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Angle Converter

Convert between degrees, radians, gradians, turns, arcminutes and arcseconds

Enter Angle

90°

All Conversions

Key Formulas

Radians = Degrees × (π / 180)
Gradians = Degrees × (10 / 9)
1 Turn = 360° = 2π rad = 400 grad
1° = 60 arcminutes = 3,600 arcseconds

How Angle Conversion Works

Angles measure the rotation between two rays from a common point. Different systems divide a full rotation differently.

Degrees

A full circle is 360°. The most common unit in everyday use, navigation, and geometry.

Radians

A full circle is 2π radians. The SI unit used in mathematics and physics. One radian is the angle where the arc length equals the radius.

Gradians

A full circle is 400 gradians (gon). Used primarily in surveying where a right angle is exactly 100 gradians.

Frequently Asked Questions

How do you convert degrees to radians?
Multiply degrees by π/180. Example: 180° = π radians, 90° = π/2 radians.
What is a gradian?
A gradian divides a right angle into 100 parts. A full circle is 400 gradians. Used in surveying.
What is a turn?
One turn equals one full rotation (360°). Half a turn is 180°.
How many arcminutes in a degree?
60 arcminutes per degree, and 60 arcseconds per arcminute (3,600 arcseconds per degree).