Sine Calculator
The Ratio Behind Every Wave
Sine started as a right-triangle ratio — the opposite side divided by the hypotenuse — but its real power shows up once it's extended to all angles and graphed, producing the smooth oscillation that describes sound waves, alternating current, and pendulum motion. This calculator evaluates sin(θ) for any angle, accepting input in either degrees or radians.
The Formula
When the input is in degrees, it's converted to radians internally before applying the sine function, since the underlying trigonometric computation is defined in radians.
Where Sine Is Used
- Physics and engineering — decomposing forces or velocities into vertical and horizontal components.
- Electrical engineering — alternating current voltage follows a sine wave over time.
- Sound and signal processing — audio waveforms are built from combinations of sine waves at different frequencies.
- Surveying and navigation — calculating heights and distances from measured angles.
| Angle | sin(θ) |
|---|---|
| 0° | 0 |
| 30° | 0.5 |
| 45° | 0.707107 |
| 60° | 0.866025 |
| 90° | 1 |
Sine values always fall between −1 and 1, reaching its maximum of 1 at 90°.
How to Use This Calculator
- Enter the Angle.
- Select the unit: Degrees or Radians.
- Select Calculate to see the sine value.
Related Calculations
Need cosine or tangent instead? See the Cosine Calculator and the Tangent Calculator, or solve for the angle given a sine value with the Trigonometric Equation Solver.