Angle converter
Degrees, radians, gradians and more
Type 45, 12° 30′ 15″, or π/4 in radians.
Result
Your answer appears here as you type.
About this tool
Convert an angle between degrees, degrees-minutes-seconds, radians, gradians, turns, arcminutes, arcseconds, mils and milliradians, with its slope, related angles and trig values.
The units, and how conversion works
Every angle unit is a fraction of a full turn, so converting is a matter of scaling by the right number of units per turn. The converter turns your input into degrees first, then into everything else.
| Unit | In one full turn | Used for |
|---|---|---|
| Degree (°) | 360 | Everyday use, building, navigation |
| Radian | 2π, about 6.283 | Mathematics, physics, programming: an arc as long as the radius |
| Gradian (gon) | 400 | Surveying in parts of Europe; a right angle is 100 gon |
| Turn | 1 | Rotation and motors |
| Arcminute and arcsecond | 21,600 and 1,296,000 | Astronomy, maps and optics: 60 of each make the next unit up |
| NATO mil | 6400 | Military and artillery sights: about 17.78 per degree |
| Milliradian | about 6,283 | Rifle scopes and engineering: about 17.45 per degree |
What you can type
A plain number in the unit you choose, degrees-minutes-seconds such as 12° 30′ 15″, or radians written with π, such as π/4 or 3π/2. The result also shows the angle as a slope, its normalized and signed forms, its reference angle, complement, supplement and explement, and its sine, cosine and tangent.
Two easy mistakes
- A calculator in the wrong mode. Most trigonometry errors come from typing degrees into a calculator set to radians, or the other way round. Convert first, then calculate.
- Mils that are not the same mil. NATO uses 6400 to a turn, some other armies use 6000, and a milliradian gives about 6283. Check which one a scale or a spec means.
Frequently asked questions
How do you convert degrees to radians?
Multiply the angle in degrees by π and divide by 180. For example, 45° × π/180 = π/4, which is about 0.7854 radians, and 180° is exactly π radians.
The converter on this page does it for any angle and also shows the result in gradians, turns, arcminutes, arcseconds and mils.
How do you convert radians to degrees?
Multiply the angle in radians by 180 and divide by π. For example, π/3 × 180/π = 60°, and 1 radian is about 57.30°.
You can type an angle in radians on this page, including forms such as π/4, and read it in degrees and every other unit.
How do you convert decimal degrees to degrees, minutes and seconds?
Keep the whole number as the degrees. Multiply the decimal part by 60 to get the minutes, then multiply the decimal part of the minutes by 60 to get the seconds.
Example: for 12.5125°, the degrees are 12. Next, 0.5125 × 60 = 30.75, so there are 30 minutes, and 0.75 × 60 = 45 seconds: the answer is 12° 30′ 45″. To go back, divide the minutes by 60 and the seconds by 3600 and add both to the degrees. Try this example.
Guides
About these measurements
Readings are estimates taken from rendered pixels and consumer device sensors. Do not rely on them for structural engineering, surveying, manufacturing inspection, navigation, or medical decisions. Check anything safety-critical with a calibrated instrument.
All processing happens in your browser. No image, camera frame or sensor reading is ever uploaded.
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