° · rad · grad · ' · " · tr
Free Angle Converter
Convert angle units instantly — degrees, radians, gradians, arcminutes, arcseconds, and turns. Free, symmetrical, no sign-up.
Why symmetrical conversion?
How This Converter Works
Degrees are used in everyday life, while radians are essential for mathematics and physics. Gradians are used in surveying, and arcminutes/arcseconds in astronomy and navigation. All 6 units update simultaneously.
Quick reference
Common Conversions
| Degrees (°) | Radians (rad) | Gradians (grad) | Context |
|---|---|---|---|
| 30° | 0.5236 rad | 33.33 grad | Interior angle of equilateral triangle |
| 45° | 0.7854 rad | 50 grad | Diagonal, 1/8 of full rotation |
| 90° | 1.5708 rad | 100 grad | Right angle |
| 180° | 3.1416 rad | 200 grad | Straight line, π radians |
| 360° | 6.2832 rad | 400 grad | Full rotation, 2π radians |
FAQ
Frequently Asked Questions
1How do I convert degrees to radians?
Multiply by π/180 (approximately 0.01745). So 90° × (π/180) = π/2 ≈ 1.5708 radians. To convert back, multiply by 180/π.
2What is a radian?
A radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. A full circle is 2π radians ≈ 6.2832 radians.
3What is a gradian?
A gradian (also called gon or grade) divides a right angle into 100 units, making a full circle 400 gradians. It is used in surveying and civil engineering.
4What are arcminutes and arcseconds?
One arcminute (') is 1/60 of a degree. One arcsecond (") is 1/60 of an arcminute or 1/3600 of a degree. These tiny units are used in astronomy and precision navigation.
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