Calculate pitch angle, rise, or run from any two values with inches, feet, cm, m, degrees, or radians using trig formulas for slopes.
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Angle Pitch Formula
The angle pitch calculator uses right-triangle trigonometry. Rise is the vertical height, run is the horizontal distance, and angle is the slope angle measured from the horizontal.
- Rise is the vertical height of the slope.
- Run is the horizontal length of the slope.
- Angle is the pitch angle measured from the horizontal line.
- tan is the tangent function.
- arctan is the inverse tangent function, used to find the angle from rise and run.
If you enter run and angle, the calculator finds the rise. If you enter rise and angle, it finds the run. If you enter rise and run, it finds the angle. Length values can be entered in inches, feet, centimeters, or meters. Angles can be entered in degrees or radians.
Common Pitch and Angle Conversions
Pitch is often written as rise over 12 units of run, especially for roofs. The table below shows common pitches and their approximate angles.
| Pitch | Rise per 12 Run | Approx. Angle |
|---|---|---|
| 2:12 | 2 in per 12 in | 9.46° |
| 4:12 | 4 in per 12 in | 18.43° |
| 6:12 | 6 in per 12 in | 26.57° |
| 8:12 | 8 in per 12 in | 33.69° |
| 12:12 | 12 in per 12 in | 45.00° |
Length and Angle Unit Reference
| Unit | Equivalent |
|---|---|
| 1 foot | 12 inches |
| 1 inch | 2.54 centimeters |
| 1 meter | 100 centimeters |
| 1 radian | 57.2958 degrees |
| 1 degree | 0.0174533 radians |
Example Calculations
Example 1: Find the angle from rise and run
Suppose the rise is 6 inches and the run is 12 inches.
The angle is approximately 26.57°.
Example 2: Find the rise from run and angle
Suppose the run is 10 feet and the angle is 30 degrees.
The rise is approximately 5.77 feet.
FAQ
What is angle pitch?
Angle pitch describes the steepness of a slope as an angle. It is based on the relationship between rise and run. A larger rise compared with the same run creates a steeper angle.
What is the difference between pitch and angle?
Pitch is commonly written as a ratio, such as 6:12, meaning 6 units of rise for every 12 units of run. Angle is measured in degrees or radians. Both describe the same slope, but in different formats.
Can rise and run use different units?
Yes. The calculator converts length units before applying the formula. For example, you can enter rise in inches and run in feet, and the calculation will still use matching base units internally.
