📐 Angle Converter
Convert angle units instantly — degrees, radians, gradians, arcminutes, arcseconds, turns and more. Used by mathematicians, engineers, surveyors, and navigation systems worldwide.
Angle Conversion Table
| Degrees | Radians | Gradians | Arcminutes |
|---|---|---|---|
| 0° | 0 rad | 0 grad | 0' |
| 30° | 0.5236 rad | 33.333 grad | 1800' |
| 45° | 0.7854 rad | 50 grad | 2700' |
| 60° | 1.0472 rad | 66.667 grad | 3600' |
| 90° | 1.5708 rad | 100 grad | 5400' |
| 180° | 3.1416 rad | 200 grad | 10800' |
| 270° | 4.7124 rad | 300 grad | 16200' |
| 360° | 6.2832 rad | 400 grad | 21600' |
Popular Angle Conversions
About Angle Converter
An angle measures the rotation between two rays sharing a common endpoint. The most familiar unit is the degree (°), where a full circle = 360°. Scientists and programmers use radians (a full circle = 2π rad) because they simplify calculus and trigonometry formulas. Gradians (400 per circle) were introduced for surveying so that a right angle = 100 grad, making decimal subdivision easier.
Degrees & Gradians
Degrees divide a circle into 360 parts — a convention inherited from Babylonian astronomy (~2400 BC), chosen because 360 has many divisors. Each degree splits into 60 arcminutes, each arcminute into 60 arcseconds. Gradians (or gon) divide the circle into 400 parts, used in European land surveying. 1 right angle = 90° = 100 grad.
Radians & Turns
A radian is the angle subtended by an arc equal in length to the radius. Since a circle's circumference = 2πr, a full circle = 2π radians ≈ 6.2832 rad. Radians are dimensionless and the natural choice for calculus. A turn (or revolution) = 360° = 2π rad = 400 grad — used in engineering and navigation.
Common Angle Conversions — Quick Reference
Popular Angle Questions
Most searched angle conversions
Who Uses the Angle Converter?
Converts between degrees, gradians, and radians for land measurement, topographic maps, and coordinate calculations.
Works in degrees, arcminutes, and arcseconds to specify celestial coordinates (RA/Dec) and telescope pointing angles.
Converts between degrees and radians for trigonometric functions in code — most programming languages use radians natively.
Converts bearing angles between degrees and radians for flight path calculations, GPS, and autopilot systems.
Converts rotation angles for beam deflection, gear ratios, and mechanical design specifications.
Converts between degrees and radians for 3D rotation math, physics engines, and camera control systems.
Quick Mental Math for Angle
Multiply by π/180 (≈0.01745) for radians. Quick: 180° = π, 90° = π/2, 45° = π/4, 30° = π/6, 60° = π/3.
Multiply by 10/9 for grad. Quick: 90° = 100g, 180° = 200g, 270° = 300g, 360° = 400g.
1° = 60′ = 3600″. Quick: 0.5° = 30′, 0.1° = 6′ = 360″. GPS coordinates often use decimal degrees.