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.
Angle from horizontal: 26.57°
Conversion results
Degrees are measured from the horizontal plane, not from vertical, and not a complementary cutting angle.
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
For other X:12 values, use the table below. Standard pitches from 1/12 to 24/12 show 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 do you convert roof pitch to degrees?
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
For 15° from horizontal: tan(15°) × 12 ≈ 3.22:12
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. This page does not measure a roof or pick materials.
- 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.
- If you do not have a pitch yet, measure roof pitch first, then come back to convert it.
- Materials, categories, or area multipliers belong on the roof pitch chart .
- A low-slope drainage fall in inches or millimeters is a different job. Use the flat roof slope calculator .
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.