Sine Calculator
Instantly find the sine of any angle in degrees. Use it when solving right triangles, modeling waves, or working through trigonometry homework and engineering problems.
About this calculator
The sine function is one of the three primary trigonometric ratios. For a right triangle, sin(θ) equals the length of the side opposite the angle divided by the hypotenuse: sin(θ) = opposite / hypotenuse. When your angle is given in degrees, it must first be converted to radians before the calculation: sin(θ) = sin(angle × π / 180). The sine function produces values that always range between −1 and 1. Key reference values include sin(0°) = 0, sin(30°) = 0.5, sin(90°) = 1, and sin(180°) = 0. Sine is widely used in physics for resolving force components, in engineering for signal analysis, and in geometry for solving oblique triangles via the Law of Sines.
How to use
Suppose you want to find the sine of 45°. Enter 45 in the Angle field. The calculator converts it to radians: 45 × π / 180 ≈ 0.7854 radians. It then computes sin(0.7854) ≈ 0.7071. This means in a right triangle with a 45° angle, the opposite side is about 70.71% of the hypotenuse length. You can verify this with the classic 45-45-90 triangle, where both legs are equal and each is √2/2 ≈ 0.7071 times the hypotenuse.
Frequently asked questions
What is the sine of an angle and how is it defined in a right triangle?
The sine of an angle θ is defined as the ratio of the length of the side opposite to that angle to the length of the hypotenuse in a right triangle: sin(θ) = opposite / hypotenuse. This ratio is constant for a given angle regardless of the triangle's size. The sine function extends beyond right triangles through the unit circle definition, where sin(θ) represents the y-coordinate of a point on the unit circle at angle θ. Its values always fall between −1 and 1.
Why does the sine calculator convert degrees to radians before computing?
Computers and mathematical libraries, including JavaScript's Math.sin(), calculate trigonometric functions using radians as their native unit. Radians are the mathematically natural measure of angles, defined as arc length divided by radius. The conversion formula is radians = degrees × π / 180, so 90° becomes π/2 ≈ 1.5708 radians. The calculator applies this conversion automatically so you can simply type in the familiar degree value.
When should I use the sine function instead of cosine or tangent?
Use sine when you know an angle and the hypotenuse and need the opposite side, or when you know the opposite side and hypotenuse and need the angle. In physics, sine is used to find the perpendicular (vertical) component of a vector, such as the vertical lift component of a force applied at an angle. Cosine is preferred for the adjacent side or horizontal component, while tangent is used when you know both legs but not the hypotenuse. Choosing the right function depends on which sides and angles are known in your problem.