Roof Pitch to Angle Calculator
The roof pitch to angle calculator turns a roof pitch, written as a rise over a 12 inch run such as 6 in 12, into a slope angle measured in degrees. The method is the standard trigonometric relationship: the angle is the arctangent of the rise divided by 12, because the tangent of the slope angle equals the rise over the run, and roof pitch always uses a 12 inch run. A 6 in 12 pitch works out to about 26.57 degrees, a moderate residential slope. Pitch and angle describe the same steepness two ways, but they are not proportional: a 12 in 12 pitch is exactly 45 degrees, where the rise equals the run. The angle is defined from the horizontal run, not the sloping rafter length, so if you only know the rafter and the rise you find the run first with the Pythagorean theorem. Enter the rise per 12 inches to set a rafter cut angle, match an existing roof, or check a design against a pitch limit. Every figure here is computed deterministically from the formula shown in full below, with a worked example that reconciles exactly to the calculator so you can follow each step and trust the result.
The roof slope angle is the arctangent of the rise over the 12 inch run: angle = arctan(rise / 12). A 6 in 12 pitch is a slope of 26.57°. A 12 in 12 pitch equals exactly 45 degrees.
Roof pitch to angle formula
Angle (degrees) = arctan(rise / run) x (180 / pi)
rise = vertical rise of the roof
run = horizontal run (12 inches for standard pitch)
The tangent of the slope angle equals rise over run, so the angle is the arctangent of that ratio. With the run fixed at 12 inches, the arctangent of rise over 12 gives the pitch angle, converted from radians to degrees.
Worked example
A roof has a 6 in 12 pitch: it rises 6 inches for every 12 inches of run.
- Ratio = 6 / 12 = 0.5
- Angle in radians = arctan(0.5) = 0.463648
- Angle in degrees = 0.463648 x (180 / pi) = 26.57°
The slope angle is 26.57 degrees. These are the calculator's default inputs, so the result above matches the widget exactly.
Pitch to angle reference
Common roof pitches and their slope angles in degrees.
| Pitch | Angle (degrees) |
|---|---|
| 4 in 12 | 18.43 |
| 6 in 12 | 26.57 |
| 9 in 12 | 36.87 |
| 12 in 12 | 45.00 |
Measurement and survey standards: US National Geodetic Survey (NOAA).
Roof pitch to angle calculator: frequently asked questions
How is roof pitch converted to an angle?
Roof pitch is usually written as a rise over a 12 inch run, such as 6 in 12. The angle in degrees is the arctangent of the rise divided by 12. For a 6 in 12 pitch, the angle is the arctangent of 6 divided by 12, which is about 26.57 degrees. The arctangent returns radians, so multiply by 180 divided by pi to get degrees.
What does a 6 in 12 pitch mean?
A 6 in 12 pitch means the roof rises 6 inches of height for every 12 inches of horizontal run. It is a moderate slope, common on residential roofs. The first number is the rise and the second is always 12, the standard run used to express pitch in inches.
What is the difference between pitch and slope angle?
Pitch is the rise over a 12 inch run, written like 6 in 12. The slope angle is that same steepness expressed as an angle in degrees. They describe the same roof two ways. A 12 in 12 pitch is a 45 degree angle, because the rise equals the run at that point.
What pitch is a 45 degree roof?
A 45 degree roof is a 12 in 12 pitch, where the rise equals the run. Steeper than that the rise exceeds 12 for a 12 inch run, and the angle climbs above 45 degrees toward a maximum of 90 degrees for a vertical wall, which is no longer a practical roof slope.
Why use the run, not the rafter length?
Pitch and slope angle are defined from the horizontal run, not the sloping rafter length. The arctangent of rise over run gives the angle directly. If you only know the rafter length and the rise, find the run with the Pythagorean theorem first, then apply the arctangent to get the angle.
Official sources
- Angle, slope and measurement standards: US National Geodetic Survey (NOAA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.