Angle Converter
Convert between degrees, radians, gradians, arcminutes, arcseconds and turns.
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Angle units
Every unit below converts to every other one in the calculator. Values are relative to the base unit, the radian (rad).
| Unit | Symbol | System | Value |
|---|---|---|---|
| Radian | rad | SI | Base unit |
| Milliradian | mrad | SI | = 0.001 rad |
| Degree | ° | SI-accepted | ≈ 0.01745329252 rad |
| Arcminute | ′ | SI-accepted | ≈ 0.0002908882087 rad |
| Arcsecond | ″ | SI-accepted | ≈ 0.000004848136811 rad |
| Gradian (gon) | grad | other | ≈ 0.01570796327 rad |
| Turn (revolution) | rev | other | ≈ 6.283185307 rad |
Radian quick reference
| Radian | Milliradian | Degree | Arcminute |
|---|---|---|---|
| 1 rad | = 1000 mrad | ≈ 57.29577951 ° | ≈ 3437.746771 ′ |
| 10 rad | = 10000 mrad | ≈ 572.9577951 ° | ≈ 34377.46771 ′ |
| 100 rad | = 100000 mrad | ≈ 5729.577951 ° | ≈ 343774.6771 ′ |
| 1000 rad | = 1000000 mrad | ≈ 57295.77951 ° | ≈ 3437746.771 ′ |
Among the 7 angle units on this page, the smallest is the arcsecond (″) and the largest is the turn (revolution) (rev).
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About angle units
The radian is the SI unit of plane angle: the angle at which the arc length equals the radius. A full circle is 2π radians, which is 360 degrees.
Degrees are divided into 60 arcminutes, and each arcminute into 60 arcseconds. A gradian is 1/400 of a turn, so a right angle is exactly 100 gradians.
Frequently asked questions
- How many degrees is one radian?
- About 57.2958 degrees: 180 ÷ π.
- Which should I use in programming, degrees or radians?
- Most math libraries (for example JavaScript Math.sin or Python math.sin) expect radians. Convert degrees by multiplying by π/180.
- How many milliradians are in one radian?
- One radian = 1000 mrad (milliradians).
- How many degrees are in one radian?
- One radian ≈ 57.29577951 ° (degrees).
- How many arcminutes are in one radian?
- One radian ≈ 3437.746771 ′ (arcminutes).