Sine Function Calculator - Sine in Degrees, Radians, or Pi

A sine function calculator evaluates sin(theta) for any real angle theta, returns the dimensionless result in [-1, 1], and shows where the angle sits on the unit circle so you can see the y-coordinate without drawing the circle by hand.

• • Trig homework and class problems: Checking sin(30 deg) = 1/2, sin(pi/4) = sqrt(2)/2, and similar unit-circle values while working through textbook exercises.
• • Wave and signal work: Reading the sine of phase angles when you only have the angle in degrees, radians, or a multiple of pi from an instrument, simulation, or sketch.
• • Geometry and right triangles: Quickly recovering the opposite-side length ratio when you know an acute angle of a right triangle, before using a side-length calculator.
• • Programming and numerical checks: Confirming that Math.sin produces the value you expect, especially for large or negative angles that need coterminal-angle reduction.

The sine of an angle equals the y-coordinate of the point where the terminal side of the angle meets the unit circle, so the result is always between -1 and 1 inclusive. A sine function calculator is the fastest way to get that y-coordinate without simplifying fractions or pulling out a calculator app.

This page accepts the angle in degrees, radians, or as a multiple of pi. The conversion happens internally, so 30 degrees, pi/6 radians, and 0.1666... in pi mode all return sin = 0.5, which makes it easy to switch between the three conventions used in textbooks, physics, and engineering.

If you only need the dimensionless sine in degrees or radians without the reduced-angle readout, the lighter sin calculator returns just the sine value for the same inputs.

The calculator takes the angle you enter, converts it to radians, reduces it to a coterminal angle in [0, 2*pi] (i.e. [0 deg, 360 deg]), applies the JavaScript Math.sin function, and then derives the unit-circle quadrant and the sign of the sine.

• angleValue: The number you type into the Angle value box, such as 30, 0.5, or 0.25.
• angleUnit: The unit selector: 'degrees' (deg), 'radians' (rad), or 'pi' (multiples of pi).
• theta_rad: The angle in radians after the unit conversion, used by Math.sin internally.

All three unit modes converge to the same radians-only sine function inside the calculator, which means you can paste an angle in any convention and still get a consistent result. The reduced-angle column is what tells you which of the infinitely many coterminal angles the calculator settled on, so 390 degrees shows up as 30 degrees in the reduced-angle field.

The unit-circle quadrant field uses the standard I, II, III, IV labelling for angles strictly between 0 and 360 degrees, and reports 'On +x axis', 'On +y axis', 'On -x axis', or 'On -y axis' when the reduced angle sits exactly on a multiple of 90 degrees. The sign of sine column then turns the result into a one-word summary you can read in physics problems.

According to Wolfram MathWorld - Sine, sine is the y-coordinate of the unit-circle point and sin(pi/6) = 1/2, sin(pi/2) = 1

When the textbook writes the angle in degrees only, sin degrees calculator returns the same dimensionless sine with a degree-mode result panel.

These four concepts are the ones to keep next to the result panel, because they explain why the sine number changes the way it does and how the reduced angle is picked.

To go the other way and recover an angle from a sine value, use the arcsin calculator, which is the inverse of the function on this page.

Five short steps are enough to read the sine of any angle and the unit-circle context the calculator reports alongside it.

1. 1 Pick the angle unit: Choose degrees, radians, or multiples of pi from the Angle unit selector before you enter the value, because the same number means something different in each mode.
2. 2 Enter the angle value: Type any real number into the Angle value box. Negative angles are accepted and reduced automatically; very large numbers such as 750 degrees are reduced modulo 360 degrees before the sine runs.
3. 3 Read the sine result: The primary Sine result is a dimensionless number in [-1, 1]. A negative result means the reduced angle is in Quadrant III or IV, and a result of exactly 0 means the angle is on the x-axis.
4. 4 Check the reduced angle: The three reduced-angle rows show the same coterminal angle expressed in degrees, radians, and as a multiple of pi, so you can copy whichever form your next calculation needs.
5. 5 Confirm the quadrant and sign: Use the Quadrant and Sign of sine rows to double-check that the sine has the right sign for the quadrant you expect. This is the fastest way to catch a sign error in homework and physics problems.

For 210 degrees, expect a Quadrant III result with a negative sine of -0.5. Type 210 in degree mode, read -0.5 in the Sine row, then confirm 'III' and 'negative' in the quadrant and sign rows before using the value in a wave equation or a triangle side-length step.

When the sine value will be used to recover a side of a right triangle, hand the angle to the sine triangle calculator, which takes sin(theta) and the hypotenuse and returns the opposite side.

These benefits focus on the workflow improvements you actually notice when you stop doing the unit conversion and the reduction by hand.

• • Three unit modes in one panel: Switch between degrees, radians, and multiples of pi without opening a separate conversion tool, which is useful when a problem mixes textbook notation and physics notation.
• • Reduced-angle readout: See the coterminal angle in three unit formats at the same time, so the value you paste into the next step always matches the form the surrounding calculation expects.
• • Quadrant and sign flags: Catch sign errors before they propagate: the calculator shows the unit-circle quadrant and the sign of sine, which is the easiest way to confirm a textbook answer.
• • Real-time updates: Edit the angle or the unit and the result panel updates in real time, which makes it easy to scan a table of angles by changing the value in 15-degree steps.
• • Works for any real angle: Negative angles, angles past 360 degrees, and angles written in any of the three conventions all reduce and evaluate the same way, with no special-case menu.

If a problem needs sine, cosine, and tangent at the same angle, the sin cosine tangent calculator returns all three ratios in one pass.

Four factors decide the sine you see, plus two important limitations to keep in mind when the calculator is the last step in a longer pipeline.

• • The calculator assumes the input is a real number. If a worksheet gives a complex angle, the result will not be meaningful and the input should be reduced to its real and imaginary parts first.
• • Special angles such as pi/6, pi/4, and pi/3 are shown as decimals, not exact radical forms. Use a separate reference table if the next step needs the value in sqrt(2)/2 or sqrt(3)/2 form.

According to Wolfram MathWorld - Unit Circle, trig functions are defined using the unit circle and the result is periodic with period 2*pi

If a problem hands you a cosine value and asks for the matching angle, the arccos calculator reverses the cosine function the same way the arcsin calculator reverses the sine function.