Roof Pitch to Degrees Converter
Convert X:12 pitch, degrees from horizontal, slope percent, or a 1:N ratio — any one updates the other three.
Quick Presets
Roof slope diagram
Angle from horizontal: 26.57°
Conversion results
Degrees are measured from the horizontal plane — not from vertical, and not a complementary cutting angle.
Mathematical conversion only. Degrees are measured from horizontal. Actual roof angles may vary due to construction tolerances.
Pitch, Degrees, Slope %, and 1:N Conversion Table
Standard X:12 pitches from 1/12 to 24/12 with the matching angle from horizontal, slope percentage, and 1:N ratio. For materials, categories, and area multipliers, use the full roof pitch chart.
| Pitch | Degrees (from horizontal) | Slope % | 1:N ratio |
|---|---|---|---|
| 1/12 | 4.76° | 8.3% | 1:12 |
| 2/12 | 9.46° | 16.7% | 1:6 |
| 3/12 | 14.04° | 25.0% | 1:4 |
| 4/12 | 18.43° | 33.3% | 1:3 |
| 5/12 | 22.62° | 41.7% | 1:2.4 |
| 6/12 | 26.57° | 50.0% | 1:2 |
| 7/12 | 30.26° | 58.3% | 1:1.714 |
| 8/12 | 33.69° | 66.7% | 1:1.5 |
| 9/12 | 36.87° | 75.0% | 1:1.333 |
| 10/12 | 39.81° | 83.3% | 1:1.2 |
| 11/12 | 42.51° | 91.7% | 1:1.091 |
| 12/12 | 45.00° | 100.0% | 1:1 |
| 13/12 | 47.29° | 108.3% | 1:0.923 |
| 14/12 | 49.40° | 116.7% | 1:0.857 |
| 15/12 | 51.34° | 125.0% | 1:0.8 |
| 16/12 | 53.13° | 133.3% | 1:0.75 |
| 17/12 | 54.78° | 141.7% | 1:0.706 |
| 18/12 | 56.31° | 150.0% | 1:0.667 |
| 19/12 | 57.72° | 158.3% | 1:0.632 |
| 20/12 | 59.04° | 166.7% | 1:0.6 |
| 21/12 | 60.26° | 175.0% | 1:0.571 |
| 22/12 | 61.39° | 183.3% | 1:0.545 |
| 23/12 | 62.45° | 191.7% | 1:0.522 |
| 24/12 | 63.43° | 200.0% | 1:0.5 |
degrees = arctan(rise ÷ 12) × (180 ÷ π). Slope % = (rise ÷ 12) × 100. 1:N = 1 unit of rise for every N units of horizontal run. Multipliers and material lists live on the roof pitch chart.
4/12 Pitch in Degrees
A 4/12 roof pitch equals 18.43° from horizontal, 33.3% slope, and a 1:3 ratio.
Pitch
4/12
Angle
18.43°
Slope
33.3%
1:N
1:3
Angle is measured from horizontal.
4 inches of rise over 12 inches of run means rise ÷ run = 1/3. The angle is arctan(4 ÷ 12) = 18.43° from horizontal. The slope percentage is (4 ÷ 12) × 100 = 33.3%. As a 1:N ratio, that is 1 unit of rise for every 3 units of run.
Enter 4 in the pitch field above to reproduce 18.43°, 33.3%, and 1:3.
5/12 Pitch in Degrees
A 5/12 roof pitch equals 22.62° from horizontal, 41.7% slope, and a 1:2.4 ratio.
Pitch
5/12
Angle
22.62°
Slope
41.7%
1:N
1:2.4
Angle is measured from horizontal.
5 inches of rise over 12 inches of run gives arctan(5 ÷ 12) = 22.62° from horizontal, the common pitch closest to 22.5°. The slope percentage is (5 ÷ 12) × 100 = 41.7%. The 1:N ratio is 12 ÷ 5 = 2.4, written 1:2.4.
Enter 5 in the pitch field above to reproduce 22.62°, 41.7%, and 1:2.4.
6/12 Pitch in Degrees
A 6/12 roof pitch equals 26.57° from horizontal, 50% slope, and a 1:2 ratio. It is not 22.5°.
Pitch
6/12
Angle
26.57°
Slope
50.0%
1:N
1:2
Angle is measured from horizontal.
Half of 12:12 is not half of 45°. Angle uses arctangent, so 6/12 is arctan(6 ÷ 12) = 26.57° from horizontal. The slope percentage is exactly 50%, and the 1:N ratio is 1:2. The pitch nearest 22.5° is 5/12 (22.62°).
Enter 6 in the pitch field above to reproduce 26.57°, 50%, and 1:2.
How Pitch to Degrees Conversion Works
The converter links four ways to write the same slope: X:12 pitch, angle from horizontal, slope percent, and 1:N ratio.
Pitch to Degrees
degrees = arctan(rise ÷ run) × (180 ÷ π)
For a 6/12 pitch: arctan(6 ÷ 12) × 57.2958 = 26.57° from horizontal
Degrees to Pitch
pitch = tan(degrees × π ÷ 180) × 12
For 30° from horizontal: tan(30 × 0.01745) × 12 = 6.93 ≈ 7/12 pitch
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
Angle from horizontal, not 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 12:12 = 100% = 45°, and why 6:12 is 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°)
Why 12?
US construction writes roof pitch as rise per 12 units of horizontal run. The 12-based system matches common framing-square markings: measure 12 units level, then measure the vertical rise at that point.
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 degrees from horizontal. The same slope is 33.3% and a 1:3 ratio. Enter 4 in the pitch field to reproduce these values.
Use degrees = arctan(rise ÷ run) × (180 ÷ π), with the angle measured from horizontal. For a 6/12 pitch: arctan(6 ÷ 12) = 26.57 degrees from horizontal.
A 5/12 roof pitch equals 22.62 degrees from horizontal — the common pitch closest to 22.5°. The same slope is 41.7% and a 1:2.4 ratio.
Angle is not linear with pitch. A 12/12 pitch is 45° from horizontal, but half the rise is not half the angle. 6/12 is arctan(6 ÷ 12) = 26.57°, with 50% slope and a 1:2 ratio. The pitch nearest 22.5° is 5/12 (22.62°).
This converter reports the roof angle from the horizontal plane. Some gauges, including the degree scale on a speed square, show the complementary angle that adds to 90° with the roof angle. For 6:12, the roof angle is 26.57° from horizontal; the complement is 63.43°.
12:12 has equal rise and run, so slope percent is (12 ÷ 12) × 100 = 100% and the angle is arctan(1) = 45° from horizontal. 100% means a 1:1 rise-to-run ratio, not 100 degrees. Enter 12 in the pitch field to confirm.