Free online angle calculator for converting between degrees, radians, and grads. Essential tool for students, engineers, mathematicians, and anyone working with trigonometry.
Enter any angle value in degrees. Can be positive, negative, or zero.
Enter an angle value to see results
The most common angle unit, where a full circle equals 360°. Used in everyday measurements, navigation, and basic geometry. Each degree represents 1/360th of a complete rotation.
The standard unit in mathematics and physics, where a full circle equals 2π radians. Essential for calculus, trigonometric functions, and advanced mathematics. One radian equals approximately 57.2958 degrees.
Also known as grads or gons, where a full circle equals 400 grads. Used in surveying, civil engineering, and some European countries. Each grad represents 1/400th of a complete rotation.
From Degrees to Radians:
radians = degrees × (π/180)
From Radians to Degrees:
degrees = radians × (180/π)
From Degrees to Grads:
grads = degrees × (400/360)
From Grads to Degrees:
degrees = grads × (360/400)
Key Values: π ≈ 3.14159, 180° = π radians, 90° = π/2 radians, 200 grads = 180° = π radians
Degrees divide a circle into 360 equal parts, while radians use the radius of the circle as the unit of measurement. A full circle equals 360° or 2π radians. Radians are the standard unit in higher mathematics and physics.
Use radians for calculus, trigonometric functions, physics calculations, and mathematical analysis. Degrees are better for everyday measurements, navigation, construction, and when working with angles that are commonly expressed in degrees (like 30°, 45°, 90°).
Gradians are primarily used in surveying, civil engineering, and some European countries. They divide a right angle into 100 equal parts, making calculations easier in decimal form. A full circle equals 400 grads.
Our angle calculator provides highly accurate conversions using JavaScript's built-in mathematical functions. It's suitable for most educational, engineering, and scientific applications with precision up to 15 decimal places.
Yes, the calculator supports negative angles. Negative angles represent clockwise rotation and can be converted between all three units. The sign is preserved in all conversions.
Common conversions include: 90° = π/2 radians = 100 grads, 180° = π radians = 200 grads, 270° = 3π/2 radians = 300 grads, 360° = 2π radians = 400 grads.
| Angle | Degrees | Radians | Grads | Common Name |
|---|---|---|---|---|
| 0 | 0° | 0 | 0 | Zero angle |
| π/6 | 30° | π/6 | 33⅓ | 30° angle |
| π/4 | 45° | π/4 | 50 | 45° angle |
| π/3 | 60° | π/3 | 66⅔ | 60° angle |
| π/2 | 90° | π/2 | 100 | Right angle |
| π | 180° | π | 200 | Straight angle |
Explore our other free math calculators for comprehensive mathematical solutions:
Calculate sin, cos, tan and their inverses
Advanced mathematical operations
Calculate areas, perimeters, and volumes
Convert between coordinate systems
Solve triangle problems and calculations
Perform vector operations and calculations