Convert an angle (degrees, radians, gradians)

The value is converted into radians, then into the target unit. The degree divides the turn into 360, the gradian into 400, and a turn is 2π radians. The gradian, inherited from the revolutionary metric system, is still used in French surveying, where a right angle conveniently equals 100 gradians.

θ(rad) = x × kfrom ; y = θ(rad) / kto

π rad = 180°

1 turn = 2π rad = 360° = 400 gon

The radian is the SI unit of plane angle: the angle subtending an arc equal in length to the radius. Trigonometric functions in programming languages, JavaScript included, expect radians. The sexagesimal degree comes from Babylonian tradition; the gradian from the metric system.

Value

The angle alone, without the unit. Negative values are accepted.

From

Starting unit. The default is the degree.

To

Target unit. The default is the radian, expected by trigonometric functions.

Assumptions

• 1 turn = 2π radians = 360 degrees = 400 gradians.
• π is the JavaScript constant Math.PI.
• Angles are not wrapped into 0–360: 720° stays 720°.

Limits

• No degrees-minutes-seconds notation (45° 30′ 15″).
• No normalisation modulo a turn.
• Solid angles, measured in steradians, are out of scope.

A right angle is 90 degrees, π/2 radians or 100 gradians. If a trigonometric calculation returns something unexpected, check the unit first: most libraries expect radians while problems are usually stated in degrees. In surveying, the gradian avoids fractions since a quarter turn comes out round.

• Passing degrees to a sine function that expects radians.

  sin(30) in radians is not 0.5. Convert first: 30° = π/6 rad.

• Confusing gradians with degrees.

  100 gradians is 90 degrees, not 100 degrees.

• Treating 45° 30′ as 45.30°.

  30 minutes of arc is half a degree, so 45.5°.

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Written by Rédaction HexaCalc (editorial team). Content last updated: August 25, 2026. No third-party medical or financial review is claimed.

• NIST Guide to the SI, Appendix B: Conversion Factors — National Institute of Standards and Technology
• Circle, area and circumference — Wolfram MathWorld