What is sine
The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the hypotenuse: sin(θ) = opposite ÷ hypotenuse. Values range from −1 to 1. For example, sin(30°) = 0.5 and sin(90°) = 1.
Because the hypotenuse is always the longest side of a right triangle, the ratio can never exceed 1 — which is exactly why sine is capped at ±1. The result is a pure number with no units, since it divides one length by another. Trigonometric functions expect radians in most software, so convert with the degrees to radians calculator when needed.
How to use this calculator
Enter the angle in degrees and read sin(θ) rounded to four decimals. To work the other way — from a ratio back to the angle — use the arcsine calculator.
The commonest mistake is feeding in a value already expressed in radians, which returns a much smaller number than expected: entering 1.5708 gives sin of 1.5708 degrees, roughly 0.0274, not the 1 you wanted for a right angle. Multiply radians by 180 ÷ π first. A few reference values are worth memorising as checks: sin(0°) = 0, sin(30°) = 0.5 and sin(90°) = 1.
Degrees and radians
This tool takes angles in degrees and converts internally to radians (rad = deg × π ÷ 180), since trig functions are defined on radians. The pairing of sine with cosine describes circular motion and waves.
Plotted against angle, sine traces a smooth wave that rises to 1 at 90°, falls back through 0 at 180°, reaches −1 at 270° and returns to 0 at 360° before repeating. That periodic shape is why sine models anything that cycles — alternating current, sound pressure, tides and orbital positions all follow it.
Frequently asked questions
- What is sin(30°)?
- sin(30°) = 0.5, the ratio of the opposite side to the hypotenuse for a 30-degree angle.
- What is the range of sine?
- The sine of any real angle is always between −1 and 1, inclusive.
- Does this calculator use degrees or radians?
- Enter the angle in degrees; the tool converts to radians automatically before computing.
- What is sin(90°)?
- sin(90°) = 1, the maximum value of the sine function.
- Can I enter an angle larger than 360° or a negative one?
- Yes. Sine is defined for every real angle and repeats every 360°, so sin(370°) equals sin(10°). Negative angles simply measure clockwise, and sin(−θ) is the negative of sin(θ).