Angle Unit Converter

Enter a value and select a starting unit to see all available conversion results.

Angle Units and Descriptions

Below are descriptions and historical context for each Angle unit available in this converter.

Degree (°)

Degree from Latin 'gradus' (step). 360° in a circle from ancient Babylonian base-60 system.

Radian (rad)

A radian is a unit of angle measurement, defined as the angle created at the center of a circle by an arc whose length is equal to the circle's radius. It's an alternative to degrees, where 360 degrees is equivalent to 2pi radians.

Milliradian (mrad)

A milliradian is a unit of angular measurement, defined as one-thousandth of a radian. It is used in fields like shooting and ballistics for measuring angles to estimate distance and make adjustments. A key feature of a milliradian is its simple relationship: at a distance of 1,000 meters, one milliradian corresponds to 1 meter (or at 1,000 yards, it's 1 yard)

Gradian (grad)

Gradian or gon, 400 gradians in a circle. Developed during French Revolution for decimal system.

Turn (turn)

One complete rotation or revolution. Also called 'cycle' in some contexts.

Arcminute (')

Arcminute, 1/60 of a degree. Used in astronomy and navigation for precise angular measurements.

Arcsecond (")

Arcsecond, 1/3600 of a degree. Used in astronomy and precision angular measurements.

Base Unit Conversion Factors

The table below shows the conversion factors from each unit to the base unit, which is the Degree (°).

  • 1 Degree (°) = 1 Degree (°)
  • 1 Degree (°) = 0.017453286279274 Radian (rad)
  • 1 Degree (°) = 17.453286279274 Milliradian (mrad)
  • 1 Degree (°) = 1.1111111111111 Gradian (grad)
  • 1 Degree (°) = 0.0027777777777778 Turn (turn)
  • 1 Degree (°) = 59.99988000024 Arcminute (')
  • 1 Degree (°) = 3599.9971200023 Arcsecond (")