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The sine function relates an angle to the ratio of the opposite side to the hypotenuse in a right triangle, and extends naturally to any angle — positive, negative, or beyond 360° — via the unit circle, where sin(θ) is simply the y-coordinate of the point at angle θ. This calculator computes sin(θ) for any angle you enter, in either degrees or radians. Sine appears throughout physics and engineering: modeling the height of a point on a rotating wheel over time, describing the vertical displacement of a wave or an oscillating spring, computing AC voltage at any instant in electrical engineering, and finding a missing side of a triangle with the Law of Sines.
How it works
Enter an angle and choose whether it's in degrees or radians. The calculator converts internally as needed (radians = degrees × π/180) and evaluates sine using the unit circle definition: sin(θ) is the y-coordinate of the point reached by rotating θ from the positive x-axis around a circle of radius 1. Because the unit circle repeats every full rotation, sin(θ) is periodic with period 360° (2π radians) — sin(390°) gives the same result as sin(30°), for example.
- Enter angle (θ).
- Enter angle unit.
- Click Calculate to see your results.
Examples
sin(30°)
sin(30°) = 0.5 exactly, one of the most common reference values in trigonometry.
sin(90°)
sin(90°) = 1, the maximum value sine ever reaches, at the top of the unit circle.
sin(45°)
sin(45°) = √2/2 ≈ 0.7071, the value at the diagonal where sine and cosine are equal.
Who should use it
- Modeling wave height, AC voltage, or oscillation over time.
- Solving a triangle side with the Law of Sines.
- Trigonometry and pre-calculus homework.
Industry applications
- Physics and electrical engineering
- Mechanical engineering (rotational motion)
- Mathematics education
Advantages
- Instant, precise results for any real angle.
- Accepts both degrees and radians.
Limitations
- Returns a decimal approximation for most angles rather than an exact symbolic value.
Common mistakes to avoid
- Forgetting to switch the unit selector to radians when entering a radian value, which produces a wildly wrong result since 1 radian ≈ 57.3°.
- Confusing sin(θ) with its inverse, arcsin — sine goes angle-to-ratio, arcsin goes ratio-to-angle.
- Assuming sine is only defined for angles between 0° and 90° because of the right-triangle definition — it's actually defined for every real number via the unit circle.
Best practices
- Always confirm whether your source angle is in degrees or radians before entering it — the two units look identical as plain numbers but mean very different angles.
- Remember sine's periodicity: sin(θ) = sin(θ + 360°) = sin(θ - 360°), which is useful for simplifying awkward angles.
- Use the reference-angle relationship sin(180° - θ) = sin(θ) to sanity-check results in the second quadrant.
Tips
- Need to go from a ratio back to an angle? Use the Arcsin Calculator.