Sine Calculator (sin and arcsin)

Find the sine of any angle in degrees or radians, work backwards from a sine value with arcsin, or get the sine straight from a right triangle’s opposite side and hypotenuse. For standard angles such as 30°, 45° and 60° the exact value (for example √2/2) is shown beside the decimal, along with the matching cosine and tangent.

How to use this tool

1. Choose what you need: the sine of an angle, the angle from a sine value, or the sine from triangle sides.
2. Enter the angle and pick degrees or radians, or enter the sine value, or the two sides.
3. Read sin θ and the extra values: exact form, cosine, tangent and quadrant.
4. For arcsin, use the general solution to list every angle with that sine.

Formula

sin θ = opposite ÷ hypotenuse

radians = degrees × π ÷ 180

In a right triangle, the sine of an angle is the side opposite it divided by the hypotenuse. On the unit circle, sin θ is the y-coordinate of the point at angle θ, which extends sine to every angle: it is positive in the first and second quadrants and negative in the third and fourth. Arcsin returns the principal angle, between −90° and 90°.

Example

A 5 m ladder touches a wall 3 m above the ground. Then sin θ = 3 ÷ 5 = 0.6, and the angle between ladder and ground is arcsin 0.6 ≈ 36.87°; the foot of the ladder is √(5² − 3²) = 4 m from the wall. For a plain angle, sin 30° = 0.5 exactly, and sin 210° = −0.5 because 210° lies in the third quadrant.