Degrees to radians: the conversion behind a roof-pitch angle
A roof pitch, a cut angle on a miter saw, a bearing on a compass — all normally given in degrees, because that's the unit people think in. But trigonometric functions in most programming languages, spreadsheets and CAD tools expect radians. Converting between the two is one multiplication, using a single constant: π.
The method
A full circle is 360° and also 2π radians, so the conversion factor is π ÷ 180 per degree:
radians = degrees × (π ÷ 180)
To go the other way:
degrees = radians × (180 ÷ π)
π is approximately 3.14159265. Any calculator or spreadsheet with a built-in PI() function carries more digits than are worth typing by hand; for hand-checking, three or four decimal places is plenty.
A worked example
A cut angle is specified as 42°. What is that in radians?
π ÷ 180 = 3.14159265 ÷ 180 = 0.0174533radians per degree.42 × 0.0174533 = 0.7330radians.
Checking it by converting back: 0.7330 × (180 ÷ π) = 0.7330 × 57.29578 = 41.998°, which rounds back to 42° — the small gap from 42.000 is just rounding in the 0.7330 figure, not an error in the method.
What this doesn't include
This converts the angle unit only — it doesn't compute rise-over-run, slope percentage, or account for how a specific saw, tool or software expects the angle to be signed or measured from a different reference line. Always confirm which reference angle (from horizontal, from vertical, from north) a given spec or tool expects before cutting or building from a converted number.
Run your own numbers
The free Angle Converter tool converts between degrees, radians, gradians, arcminutes and full turns instantly, entirely on your device.