Sine Calculator (sin)

The sine function (sin) is one of the fundamental trigonometric functions. For a right triangle, sin(x) equals the length of the opposite side divided by the hypotenuse. On the unit circle, sin(x) represents the y-coordinate of the point at angle x. Its output range is always between -1 and 1.

Select 'Degrees' as the unit, enter your angle value, and click Calculate. For example, sin(30°) = 0.5. The calculator converts degrees to radians internally using the formula radians = degrees × (π / 180) before computing the sine.

Degrees and radians are two units for measuring angles. A full circle is 360° or 2π radians. To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π. For example, 90° equals π/2 radians.

Some essential sine values are: sin(0°) = 0, sin(30°) = 0.5, sin(45°) = √2/2 ≈ 0.7071, sin(60°) = √3/2 ≈ 0.8660, and sin(90°) = 1. These values repeat in a periodic pattern with a period of 360° (or 2π radians).

The domain of sin(x) is all real numbers — you can input any angle. The range is [-1, 1], meaning the output always falls between -1 and 1 inclusive. sin(x) equals 1 at 90° (π/2) and equals -1 at 270° (3π/2).

Sine is an odd function, which means sin(-x) = -sin(x). This symmetry means the sine graph is symmetric about the origin. For example, sin(-30°) = -0.5, which is the negative of sin(30°) = 0.5.

A sine wave is the graph of y = sin(x) plotted over all real values of x. It is a smooth, periodic oscillation that repeats every 360° (2π radians). Sine waves appear widely in physics, engineering, and signal processing to represent oscillations, sound, and alternating current.

On the unit circle (a circle with radius 1 centered at the origin), if you draw a radius at angle x from the positive x-axis, the y-coordinate of the endpoint equals sin(x). This geometric definition extends the sine function beyond right triangles to all angles.