Degrees vs Radians
Degrees and radians are two ways to measure the same angle. Knowing which one your calculator is using is the most common fix for “wrong” sine, cosine and tangent results.
What they mean
- A degree is 1/360 of a full circle. A right angle is 90°.
- A radian is the angle that uses an arc as long as the circle’s radius. A full circle is 2π radians (about 6.283), so a right angle is π/2 (about 1.571).
Converting between them
| To convert | Formula | Example |
|---|---|---|
| Degrees to radians | degrees × π ÷ 180 | 90° = 1.5708 rad |
| Radians to degrees | radians × 180 ÷ π | π rad = 180° |
On a calculator, type 90 × π ÷ 180 = to get 1.5708.
Common angles
| Degrees | Radians | sin | cos |
|---|---|---|---|
| 0° | 0 | 0 | 1 |
| 30° | π/6 ≈ 0.5236 | 0.5 | 0.866 |
| 45° | π/4 ≈ 0.7854 | 0.707 | 0.707 |
| 60° | π/3 ≈ 1.0472 | 0.866 | 0.5 |
| 90° | π/2 ≈ 1.5708 | 1 | 0 |
| 180° | π ≈ 3.1416 | 0 | −1 |
Which mode should you use?
- DEG for everyday geometry, surveying, navigation and most school problems that give angles with a degree sign.
- RAD for calculus, physics and programming, where formulas assume radians.
On CalcWindow
Open a calculator, choose the Scientific tab and press the DEG / RAD key to switch. Each window keeps its own setting, so you can compare the same angle in both modes side by side. Try 30 then sin in DEG mode (0.5), then 0.5236 then sin in RAD mode (also about 0.5).
If your answer looks wrong: check the mode first. In RAD mode, sin(30) is about −0.988 because 30 is treated as 30 radians.
More functions are covered in the scientific calculator guide.