Degree To Radian Converter

What this converter does

Degrees are what most of us grew up with: 90 for a right angle, 360 for a full turn. But once you get into real trigonometry, calculus, or physics, angles are measured in radians instead, because the maths comes out cleaner. So you often need to switch a familiar degree figure into radians.

Type the angle in degrees, and the tool returns it in radians.

Using the converter

1. Enter the angle in degrees.
2. Press Calculate.

The result is the same angle written in radians.

Two ways to measure an angle

Angles come in two units. Degrees split a full circle into 360, a system handed down from the ancient Babylonians and convenient because 360 divides so many ways. Radians measure the same angles on a different scale, where a full circle is 2π radians. So a half circle, 180°, is π radians, and a right angle, 90°, is π ÷ 2.

The conversion | multiply by π ÷ 180

To turn degrees into radians, multiply by π ÷ 180. That factor is nothing more than the ratio of π radians to 180°. So 180° becomes π, about 3.14; 90° becomes π ÷ 2, about 1.57; and 360° becomes 2π, about 6.28. The tool shows the decimal value.

Why radians exist

Radians are the natural unit once maths moves past basic geometry. In calculus, the neat formulas for the trigonometric functions hold only when angles are measured in radians. They also make arc length effortless: the length of an arc is just the radius times the angle in radians. That tidiness is why science, physics, and engineering reach for radians rather than degrees.

A worked example | 180°

Convert 180°.

1. Multiply by π ÷ 180: 180 × π ÷ 180.
2. The 180s cancel, leaving π, about 3.14 radians.

A half circle comes to π radians, exactly as expected.

Questions people ask

How do you convert degrees to radians?

Multiply the degrees by π ÷ 180.

What is 180° in radians?

π, which is about 3.14 radians.

Why use radians at all?

Because they make calculus formulas and arc-length calculations come out clean, which is why higher maths prefers them.

How do I go the other way?

Use the radian to degree converter, which multiplies by 180 ÷ π.

References

A note on the idea behind it. Degrees and radians are two units for angles, with a full circle equal to 360° or 2π radians. Converting from degrees to radians multiplies by π ÷ 180, so that 180° equals π radians. For further reading, see Radian.

1. Converting degrees to radians by multiplying by π ÷ 180, with 180° equal to π radians.