How many radians is 180 degrees?

π radians (approximately 3.14159) — exactly half a full circle, since a complete revolution is 2π radians.

How many radians is 90 degrees?

π/2 radians (approximately 1.5708) — a right angle, or one quarter of a full 2π-radian circle.

Why do programming languages use radians?

Radians make calculus formulas elegant — the derivative of sin(x) is cos(x) only when x is in radians. Degrees would require constant π/180 conversion factors in every formula.

Degrees to Radians Converter

Convert degrees to radians for trigonometry, physics, engineering, and programming. Almost all mathematical functions in code (sin, cos, tan) require input in radians, making this an essential conversion for developers and engineers.

Formula

Multiply degrees by π/180 (approximately 0.017453) to get radians. To reverse, multiply radians by 180/π (approximately 57.2958) to get degrees.

Quick reference

Degree (°)	Radian (rad)
15	0.2617994
30	0.5235988
45	0.7853982
60	1.047198
90	1.570796
120	2.094395
135	2.356194
150	2.617994
180	3.141593
360	6.283185

About these units

Degree

The degree (1/360 of a full circle) dates to ancient Babylonian astronomy, which used a base-60 number system. The Babylonians divided the circle into 360 parts, possibly because the solar year was approximately 360 days.

Radian

The radian was formalized in the 19th century and is the SI-coherent angle unit. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. There are exactly 2π radians in a full circle.

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