Sine CalculatorFree online math calculator — instant results, no sign-up
Calculate the sine of an angle in degrees.
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About the Sine Calculator
The Sine Calculator calculates the sine of an angle entered in degrees. It converts the angle to radians for evaluation and returns a dimensionless value between −1 and 1. With the default angle of 30 degrees, the result is 0.5.
- Angle (degrees)
- The angle whose sine you want to calculate, measured in degrees and set to 30 by default.
Formula and method
r = θ × π / 180; y = sin(r) = sin(θ × π / 180). For θ = 30°, r = π/6 radians and y = sin(π/6) = 0.5.
- θThe input angle measured in degrees.
- rThe equivalent angle in radians.
- πPi, the mathematical constant used to convert degrees to radians.
- yThe dimensionless sine value displayed as the result.
Multiply the angle in degrees by π/180 to obtain its radian equivalent, then evaluate the sine of that radian angle. For the default input, 30 × π/180 = π/6, and sin(π/6) = 0.5.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Angle (degrees)30
Results
- Result0.5
How to use the Sine Calculator
- 1Enter your angle in the Angle (degrees) field, or leave the default value of 30.
- 2Confirm that your input is in degrees rather than radians.
- 3Run the calculation to evaluate the sine of the entered angle.
- 4Read the Result row; for the default angle of 30 degrees, it shows 0.5.
Reading your result
The Result row shows the sine of the input angle, with no units. For 30 degrees, Result = 0.5 means that the corresponding point on the unit circle has a vertical coordinate of 0.5. In a right triangle with a 30-degree angle, it also means the opposite side is 0.5 times the hypotenuse. A negative result indicates a point below the unit circle's horizontal axis.
Limitations
The input is interpreted as degrees, not radians. Sine is defined for every finite real angle and always lies between −1 and 1, but numerical evaluation and display rounding can introduce small differences from exact values. Very large angle inputs may lose precision in finite-precision arithmetic. A sine value alone does not uniquely identify an angle because sine repeats and different angles can share the same value.
Common questions
Why does entering 30 give a sine result of 0.5?+
The calculator interprets 30 as degrees, equivalent to π/6 radians. The exact sine of that angle is 1/2, or 0.5.
Can I enter an angle in radians for the sine function?+
This calculator expects degrees. Convert a radian angle to degrees by multiplying it by 180/π before entering it.
How does sine behave for negative angles or angles beyond a full turn?+
Sine satisfies sin(−θ) = −sin(θ) and repeats every 360 degrees. Adding or subtracting a full turn therefore leaves the sine value unchanged.
Does a result of 0.5 mean the angle is uniquely determined?+
No. Although the default angle of 30 degrees gives 0.5, sine is periodic and has reflection symmetry, so multiple angles produce that same result. This calculator evaluates sine from an angle; it does not solve for all possible angles from a sine value.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.