Degrees are familiar from everyday geometry, but mathematics and programming libraries commonly use radians, surveying uses gradians, and some modern APIs use fractional turns. This converter handles all four units simultaneously, updating in real time as you type.
A full rotation is 360°, 2π radians (~6.2832), 400 gradians, or exactly 1 turn. Radians are the SI-preferred unit because they simplify calculus and appear directly in trigonometric functions across all major programming languages. Gradians divide a right angle into 100 units, making decimal arithmetic on survey angles cleaner. Turns are used in CSS animations (transform: rotate(0.5turn)) and some physics simulations.
Multiply degrees by π/180. For example, 90° × (π/180) = π/2 ≈ 1.5708 radians. Going the other direction, multiply radians by 180/π.
Gradians (also called gon or grad) are used in land surveying and civil engineering. A right angle is exactly 100 gradians, making decimal subdivision of survey angles straightforward.
CSS accepts turn in rotation transforms and animations. rotate(0.25turn) is equivalent to rotate(90deg). One full turn equals 360°.
Because the derivative of sin(x) is cos(x) only when x is in radians. Using degrees introduces a constant factor of π/180 everywhere, complicating calculus and numerical analysis.
See also the Unit Converter for length, weight, and temperature conversions.