ConverterHub

Sine Calculator

Calculate the sine of an angle

How it is calculated

The tool computes sin(θ). When the unit is degrees (deg) the angle is first converted to radians with θrad = θ × π ÷ 180; any other unit value is treated as radians and used directly. Any number is accepted, including negative angles and angles beyond 360°, because the sine repeats every 360° (2π). The result always lies between −1 and 1 and is rounded to two decimals, so small values may show as 0.00. In a right triangle, the sine of an angle is the opposite side divided by the hypotenuse.

Worked example

Find the sine of 40 degrees. Convert to radians: 40 × π ÷ 180 = 0.6981 rad. The sine of 0.6981 is 0.64. In a right triangle with a 40° angle and a hypotenuse of 10, the side opposite that angle is therefore about 10 × 0.64 = 6.4. Entering 1.5708 with radians selected gives 1.00, the sine of a right angle.

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Common mistakes

  • Leaving the unit on degrees while typing a radian value. Entering 1.57 as degrees gives 0.03, not 1.
  • Typing a degree value with radians selected. 30 radians gives -0.99, not 0.50.
  • Expecting a result above 1 for large angles. A sine never exceeds 1 in size.
  • Using sine when the other leg of a triangle is needed. The adjacent side uses cosine, and opposite over adjacent uses tangent.
  • Rounding too early: the tool shows two decimals, so use the figure as an approximation and not as an exact multiplier on large values.

About this calculator

The sine of an angle is the ratio of the length of the side opposite that angle to the hypotenuse in a right triangle, or equivalently the y-coordinate of a point on the unit circle at that angle. This calculator accepts the angle in either degrees or radians and converts internally (radians = degrees × π/180) before evaluating, since most math libraries and calculators compute sine in radians natively.

It's a foundational operation in trigonometry homework, but also in real engineering: sine drives the vertical component of projectile motion, the voltage waveform of AC electricity, sound wave synthesis, and the rotation matrices used in computer graphics and robotics.

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