CelsiustoFahrenheit.pro

Degrees to Radians Converter

Radians0.785398 rad
In terms of π
π/4 rad
Degrees
45°
Gradians
50 grad
sin / cos / tan
0.707107 / 0.707107 / 1

radians = degrees × π/180; degrees = radians × 180/π.

Convert angles between degrees and radians. Results are given as decimals and in terms of π, along with the angle’s sine, cosine and tangent.

How to use the Degrees to Radians Converter

  1. Enter the angle.
  2. Choose degrees → radians or radians → degrees.
  3. Read the converted angle and the trigonometric values.

How it works

A full circle is 360° = 2π radians, so 180° = π radians. To convert degrees to radians multiply by π/180; to convert radians to degrees multiply by 180/π. 45° × π/180 = π/4 ≈ 0.785398 rad. One radian is the angle where the arc length equals the radius — about 57.2958°.

Radians are the natural unit in calculus, physics and programming: functions like Math.sin() expect radians, not degrees.

Common angles

DegreesRadians (π)Radians (decimal)
0°00
30°π/60.523599
45°π/40.785398
60°π/31.047198
90°π/21.570796
120°2π/32.094395
135°3π/42.356194
180°π3.141593
270°3π/24.712389
360°2π6.283185

Frequently asked questions

How many radians is 90 degrees?

π/2 ≈ 1.5708 radians.

How many degrees is 1 radian?

About 57.2958°.

How do I convert radians to degrees?

Multiply by 180/π. π/3 radians = 60°.

Why are radians used?

Radians make many formulas simpler — for example, arc length = radius × angle and the derivative of sin x is cos x only when x is in radians.

Related tools