If sin 30 gives −0.988… instead of 0.5, the calculator is in radian (RAD) mode and read 30 as 30 radians. Tap the angle indicator at the top of the screen to switch to DEG and you get 0.5. To convert, radians = degrees × π/180.
What a radian is
A degree is 1/360 of a full turn. A radian is the angle made by an arc as long as the radius. A full circle’s arc is 2πr long, so a full turn is 2π radians.
- 360° = 2π rad, 180° = π rad
- 1 rad = 180°/π ≈ 57.29577951°
- Degrees → radians: × π/180. Radians → degrees: × 180/π.
Common angles
| Degrees | Radians | sin | cos |
|---|---|---|---|
| 0° | 0 | 0 | 1 |
| 30° | π/6 | 1/2 | √3/2 |
| 45° | π/4 | √2/2 | √2/2 |
| 60° | π/3 | √3/2 | 1/2 |
| 90° | π/2 | 1 | 0 |
| 180° | π | 0 | −1 |
| 360° | 2π | 0 | 1 |
This calculator returns these values exactly, as in the table. Tap S⇔D for the decimal (for example √3/2 → 0.8660254038).
When to use which
- DEG: triangles, geometry, surveying, slopes and bearings, anywhere you measure angles with a protractor.
- RAD: calculus, arc length (s = rθ), angular velocity, oscillations and waves. The rule that the derivative of sin x is cos x only holds in radians.
- GRA (gradians): a right angle is 100 gradians. Used in some surveying; you will rarely need it.
The SIN and COS functions in Excel and in programming languages take radians. In Excel, the sine of 30° is =SIN(RADIANS(30)).
Changing the mode here
- Tap DEG, RAD or GRA at the top left of the screen to cycle through them, or choose in Settings.
- Enter degrees-minutes-seconds with the °′″ key (SHIFT + bracket). 30°15′ is 30.25°.
- To see a result in degrees-minutes-seconds, tap °′″ under the result.
Published 2026-10-06 · Updated 2026-10-06 · Lumen Lab