Angle Converter: Degrees and Radians
Convert angles between degrees, radians, gradians, turns, arcminutes and arcseconds.
Good to know. A radian is the angle where the arc is as long as the radius. There are just over six in a circle.
How it works
In plain words
A full circle is 360 degrees, 2π radians, 400 gradians or one turn. To go from degrees to radians, multiply by π and divide by 180; from radians to degrees, multiply by 180 and divide by π.
The formula
radians = degrees × π ÷ 180 degrees = radians × 180 ÷ π 1° = 60′ = 3,600″ · 360° = 400 gon
Worked example
90° × π ÷ 180 = π/2 = 1.570796 rad.
Sources
Sources checked September 30, 2026. 4 automated tests check its answers on every change.
About the angle converter: degrees and radians
Angles are measured in degrees in everyday life, with 360 in a full circle, a number that goes back to Babylonian astronomy. Mathematics, physics and most programming languages use radians instead, and surveyors in parts of Europe use gradians, with 400 in a circle. This converter translates between them, with every unit shown at once.
A radian is the angle at the centre of a circle where the arc is exactly as long as the radius. A full circle holds 2π radians, about 6.283, so 180° is π radians and 1 radian is about 57.3°. Spreadsheet and programming functions like SIN and COS expect radians, which is the most common reason they give an unexpected answer.
Degrees are divided into 60 arcminutes, and each arcminute into 60 arcseconds, like hours on a clock. They are used for map coordinates, astronomy and rifle scopes: 1 arcminute of latitude is about one nautical mile, 1,852 metres.
Handy values: 30° = π/6 ≈ 0.5236 rad, 45° = π/4 ≈ 0.7854 rad, 60° = π/3 ≈ 1.0472 rad and 90° = π/2 ≈ 1.5708 rad.
Questions people ask
How do I convert degrees to radians?
Multiply by π and divide by 180. 90° is π/2, about 1.5708 radians.
How many degrees is one radian?
About 57.2958°: 180 ÷ π.
What is a gradian?
A 400th of a circle, also called a gon. A right angle is 100 gradians.