The sine function assigns a dimensionless value to an angle. In a right triangle, sine is the length of the side opposite the angle divided by the hypotenuse. On the unit circle, it is the vertical coordinate of the point reached by rotating through the angle. This calculator accepts degrees or radians, displays the angle in both units, and returns sine rounded to six decimal places.
Sine Calculator
Calculate the sine of an angle entered in degrees or radians and locate its normalized angle on the unit circle.
Calculator inputs
Trigonometry
Enter your values
Calculated output
Result summary
Your result will appear here
Complete the required fields and select the calculate button.
Sine valuesin(θ) = opposite ÷ hypotenuse
- sin(θ)
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- Angle in degrees
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- Angle in radians
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- Normalized degrees
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- Unit-circle position
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Confirm the selected angle unit. Degree and radian values that look identical represent different angles.
Table of Contents
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What is Sine Calculator?
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How to Use This Calculator
- Enter the angle. Positive and negative values are allowed, as are angles beyond one full turn.
- Select degrees or radians. The page converts degrees to radians because the underlying trigonometric function uses radians; a radian input is used directly.
- Select Calculate. The result is a number from −1 through 1. Angles that differ by a complete turn have the same sine.
Use enough input precision for the problem. A small angular rounding difference can matter when the sine is multiplied by a long distance or used in several later steps.
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Formula Used
Right triangle: sin θ = opposite side ÷ hypotenuse.
Degree conversion: radians = degrees × π ÷ 180.
Periodicity: sin(θ + 2πk) = sin θ for any integer k. In degrees, one complete period is 360°. The output is unitless because it is a ratio of two lengths.
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Variables Explained
| Item | Meaning |
|---|---|
| θ or α | The angle supplied to the sine function. |
| Degrees | An angle scale with 360 degrees in one complete turn. |
| Radians | An angle scale with 2π radians in one complete turn. |
| Opposite side | The right-triangle side across from the selected acute angle. |
| Hypotenuse | The side opposite the right angle and the triangle’s longest side. |
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Worked Example
Enter 30 and select degrees. Conversion gives 30 × π ÷ 180 = π/6 ≈ 0.523599 radians. On the unit circle, the vertical coordinate at that angle is 0.5, so sin 30° = 0.500000. Entering π/6 with radians selected produces the same sine, subject to the precision of the decimal entered.
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Why Use This Calculator?
A positive result places the unit-circle point above the horizontal axis, while a negative result places it below. Sine is zero at integer multiples of 180° or π radians, reaches 1 at 90° plus full turns, and reaches −1 at 270° plus full turns. Values near these familiar points can be tiny decimals rather than exact zero because computers approximate π and floating-point arithmetic.
In an acute right triangle, the value is a positive ratio smaller than or equal to one. The unit-circle definition extends sine to all real angles, including obtuse, negative and multi-turn angles. To find an unknown side, rearrange the triangle relationship only after confirming which side is opposite and which is the hypotenuse.
This calculator evaluates sine; it does not find an angle from a sine value. That reverse task uses arcsine and has a restricted principal range, with additional solutions possible because sine repeats. Keep the angle-unit setting visible when transferring work between a calculator, drawing and formula.
Quadrants provide a quick sign check. Sine is positive in the first and second quadrants, negative in the third and fourth, and zero on the horizontal axis. Reference angles can then help estimate magnitude. For example, 150° has the same positive sine as 30°, while 210° has the same magnitude with a negative sign. This check catches many unit and sign mistakes before the result enters a longer calculation. If the angle came from measured sides, its uncertainty also carries into the sine value and any distance calculated from it.
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Common Mistakes
- Entering a degree measure while radians are selected, or the reverse.
- Dividing hypotenuse by opposite side instead of opposite by hypotenuse.
- Expecting the sine output to carry degrees or a length unit.
- Reading a very small floating-point result near zero as a meaningful nonzero measurement.
- Using arcsine as though it returned every angle with the requested sine.
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Frequently Asked Questions
What is the difference between degrees and radians?
They are two scales for the same angle. A half-turn is 180 degrees or π radians, and a full turn is 360 degrees or 2π radians.
Why is sine always between −1 and 1?
On the unit circle it is a vertical coordinate, and no point on that circle is more than one unit above or below the centre.
Does sine have a unit?
No. In a triangle it is a ratio of lengths measured in the same unit, so the units cancel.
Why does sin 180° sometimes look slightly different from zero?
The calculation uses finite approximations for π and decimal arithmetic. A tiny residual near an exact special angle is a numerical effect.
Can I enter a negative angle?
Yes. Negative angles rotate in the opposite direction; sine is an odd function, so sin(−θ) = −sin θ.
Can the calculator handle angles above 360°?
Yes. Sine repeats every 360 degrees or 2π radians, so full turns do not change the value.
Is this the same as inverse sine?
No. This page takes an angle and returns its sine. Inverse sine takes a ratio and returns a principal angle.
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