Degrees and radians
A full circle is 360 degrees or 2π radians. Radians are dimensionless and make calculus formulas cleaner — sin, cos and their derivatives only line up neatly when angles are in radians.
Angle conversion
Convert any angle,
instantly.
From arcseconds to full revolutions — every common scale, side by side.
°
0.017453293
rad1 ° = 0.017453293 rad
Quick to:
1 ° in all units
| Radians | 0.017453293 | rad |
| Gradians | 1.1111111 | gon |
| Arcminutes | 60 | ' |
| Arcseconds | 3600 | " |
| Turns (revolutions) | 0.0027777778 | tr |
| NATO mils | 17.777778 | mil |
About angle conversion
Angles describe rotation and direction. Different fields use different units: math and physics prefer radians, engineering uses degrees, surveyors use gradians, and astronomers use arcminutes and arcseconds for tiny angles in the sky.
Gradians
A gradian splits a right angle into 100 parts (full circle = 400 gon). It was introduced during the French Revolution as a decimal alternative and survives in continental European surveying.
Arcminutes & arcseconds
Astronomers and cartographers need to express tiny angles. One degree splits into 60 arcminutes, and each into 60 arcseconds. The Moon spans about 30 arcminutes in our sky.
Turns and mils
A turn is one full revolution (360°). NATO mils divide the circle into 6,400 parts for military rangefinding, where 1 mil at 1,000 m equals about 1 m of horizontal offset.
Frequently asked questions
- How do I convert degrees to radians?
- Multiply degrees by π/180. For example, 180° = π rad ≈ 3.14159 rad. A full circle is 360° or 2π rad.
- What is a gradian?
- A gradian (gon) divides a right angle into 100 parts, so a full circle is 400 gradians. It's used in surveying and some European engineering.
- What are arcminutes and arcseconds?
- One degree is divided into 60 arcminutes ('), and each arcminute into 60 arcseconds ("). They're used in astronomy and geodesy for very small angles.
- What is a NATO mil?
- A NATO mil divides a circle into 6,400 equal parts, used by military for artillery and rifle scopes. 1 mil ≈ 0.05625° (one mil at 1 km ≈ 1 m).