Degrees ↔ Radians Converter

Convert between degrees and radians with π notation.

Degrees

Radians (decimal)

1.57079633

π notation

π/2

Common angles

Degrees	Radians	π notation
0°	0.0000	0
30°	0.5236	π/6
45°	0.7854	π/4
60°	1.0472	π/3
90°	1.5708	π/2
120°	2.0944	2π/3
135°	2.3562	3π/4
150°	2.6180	5π/6
180°	3.1416	π
270°	4.7124	3π/2
360°	6.2832	2π

How degrees and radians relate

Degrees and radians are two ways to measure angles. A full circle is 360° or 2π radians. To convert degrees to radians multiply by π/180; to convert radians to degrees multiply by 180/π. Radians are preferred in mathematics and programming because trigonometric functions (sin, cos, tan) in most languages expect radians.

For other angle conversions see the Angle Converter. For general math tools, try the Scientific Calculator.

Built and maintained by Meet Shah · Last updated 30 July 2026

What this tool is used for

Converting an angle for a maths library whose trigonometric functions take radians.
Reading a radian value from a specification into degrees for intuition.
Producing an exact multiple of pi rather than a rounded decimal.
Converting a rotation value for a graphics or animation API.
Checking whether a wrong result comes from using the wrong angle unit.

Frequently Asked Questions

What is the conversion factor?: π/180 going from degrees to radians and 180/π coming back, because a full turn is both 360° and 2π radians. 90° is π/2 ≈ 1.5708 and 180° is π exactly. The factor is irrational, so almost every conversion produces a decimal that never terminates.
Why show the answer as a fraction of π?: Because that is the form worth reading. The result is divided by π and denominators up to 360 are searched for a near-exact rational, so 90° reports π/2 rather than 1.5707963. The decimal is what you paste into code; the π form tells you whether the angle is a familiar one.
Why do programming languages want radians?: Because the calculus only works out cleanly in radians: the derivative of sin is cos exactly, and the series expansions carry no stray constants. Degrees would thread a π/180 factor through every one of those identities, so `Math.sin` in JavaScript, C and Python all take radians.
What is a radian, physically?: The angle subtending an arc equal in length to the radius. Lay a piece of string the length of the radius along the circle's edge and the angle it covers is one radian — about 57.2958°. That is why a full circle is 2π: the circumference is 2πr, so it takes 2π radius-lengths.
Are gradians ever used?: Rarely, but they exist: 400 to a full turn, so a right angle is exactly 100. They survive in some European surveying and as the third mode on most scientific calculators — usually discovered by accident when every trigonometric answer comes out slightly wrong.

Common errors and gotchas

Passing degrees to a function expecting radians, which is the single most common trigonometry bug there is.
Rounding pi too early, which compounds through a chain of calculations.
Confusing radians with gradians, which some calculators also offer.
Assuming a CSS or SVG rotation takes radians, when both take degrees by default.
Losing the sign convention, where one system measures clockwise and another anticlockwise.