Angle Units Explained: Degrees, Radians, and Gradians

Relate degrees, radians, and gradians through a full turn while separating exact π expressions from finite decimal output.

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Use the Degrees to Radians tool for the direct action. This guide stays focused on the explanation, tradeoffs, mistakes, and reference context behind that task.

One Turn In Three Units

Unit Full turn Quarter turn
Degrees 360° 90°
Radians 2π rad π/2 rad
Gradians 400 gon 100 gon

Exact Pi Relation, Approximate Decimal

Radians equal degrees multiplied by π/180, and degrees equal radians multiplied by 180/π. Those symbolic relationships are exact.

A browser displays a finite decimal approximation of a π-based result. For example, 180° equals π rad exactly but appears numerically as approximately 3.1415926536 rad under this page display policy.

Unit Conversion Does Not Normalize The Angle

Negative and multi-turn values retain their sign and turn count. The tools do not wrap input modulo 360°, 2π rad, or 400 gon.

A common integration error is supplying degrees to a function that expects radians. Check the API or formula unit before using a converted value.

Related Tools

Angle

Radians to Degrees

Express a radian angle in degrees. Signed angles are preserved; no modulo normalization is applied.

 Angle

Degrees to Gradians

Convert a degree angle into gradians for surveying or decimal-turn notation. Signed angles are preserved; the tool does not normalize a value to one turn.

 Angle

Gradians to Degrees

Convert gradians into degrees. Signed angles are preserved; the tool does not normalize a value to one turn.

References

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