Degrees, Radians and Gradians Converter

How do you convert degrees to radians?

A full turn is 360 degrees or 2π radians. That makes 180 degrees = π radians, so the conversion is one multiplication: radians = degrees × π / 180.

Example: 30 degrees is 30 × π / 180 = π/6 = 0.5236 radians.

How do you convert radians to degrees?

Going the other way, multiply by 180 / π: degrees = radians × 180 / π. One radian is about 57.2958 degrees.

When the angle is given as a multiple of π, simply replace π with 180: 3π/4 = 3 × 180 / 4 = 135 degrees.

Common angles

• 30° = π/6
• 45° = π/4
• 60° = π/3
• 90° = π/2
• 180° = π
• 270° = 3π/2
• 360° = 2π

What is a gradian?

The gradian (gon) divides a right angle into 100 equal parts, so a full turn is 400 gradians. It is used in surveying and on some instruments. Multiply by 9 / 10 to get degrees: 100 gradians = 90 degrees.

Turns

For rotating machinery an angle is also given as a number of turns. One turn is 360 degrees or 2π radians.

Which one when?

Degrees are used on site and on drawings. Formulas, derivatives and integrals, and the sin and cos functions of programming languages take radians. Leaving a calculator in the wrong mode (DEG, RAD, GRAD) is the most common mistake.

Limits

The calculator works with decimal degrees. Degrees, minutes and seconds are not covered here.