How do I convert degrees to radians?

Multiply the angle in degrees by π and divide by 180. For example, 180° × π ÷ 180 = π ≈ 3.14159 radians.

How many radians are in 360 degrees?

360 degrees equals 2π radians, which is approximately 6.28319 radians (a full turn).

Why are radians used instead of degrees?

Radians tie the angle directly to arc length on a unit circle — an angle of 1 radian subtends an arc equal to the radius. This makes calculus and physics formulas (like the derivative of sine) clean, which is why scientific work and most programming math functions use radians.

How do I convert radians back to degrees?

Multiply the radian value by 180 and divide by π. For example, π radians × 180 ÷ π = 180°. This converter does the reverse automatically when you type into the radians field.

What is 1 radian in degrees?

1 radian is about 57.2958 degrees (180 ÷ π). It is the angle where the arc length equals the circle's radius.

Is anything uploaded?

No — the conversion runs entirely in your browser and no data is sent to any server.

Degrees to Radians Converter

This free angle converter changes degrees (°) into radians (rad) and back again. Degrees split a full turn into 360 parts, while radians measure angles by arc length on a circle. Radians are the standard unit in trigonometry, calculus, physics and most programming math libraries, so converting between the two is a frequent task for students and engineers.

How it works

The exact relationship comes from a full circle being 360° or 2π radians:

radians = degrees × π ÷ 180 and degrees = radians × 180 ÷ π

Type a value in either field and the other updates in real time using these formulas — the conversion is bidirectional. Because π is irrational, radian results are shown to several decimal places; common angles like 180° map to exactly π.

Example

Convert 90°:

90 × π ÷ 180 = π/2 ≈ 1.570796 radians

Going the other way, π radians × 180 ÷ π = 180°.

Degrees (°)	Radians (rad)
30°	0.523599 rad
45°	0.785398 rad
90°	1.570796 rad
180°	3.141593 rad
360°	6.283185 rad

All calculations run entirely in your browser with no data sent to any server.