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Angle Converter

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Angle Units

Angle Units Description

Degree (°)

The most commonly used angle unit. A circle is divided into 360 equal parts, each equal to 1 degree. One full circle equals 360 degrees.

Radian (rad)

A standard angle unit in mathematics. 2π radians equals 360 degrees. Defined as arc length divided by radius.

Gradian (grad)

Divides a circle into 400 equal parts, each equal to 1 grad. Used in surveying and engineering.

Arcminute (')

One sixtieth of a degree. 1 degree = 60 arcminutes. Used for precise angular measurements.

Arcsecond ('')

One sixtieth of an arcminute. 1 arcminute = 60 arcseconds. Used for high-precision angular measurements.

Turn (turn)

One complete revolution. 1 turn = 360 degrees.

Milliradian (mrad)

One thousandth of a radian. Common in precision measurement.

Mil (mil)

Used mainly in military and engineering. 1 mil = 1/6400 turn.

Common Angle References

Basic angles

  • Right angle: 90° = π/2 rad = 100 grad
  • Straight angle: 180° = π rad = 200 grad
  • Full angle: 360° = 2π rad = 400 grad

Special angles

  • 30° = π/6 rad ≈ 0.524 rad
  • 45° = π/4 rad = 50 grad
  • 60° = π/3 rad ≈ 1.047 rad