Measure angles with flexible input modes. Review normalized radians, unit circle points, and sector values. Fast visuals make advanced trigonometry practice easier for everyone.
The graph shows the normalized angle on the unit circle.
| Input type | Example input | Exact radians | Decimal radians |
|---|---|---|---|
| Degrees | 30° | π/6 | 0.523599 |
| Degrees | 180° | π | 3.141593 |
| DMS | 45° 30′ 0″ | 91π/360 | 0.794125 |
| Gradians | 100 gon | π/2 | 1.570796 |
| Revolutions | 0.75 rev | 3π/2 | 4.712389 |
| Arc and radius | s = 12, r = 4 | s / r | 3 |
These formulas connect common angle units. The calculator also returns equivalent degrees, DMS format, coterminal angles, and the unit circle point.
A radian measures an angle by comparing arc length to radius. One radian appears when the arc length equals the circle radius.
Radians simplify trigonometry and calculus formulas. Many derivatives, integrals, and circular motion equations work naturally in radians.
Multiply the degree value by π and divide by 180. For example, 60° becomes 60π/180, which simplifies to π/3.
Coterminal angles end at the same terminal side. You find them by adding or subtracting full turns, usually 2π radians.
Use arc length mode when you know the arc length and radius. The angle in radians equals arc length divided by radius.
Normalized radians place the angle inside one full turn, from 0 up to but not including 2π. This helps graphing and quadrant checks.
Yes. Negative inputs are accepted. The tool converts them, then also reports a normalized positive angle for easier interpretation.
Radians only need an angle conversion. Radius becomes useful when you also want arc length and sector area from that angle.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.