 1:2.414 | |
| 25° | 5.60:12 | 6/12 | 46.6% | 1:2.145 | |
| 30° | 6.93:12 | 7/12 | 57.7% | 1:1.732 | |
| 35° | 8.40:12 | 8/12 | 70.0% | 1:1.428 | |
| 40° | 10.07:12 | 10/12 | 83.9% | 1:1.192 | |
| 45° | 12.00:12 | 12/12 | 100.0% | 1:1 | |
| 60° | 20.78:12 | 21/12 | 173.2% | 1:0.577 |
The four formats describe one slope
Pitch X:12 is rise per 12 units of run. Slope percent is (rise ÷ run) × 100. The 1:N ratio is run per unit of rise, so N = 12 ÷ X. Changing any one value updates the other three.
6:12 = 26.57° from horizontal = 50% = 1:2
Is the roof angle from horizontal, or the complementary cut?
This tool reports the roof angle from the horizontal plane: the angle between the roof surface and a level line. A protractor shows the same angle when one leg is level and the other follows the slope.
Some tools, including the degree scale on a speed square, show the complementary angle. That value and the roof angle add to 90°. If a gauge reads about 63.43° on a 6:12 roof, it is reporting the complement, not the 26.57° roof angle from horizontal.
6:12 roof angle = 26.57° from horizontal; complementary cut angle = 90° − 26.57° = 63.43°
Why does 12:12 equal 100% and 45°, and why is 6:12 not 22.5°?
A 12:12 pitch has equal rise and run, so slope percent is 100% and the angle is arctan(1) = 45° from horizontal. Percent grade and degrees are different scales: 100% means a 1:1 rise-to-run ratio, which is 45°, not 100 degrees.
Pitch and angle do not scale in a straight line. Halving the rise does not halve the angle. A 6:12 pitch is arctan(0.5) = 26.57°, not half of 45°. The pitch nearest 22.5° is 5:12 (22.62°).
12:12 → 45.00° and 100%; 6:12 → 26.57° and 50%; 5:12 → 22.62° (closest to 22.5°)
After you have a conversion
Copy the four results from the converter, or change any field to convert another set. If your next step involves physical measurements, area multipliers, framing cuts, or drainage fall, continue below:
- Copy the pitch, degrees from horizontal, slope percent, and 1:N from the converter if you are taking the numbers with you.
- Change any of the four fields, or tap a 1/12 to 12/12 preset, to convert another set.
- Have actual rise and run dimensions in inches, feet, centimeters, or meters? Enter them in the roof slope calculator to compute pitch, angle, and slope length directly from measurements.
- Need pitch multipliers, slope factors, hip/valley factors, or roofing material guidelines? Open the roof pitch chart .
- Ready to turn your roof pitch or angle into rafter length, eave overhang, and birdsmouth cuts? Use the rafter length calculator .
- Designing a low-slope drainage fall (0:12 to 4:12 or 1:40 / 1:80) in inches or millimeters? Use the flat roof slope calculator .
- Still need to find the slope of an existing roof? Follow the how to measure roof pitch guide first, then come back to convert it.
Frequently Asked Questions
Common questions about converting roof pitch, degrees from horizontal, slope percent, and 1:N ratios.
A 4/12 roof pitch equals 18.43° from horizontal (33.3% slope, 1:3 ratio, 71.57° complementary cut). A 5/12 roof pitch equals 22.62° from horizontal (41.7% slope, 1:2.4 ratio, 67.38° complementary cut). A 6/12 roof pitch equals 26.57° from horizontal (50.0% slope, 1:2 ratio, 63.43° complementary cut).
To convert X:12 roof pitch to degrees, use degrees = arctan(rise ÷ 12) × (180 ÷ π). For example, 6/12 = arctan(6 ÷ 12) = 26.57°. To reverse-convert degree to roof pitch, use rise = tan(degrees × π ÷ 180) × 12. For example, 30° = tan(30°) × 12 = 6.93:12 (about a 7/12 pitch), and 22° = tan(22°) × 12 = 4.85:12 (just under 5/12).
A 3/12 roof pitch is 14.04° from horizontal (25.0% slope, 1:4 ratio). An 8/12 roof pitch is 33.69° from horizontal (66.7% slope, 1:1.5 ratio). A 12/12 roof pitch is exactly 45.00° from horizontal (100% slope, 1:1 ratio) because the vertical rise equals the 12-inch horizontal run.
A 1/12 roof pitch (1:12 slope) equals 4.76° from horizontal (8.3% grade, 85.24° complementary angle). A 2/12 roof pitch equals 9.46° from horizontal (16.7% grade, 1:6 ratio). Half-pitches are also common on low-slope roofs: 0.5/12 is 2.39°, 1.5/12 is 7.13°, and 2.5/12 is 11.77°. Calculate flat roof drainage fall
Roof angle is governed by trigonometry (arctangent), not linear division. Although a 12/12 pitch is 45°, cutting the vertical rise in half to 6/12 produces arctan(6 ÷ 12) = 26.57°, not 22.5°. A 22.5° roof angle actually corresponds to 4.97:12 — making 5/12 (22.62°) the closest standard whole pitch.
Roof pitch angle in degrees is always measured from the horizontal plane (level). However, the degree scale on a standard rafter speed square and many miter saws reads the complementary angle from plumb (90° − θ). For a 6/12 roof, the slope angle is 26.57° from horizontal, while the complementary cut angle is 90° − 26.57° = 63.43°.
Most standard residential pitched roofs sit between 4/12 (18.43°) and 9/12 (36.87°), with 5/12 (22.62°) and 6/12 (26.57°) being the most common walkable pitches. Slopes from 2/12 (9.46°) to 4/12 (18.43°) are considered low-slope residential roofs. See the full roof pitch chart
If you measured physical rise and run in inches, feet, centimeters, or meters (for example, 28 inches of rise over 7 feet of run) rather than an X:12 ratio, divide rise by run in the same unit and multiply by 12 to get X:12, or enter your measurements directly in the main calculator. Open the roof slope calculator