How to convert
- Degrees to radians: multiply by π/180. 90° × π/180 = π/2 ≈ 1.5708 radians.
- Radians to degrees: multiply by 180/π. 1 radian × 180/π ≈ 57.2958°.
Where does π come from? A radian is the angle you get when the arc around a circle is as long as the radius. The whole way around a circle is 2π radii long, so a full turn is 2π radians, and 360° = 2π means 180° = π.
Common angles
| Degrees | Radians (exact) | Radians (decimal) | sin | cos |
|---|---|---|---|---|
| 0° | 0 | 0 | 0 | 1 |
| 30° | π/6 | 0.5236 | 1/2 | √3/2 |
| 45° | π/4 | 0.7854 | √2/2 | √2/2 |
| 60° | π/3 | 1.0472 | √3/2 | 1/2 |
| 90° | π/2 | 1.5708 | 1 | 0 |
| 180° | π | 3.1416 | 0 | −1 |
| 270° | 3π/2 | 4.7124 | −1 | 0 |
| 360° | 2π | 6.2832 | 0 | 1 |
Why sin(30) isn't 0.5 on some calculators
In degree mode, sin(30) means the sine of 30°, which is 0.5. In radian mode it means the sine of 30 radians (about 1,719°), which is about −0.988. Neither calculator is broken; they read the 30 differently. If an answer looks wrong, check the mode first.
Calcist's scientific calculator has a Deg/Rad switch. In the ask bar, "sin of 30 degrees" uses degrees and "sin of 2 radians" uses radians, and if your angle contains π (like sin(π/6)) Calcist treats it as radians, because that's almost always what's meant.
Which should you use?
Degrees for everyday angles: building, navigation, a roof pitch or a triangle in geometry class. Radians for calculus, physics and programming, because the formulas come out simpler (the slope of sin x is cos x only when x is in radians). Most programming languages, including JavaScript, Python and Excel's SIN function, expect radians.
Every worked example on this page was checked with Calcist's own engine and an independent reference.