Free online angle converter
Angle measurement uses several unit systems. This converter handles all major angle units — degrees, radians, gradians, and more — with a full conversion table.
How to use
- Enter a value.
- Select the unit you are converting from.
- Select the unit you want to convert to.
- The result and full conversion table appear instantly.
Supported units
| Unit | Symbol | Notes |
|---|---|---|
| Degrees | ° | Most common; 360° = full circle |
| Radians | rad | SI standard; 2π = full circle |
| Gradians | grad | 400 = full circle; used in surveying |
| Turns | — | 1 = full circle |
| Arcminutes | ′ | 1° = 60′ |
| Arcseconds | ″ | 1° = 3,600″ |
| NATO mils | mil | 6,400 = full circle |
Key conversions
| From | To | Factor |
|---|---|---|
| 1 degree | radians | π / 180 ≈ 0.017453 |
| 1 radian | degrees | 180 / π ≈ 57.2958 |
| 1 degree | gradians | 10/9 ≈ 1.1111 |
| 1 turn | degrees | 360 |
| 1 degree | arcminutes | 60 |
| 1 degree | arcseconds | 3,600 |
Worked example
180 degrees to radians:
180° × (π / 180) = π rad ≈ 3.14159 rad
This is the most common conversion — a half-circle (180°) equals exactly π radians.
Frequently asked
What is a radian?
A radian is the angle subtended when the arc length equals the radius. One full circle = 2π radians ≈ 6.2832 rad. Radians are the SI standard unit for angles in mathematics and physics.
What is the difference between degrees and gradians?
A full circle has 360 degrees or 400 gradians. Gradians (also called gon or grade) divide the right angle into 100 equal parts, making some surveying calculations simpler.
What is a turn?
One turn is a full rotation (360°). It simplifies cyclic calculations — 0.25 turn = 90°, 0.5 turn = 180°, etc. Also called revolution or cycle.
What are arcminutes and arcseconds?
One degree = 60 arcminutes (′). One arcminute = 60 arcseconds (″). These units are used in astronomy, GPS coordinates, and precise navigation.
What are NATO mils?
NATO mils divide a full circle into 6,400 units. One degree ≈ 17.78 mils. Mils are used in artillery and military targeting because small angular changes translate predictably to distance changes at range.