Angle Converter
Convert between degrees, radians, gradians, and arcseconds.
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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 |
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Angle Unit Reference
Degrees: 360° in a full circle — the most familiar system. Radians: 2π in a full circle — used in math and programming. Gradians: 400 in a full circle — used in surveying.
| Degrees | Radians | Gradians |
|---|---|---|
| 30° | π/6 | 33.33 |
| 45° | π/4 | 50 |
| 90° | π/2 | 100 |
| 180° | π | 200 |
| 360° | 2π | 400 |
When Radians Matter
Trigonometric functions in most programming languages — including JavaScript, Python, C, and Java — expect angles in radians, not degrees. If you pass degrees to Math.sin(), you'll get wrong results.
To convert degrees to radians in code, multiply by π/180:
Math.sin(angle * Math.PI / 180)This is one of the most common bugs in geometry and physics calculations. Always check whether your library or language expects radians or degrees before plugging in values.
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.
Quick Reference
| Degrees | Radians | Gradians | Context |
|---|---|---|---|
| 0° | 0 | 0 grad | Starting point |
| 30° | pi/6 (0.524) | 33.33 grad | Common trig angle |
| 45° | pi/4 (0.785) | 50 grad | Diagonal / 45° angle |
| 60° | pi/3 (1.047) | 66.67 grad | Equilateral triangle |
| 90° | pi/2 (1.571) | 100 grad | Right angle |
| 120° | 2pi/3 (2.094) | 133.33 grad | Obtuse angle |
| 180° | pi (3.142) | 200 grad | Straight line |
| 270° | 3pi/2 (4.712) | 300 grad | Three-quarter turn |
| 360° | 2pi (6.283) | 400 grad | Full circle |