Pitch to Angle: Slope Conversion Calculator
- Slope percentage
- %
- Result
- Rise (inches per 12 in)
- 6 in
- You entered
This calculator converts a roof pitch (rise over run, given in inches per foot or as a ratio) into an angle in degrees, and also shows the slope percentage. Enter your pitch, and you get the angle, which is useful for cutting rafters, setting bevels, or comparing with manufacturer specifications.
Formula
The angle of a roof (or any slope) is the arctangent of the rise divided by the run. The standard run for roof pitch is 12 inches, so:
Angle (degrees) = atan(rise / run)
Where:
- rise = vertical rise in inches (for the given run)
- run = horizontal run in inches (usually 12)
If you enter rise in inches per foot, the run is 12. The result is in degrees. To get slope percentage, multiply the rise/run ratio by 100.
Worked Example
Using the default values: rise = 6 inches per foot, run = 12 inches.
- Ratio = 6 / 12 = 0.5
- Angle = atan(0.5) = 26.565° (rounded to 26.57°)
- Slope percentage = 0.5 × 100 = 50%
The calculator shows 26.57° and 50%.
Why Convert Pitch to Angle?
Roof pitch is traditionally expressed as a ratio like “6/12” (rise over run). But many tools, materials, and design specs use degrees. For example, a circular saw bevel gauge is set in degrees, and some solar panel mounts specify tilt in degrees. Converting pitch to angle lets you work across both systems without guesswork.
Common Pitfalls and Misconceptions
The most common mistake is mixing up rise and run. Rise is always the vertical change, run is the horizontal. A “4/12” roof means 4 inches up for every 12 inches across—not the other way around. Another error is using the wrong run unit: if you measure rise in centimeters, run must also be in centimeters. The ratio is unitless, so the angle is the same regardless of unit, but the numbers must be consistent.
Also, don’t confuse pitch with slope percentage. A 6/12 pitch is 50% slope, not 6%. The percentage is the ratio times 100.
How to Choose the Right Pitch
Pitch affects water shedding, snow load, and available attic space. In snowy climates, steeper pitches (8/12 and above) shed snow better. Low slopes (2/12 to 4/12) are common on commercial buildings and require special waterproofing. For residential roofs, 4/12 to 9/12 is typical. Your local building code may dictate minimum pitch for certain materials—always check that first.
Limits of the Formula
The arctangent formula assumes a straight-line slope—which is fine for most roofs. It does not account for curved or arched roofs. Also, the angle is the geometric angle from horizontal; it is not the same as the “pitch angle” sometimes used in engineering (which can be measured from vertical). For standard construction, this is the correct conversion.
Safety and Accuracy Tips
When working on a roof, always use fall protection and follow local safety regulations. For accurate measurements, use a level and a tape measure. Measure rise over a full 12-inch run, not a shorter segment, to reduce error. If you are cutting rafters, double-check your angle with a speed square before making the cut.
Frequently Asked Questions
What is a 6/12 pitch in degrees?
A 6/12 pitch is 26.57 degrees. This is calculated by taking the arctangent of 6 divided by 12.
How do I convert degrees back to pitch?
Use the tangent function: rise/run = tan(angle). For example, a 30° angle has a tangent of 0.577, so the pitch is 0.577 × 12 = 6.93, or about 7/12.
What is the difference between pitch and slope?
Pitch is usually the rise over a 12-inch run, while slope is the rise over any run, often expressed as a percentage. They are related: pitch = (slope percentage / 100) × 12.
Can I use this for stairs or ramps?
Yes, the same math applies to any slope. For stairs, building codes often specify a maximum rise and minimum run, not an angle, but converting can help you visualize the steepness.
Why do some roofs use a 12-inch run?
It’s a historical convention in the US and some other countries, making it easy to measure with a framing square. Metric countries often use degrees or a percentage instead.