Angle Converter
Convert angle units: degrees, radians, gradians
Result
0.01745329
1 Degrees (°) = 0.01745329 Radians (rad)
What angle measures
An angle describes the amount of turn between two rays. The SI unit is the radian (rad), which by definition is a ratio of lengths and so is treated as dimensionless. A full turn is 2 pi radians.
Main units and where they are used
- Degree - everyday geometry and navigation: a full turn is 360 degrees.
- Radian (rad) – mathematics, physics and programming: pi rad = 180 degrees, and 1 rad is about 57.2958 degrees.
- Gradian (gon) – surveying and construction: a full turn is 400 gradians.
- Arcminute (1/60 degree) and arcsecond (1/3600 degree) – astronomy and maps; the turn – used in some software.
Common pitfalls
The most frequent mistake is the calculator or programming-language mode: most sin and cos functions expect radians, not degrees, so sin(90) gives completely different results in degrees and radians. Another is treating degrees, minutes and seconds as decimals: 30 degrees 30 minutes is 30.5 degrees, not 30.30.