Angle Converter
Convert angles between degrees, radians, gradians, full turns, arcminutes and arcseconds.
How it works
A full turn is 360 degrees, 2π radians, 400 gradians or 1 turn — the same rotation described four ways. Converting between them is a single multiplication.
Radians are the natural unit for mathematics because one radian is the angle where the arc length equals the radius, which makes calculus on trigonometric functions come out clean. Degrees are the practical unit because 360 divides neatly by so many numbers.
Arcminutes and arcseconds subdivide the degree by sixties, the same sexagesimal system as clock time. They appear in astronomy, navigation and surveying where a degree is far too coarse.
The formula
Degrees → radians
rad = deg × π ÷ 180
Radians → degrees
deg = rad × 180 ÷ π
Full turn
360° = 2π rad = 400 grad = 1 turn
Worked examples
| Scenario | Working | Result |
|---|---|---|
| 180 degrees to radians | 180 × π ÷ 180 | π ≈ 3.1416 rad |
| 90 degrees to gradians | 90 × 400 ÷ 360 | 100 grad |
| 1 degree to arcseconds | 1 × 3600 | 3,600 arcsec |
When you'd use it
- Converting an angle for a trigonometry function that expects radians
- Reading a surveying or astronomy figure in arcminutes
- Working with gradians on European surveying equipment
- Coursework in mathematics or physics
Common questions
How do I convert degrees to radians?
Multiply by π and divide by 180. A right angle of 90° is π/2 radians, about 1.5708. Most programming languages' trigonometric functions expect radians, which is a frequent source of wrong answers.
Why does mathematics prefer radians?
Because they make the calculus clean — the derivative of sin(x) is cos(x) only when x is in radians. One radian is the angle at which the arc length equals the radius, which is a property of the circle rather than an arbitrary division.
What is a gradian?
A hundredth of a right angle, so a full turn is 400 gradians. It was introduced with the metric system to make right angles come out at a round 100, and it survives mainly in European surveying.
Is anything I enter sent anywhere?
No. Every conversion runs in your browser, so nothing you type is uploaded, logged or stored. There is no account and no record of what you converted.