📐 Angle Converter
Convert between Degrees, Radians, Gradians, Turns, Arcminutes, and Arcseconds instantly.
Quick Reference
How to Convert Angle Units
Angle conversion works by converting any input to the base unit (degrees), then to the target unit. Angles are fundamental in geometry, trigonometry, navigation, astronomy, and engineering.
Common Conversion Factors
| From | To | Multiply by |
|---|---|---|
| Degree | Radian | π/180 ≈ 0.01745 |
| Radian | Degree | 180/π ≈ 57.2958 |
| Degree | Gradian | 10/9 ≈ 1.1111 |
| Turn | Degree | 360 |
| Degree | Arcminute | 60 |
| Degree | Arcsecond | 3,600 |
| Turn | Radian | 2π ≈ 6.2832 |
Angles in Everyday Life
Navigation: Compass bearings use degrees (0–360°). Mathematics: Calculus and physics prefer radians because derivative formulas (sin, cos) are simplest in radians. Surveying: Some countries use gradians, where a right angle is exactly 100 grad. Astronomy: Arcminutes and arcseconds measure tiny angular separations between stars.
Common Angles Reference
| Degrees | Radians | Gradians | Turns |
|---|---|---|---|
| 0° | 0 | 0 | 0 |
| 30° | π/6 ≈ 0.5236 | 33.33 | 0.0833 |
| 45° | π/4 ≈ 0.7854 | 50 | 0.125 |
| 90° | π/2 ≈ 1.5708 | 100 | 0.25 |
| 180° | π ≈ 3.1416 | 200 | 0.5 |
| 360° | 2π ≈ 6.2832 | 400 | 1 |
Frequently Asked Questions
A radian is the angle formed when an arc length equals the circle's radius. One full revolution is 2π radians (≈ 6.2832). Since 1 radian ≈ 57.296°, radians are larger than degrees. They are the natural unit in calculus and physics.
A full circle contains exactly 360 degrees. This convention originated with the ancient Babylonians, who used a base-60 number system. A circle also equals 2π radians, 400 gradians, or 1 turn.
A gradian (gon or grade) divides a right angle into 100 equal parts, making a full circle 400 gradians. This decimal-friendly system is used in surveying and land measurement, particularly in France and some other European countries.
Use radians in mathematics, physics, and programming — calculus formulas (derivatives, Taylor series) only work cleanly in radians. Use degrees for everyday measurement, navigation, and architecture. Most programming languages' trig functions (sin, cos, tan) expect radians.