Angle Converter
Convert between degrees, radians, gradians, arcminutes, and arcseconds.
1 ° = 0.01745329252 rad
| Degrees (°) | Radians (rad) |
|---|---|
| 1 | 0.01745329252 |
| 2 | 0.03490658504 |
| 5 | 0.0872664626 |
| 10 | 0.1745329252 |
| 15 | 0.2617993878 |
| 20 | 0.3490658504 |
| 25 | 0.436332313 |
| 50 | 0.872664626 |
| 75 | 1.308996939 |
| 100 | 1.745329252 |
| 150 | 2.617993878 |
| 200 | 3.490658504 |
| 250 | 4.36332313 |
| 500 | 8.72664626 |
| 1,000 | 17.45329252 |
☕ This tool is free forever. If it saved you time, buy me a coffee.
Helpful answers
Frequently asked questions
- What angle units can I convert between?
- Degrees, radians, gradians (grads), arcminutes, and arcseconds. These cover trigonometry, surveying, astronomy, and navigation applications.
- How do I convert degrees to radians?
- Radians = degrees x (pi/180). A full circle is 360 degrees = 2*pi radians. Common values: 90 degrees = pi/2 radians, 180 degrees = pi radians, 45 degrees = pi/4 radians.
- What is a gradian?
- A gradian (grad or gon) divides a right angle into 100 parts, making a full circle 400 gradians. It is primarily used in surveying because 100 grads = 90 degrees simplifies certain calculations.
Navigation
Private by default
Your inputs never leave your browser. Nothing is stored or sent anywhere.
When to use this
You are working through a calculus problem and the textbook gives an angle in degrees, but the trig function on your calculator expects radians. Or you are programming a game engine where rotation functions use radians while your design specs are in degrees. Degrees-to-radians is the most frequently searched angle conversion, and this tool handles it along with gradians, arcminutes, and arcseconds.
Angle conversions come up in mathematics, physics, engineering, surveying, astronomy, and software development. Surveyors often work in degrees-minutes-seconds (DMS) notation and need to convert to decimal degrees for GPS coordinates. Astronomers use arcseconds to describe tiny angular separations between stars. Programmers converting between coordinate systems need radians for most math libraries.
Good to know
The key formula: radians = degrees x (pi / 180). A full circle is 360 degrees or 2pi radians. So 180° = pi radians, 90° = pi/2, and 45° = pi/4. Memorizing these anchor points covers most common conversions.
Most programming languages use radians. JavaScript's Math.sin(), Python's math.sin(), and virtually every math library expect radians as input. Forgetting to convert from degrees is one of the most common bugs in graphics and game programming.
Gradians are used in surveying. A full circle is 400 gradians (also called gons). This makes right angles exactly 100 gradians, which simplifies certain surveying calculations. You will rarely encounter gradians outside of European surveying contexts.
Arcminutes and arcseconds divide a degree. One degree equals 60 arcminutes or 3,600 arcseconds. Surveying, navigation, and astronomy often use degrees-minutes-seconds notation when decimal degrees are not precise enough.
Quick Reference
| Degrees | Radians | Gradians | Arcminutes | Arcseconds | Context |
|---|---|---|---|---|---|
| 0° | 0 | 0 grad | 0 | 0 | Starting point |
| 30° | pi/6 (0.524) | 33.33 grad | 1,800 | 108,000 | Common trig angle |
| 45° | pi/4 (0.785) | 50 grad | 2,700 | 162,000 | Diagonal / 45° angle |
| 60° | pi/3 (1.047) | 66.67 grad | 3,600 | 216,000 | Equilateral triangle |
| 90° | pi/2 (1.571) | 100 grad | 5,400 | 324,000 | Right angle |
| 120° | 2pi/3 (2.094) | 133.33 grad | 7,200 | 432,000 | Obtuse angle |
| 180° | pi (3.142) | 200 grad | 10,800 | 648,000 | Straight line |
| 270° | 3pi/2 (4.712) | 300 grad | 16,200 | 972,000 | Three-quarter turn |
| 360° | 2pi (6.283) | 400 grad | 21,600 | 1,296,000 | Full circle |