Angle unit conversion
A full turn is 360 degrees, which is the same as 2π radians, 400 gradians or 6,400 NATO mils. The table below gives the size of each common angle unit in degrees and in turns so you can convert without a calculator.
| Unit | Symbol | Degrees | Turns |
|---|---|---|---|
| Degree | ° | 1 | 0.002778 |
| Radian | rad | 57.2958 | 0.159155 |
| Gradian | gon | 0.9 | 0.0025 |
| Turn | tr | 360 | 1 |
| Arcminute | arcmin | 0.016667 | 0.0000463 |
| Arcsecond | arcsec | 0.000278 | 0.000000772 |
| Milliradian | mrad | 0.057296 | 0.000159 |
| Mil | mil | 0.05625 | 0.000156 |
Notes
- There are 60 arcminutes in a degree and 60 arcseconds in an arcminute, so one degree equals 3,600 arcseconds.
- A NATO mil divides a circle into 6,400 parts, but some countries use 6,000 artillery mils, giving a slightly different angle per mil.
- For quick mental maths, multiply degrees by π/180 (about 0.01745) to get radians, or divide by 0.9 to get gradians.
Frequently asked questions
- How many radians are in a degree?
- One degree equals π/180 radians, about 0.01745 radians. To convert, multiply the number of degrees by π/180 or by 0.01745.
- What is a gradian?
- A gradian (also called a grad or gon) divides a right angle into 100 parts, so a full circle is 400 gradians. One gradian equals 0.9 degrees.
- What is the difference between a mil and a milliradian?
- A milliradian is exactly one thousandth of a radian. A mil is a practical unit used for sighting: the NATO mil equals 1/6400 of a circle, which is about 0.05625 degrees — close to, but not exactly, one milliradian.
- How many arcminutes are in a degree?
- There are 60 arcminutes in one degree and 60 arcseconds in one arcminute, so a degree contains 3,600 arcseconds. These units are used mainly in astronomy and navigation.