How to use the angle converter
- Type the angle in Value as a decimal, for example 12.5.
- Choose its unit in From: degrees, radians, gradians, arcminutes, arcseconds, turns, milliradians or NATO mils (1/6400 turn).
- Choose the unit you want in To. The default converts 180 degrees to radians.
- Read the main result, or the table below it with all eight units. The swap button reverses the direction.
What it does and when to use it
Most people think in degrees, but much of the world measures angles in other ways. Programming languages and physics formulas use radians, so Math.sin(30) in code is not the sine of 30°. Surveyors may use gradians. Rifle scopes and optics use milliradians or minutes of angle. Military maps and compasses often use mils, and astronomers use arcseconds for tiny angles.
This tool changes one unit into another. To solve a triangle or find a sine, use the trigonometry calculator. For the length of a curve from its angle and radius, try the arc length calculator. For angles that turn per second, such as rad/s, the frequency converter links rotation rates with hertz and rpm.
How it works
Every unit is stored as radians and the tool goes through radians in the middle.
| Unit | Radians | Per full turn |
|---|---|---|
| degree | π/180 ≈ 0.0174532925 | 360 |
| gradian | π/200 ≈ 0.0157079633 | 400 |
| arcminute | π/10,800 | 21,600 |
| arcsecond | π/648,000 | 1,296,000 |
| milliradian | 0.001 | ≈ 6,283.19 |
| NATO mil | 2π/6,400 ≈ 0.000981747704 | 6,400 |
| turn | 2π | 1 |
These are exact by definition. The value of π comes from JavaScript, accurate to about 16 digits, and results are shown to 12 significant figures. NIST’s Appendix B.8 lists the same degree, gon and mil factors.
Worked examples
A 30° slope for a formula. 30 degrees = 0.523598775598 radians. The table also shows 33.3333333333 gradians and 533.333333333 NATO mils.
One mil on a compass. 1 NATO mil = 0.05625 degrees, which is 3.375 arcminutes or 0.981747704247 milliradians.
A tiny angle. 1 arcsecond = 0.004848136811 milliradians. That is roughly the angle of a 5 mm object seen from 1 km.
Limits and tips
- Other mils exist. Some armies have used 6,000 or 6,300 per circle. This tool uses only the NATO 6,400 version.
- Large angles are not wrapped. 720° converts to 2 turns, not to 0°.
- Very small results switch to scientific notation once they fall below 10⁻⁹.
Frequently asked questions
How do I convert degrees to radians by hand?
Can I enter degrees, minutes and seconds like 12° 30′ 15″?
What is the difference between a milliradian and a mil?
Is MOA the same as an arcminute?
What are gradians used for?
Sources
- NIST Guide to the SI, Appendix B.8: Factors for units listed alphabetically — NIST, accessed 2026-10-08
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