Angle Unit Converter

Three ways to slice a circle

Degrees split a full circle into 360 parts (an ancient Babylonian convention), radians measure angle by arc length relative to radius (the natural unit for calculus and most programming math functions), and gradians split a circle into 400 parts, used mainly in surveying.

Worked example

For a 90 degree angle (a right angle):

Result = 90.0 deg = 1.570796 rad = 100.0 gon

Fraction of Circle	Degrees	Radians	Gradians
Quarter circle	90	pi/2 (~1.5708)	100
Half circle	180	pi (~3.1416)	200
Full circle	360	2pi (~6.2832)	400

Most programming languages' built-in trigonometric functions (sin, cos, tan) expect input in radians, not degrees - forgetting to convert is one of the most common bugs when writing code involving angles.