How to convert roof pitch into degrees
A rise-per-12 roof slope uses 12 inches of horizontal run. Convert it to degrees with angle = arctangent(rise ÷ 12) × 180 ÷ π. For example, a 6:12 roof has an angle of arctangent(6 ÷ 12), or approximately 26.57 degrees.
To convert degrees back to roof pitch, use rise per 12 = tangent(angle) × 12. A 30-degree roof therefore has a rise of about 6.93 inches per 12 inches of run, which is close to a 7:12 slope but is not exactly the same angle.
Field language sometimes uses pitch and slope interchangeably, while technical definitions can distinguish rise-to-span from rise-to-run. This chart uses the common rise-per-12 slope convention shown in the first column.
How do you calculate roof pitch, angle, and rafter factor?
In US framing, roof pitch is written as rise : 12—the number of vertical inches the roof rises for every 12 inches of horizontal level run. Treating the roof profile as a right triangle, we derive the roof angle and the framing-square slope multiplier:
where:
- Rise – Vertical rise in inches per 12 inches of horizontal run (for example, 6 in a 6:12 pitch);
- θ – Roof slope angle measured in degrees above horizontal;
- M – Slope multiplier (rafter factor) used to convert flat horizontal area or run into sloped surface length (see the roofing calculator); and
- L_slope – Geometric rafter slope length (L_slope = Run × M). For ridge deduction and overhang tails, open the rafter length calculator.
Roof pitch to degrees chart
| Rise per 12 | Angle | Slope multiplier | 100 sq ft horizontal becomes |
|---|---|---|---|
| 1:12 | 4.76° | 1.003 | 100.3 sq ft |
| 2:12 | 9.46° | 1.014 | 101.4 sq ft |
| 3:12 | 14.04° | 1.031 | 103.1 sq ft |
| 4:12 | 18.43° | 1.054 | 105.4 sq ft |
| 5:12 | 22.62° | 1.083 | 108.3 sq ft |
| 6:12 | 26.57° | 1.118 | 111.8 sq ft |
| 7:12 | 30.26° | 1.158 | 115.8 sq ft |
| 8:12 | 33.69° | 1.202 | 120.2 sq ft |
| 9:12 | 36.87° | 1.250 | 125.0 sq ft |
| 10:12 | 39.81° | 1.302 | 130.2 sq ft |
| 11:12 | 42.51° | 1.357 | 135.7 sq ft |
| 12:12 | 45.00° | 1.414 | 141.4 sq ft |
Degrees to roof pitch conversion chart
The reverse chart answers questions such as “what roof pitch is 22.5 degrees?” and “what pitch is a 30-degree roof?” The rise-per-12 value is calculated from the exact angle, so it may fall between the whole-number pitches commonly used in the field.
| Roof angle | Approx. rise per 12 | Slope percent | Useful comparison |
|---|---|---|---|
| 5° | 1.05:12 | 8.7% | Near 1:12 |
| 10° | 2.12:12 | 17.6% | Near 2:12 |
| 15° | 3.22:12 | 26.8% | Near 3:12 |
| 18° | 3.90:12 | 32.5% | Near 4:12 |
| 20° | 4.37:12 | 36.4% | Between 4:12 and 5:12 |
| 22.5° | 4.97:12 | 41.4% | Approximately 5:12 |
| 25° | 5.60:12 | 46.6% | Between 5:12 and 6:12 |
| 30° | 6.93:12 | 57.7% | Approximately 7:12 |
| 33° | 7.79:12 | 64.9% | Near 8:12 |
| 35° | 8.40:12 | 70.0% | Between 8:12 and 9:12 |
| 40° | 10.07:12 | 83.9% | Approximately 10:12 |
| 45° | 12.00:12 | 100.0% | Exactly 12:12 |
| 60° | 20.78:12 | 173.2% | Steeper than 12:12 |
Common roof pitch examples
A 5:12 roof pitch equals approximately 22.62 degrees. A 7:12 roof pitch equals approximately 30.26 degrees. An 8:12 pitch equals approximately 33.69 degrees, and a 10:12 pitch equals approximately 39.81 degrees.
A degree value and a rounded whole-number pitch are not always interchangeable. For example, 30 degrees converts to about 6.93:12, while an exact 7:12 slope is about 30.26 degrees. Preserve the exact input when checking drawings, measurements or specifications.
How to use the roof slope multiplier
- 01
Check simple slope length
Multiply verified horizontal run by the factor to estimate the triangle hypotenuse.
- 02
Check a simple roof plane
Multiply horizontal projection area by the factor when one uniform slope describes that plane.
- 03
Compare a measured result
Use the conversion as a reasonableness check against drawings, aerial measurements or contractor takeoffs.
- 04
Separate mixed pitches
Calculate additions, dormers and other slopes as distinct planes before combining them.
Worked example: 8:12 roof over a 15 ft run
An 8:12 slope is approximately 33.69 degrees and uses a multiplier near 1.202. Multiplying a 15 ft horizontal run by 1.202 gives a simple slope length near 18.03 ft.
That number is the geometric diagonal only. A finished rafter or material estimate can require ridge, seat, tail, overhang and connection details. For roof area, apply the factor only to the horizontal projection represented by the same 8:12 plane.
Mistakes the chart cannot correct
- Entering total building span when the calculation requires one horizontal run.
- Using one multiplier across roof planes with different slopes.
- Omitting overhangs from one part of the takeoff and including them elsewhere.
- Treating geometric slope length as a finished cut dimension.
- Assuming an angle alone establishes material or installation suitability.
- Taking unsafe roof measurements when drawings or professional measurement should be used.
Frequently asked questions
How many degrees is a 5:12 roof pitch?
A 5:12 roof pitch is approximately 22.62 degrees. The result comes from arctangent(5 ÷ 12).
What roof pitch is 22.5 degrees?
A 22.5-degree roof converts to approximately 4.97:12, which is very close to a 5:12 slope.
What roof pitch is 30 degrees?
A 30-degree roof converts to approximately 6.93:12. That is close to 7:12, but an exact 7:12 pitch is approximately 30.26 degrees.
What roof pitch is 35 degrees?
A 35-degree roof converts to approximately 8.40:12, placing it between an 8:12 and 9:12 slope.
How do I convert roof degrees to rise per 12?
Multiply the tangent of the roof angle by 12. For a 25-degree angle, tangent(25°) × 12 gives approximately 5.60 inches of rise per 12 inches of run.
Can I use the angle or multiplier as a finished rafter length?
No. The multiplier gives a simple geometric diagonal. Finished rafter layout can also require ridge, seat, tail, overhang, connection and project-specific structural details.