Sine Calculator
Find the sine of any angle in degrees or radians instantly, with the cosecant too — for triangles and waves.
sin(30°) = 0.5
sin(30°)
0.5
Cosecant (1/sin)
2
Only defined when sin θ ≠ 0
Sine is the ratio of the opposite side to the hypotenuse in a right triangle. Values always lie between −1 and 1.
Last updated: August 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
Sine is the workhorse of height-and-distance problems in India, from ladder angles to kite-string altitudes and tower heights. A mistry checking how high a bamboo scaffold rises at a given lean, a surveyor measuring a temple's height from a fixed baseline, and a drone pilot estimating clearance over a building all multiply a known length by a sine value. Electricians use it to compute the vertical drop of a cable pulled at an angle, and tilers use it when cutting skirting for sloped stair strings. Students preparing for board exams and JEE repeatedly evaluate sine at 0°, 30°, 45°, 60° and 90° — the five standard values this tool returns instantly. In radians mode it supports physics work with waves, oscillations and simple harmonic motion, where angles are naturally measured in radians.
How to Use This Calculator
- Step 1: Choose whether your angle is in degrees or radians.
- Step 2: Enter the angle, such as 30 for 30 degrees or 0.5 for half a radian.
- Step 3: Read the sine value, which always lies between −1 and 1.
- Step 4: The cosecant (1 divided by sine) is shown alongside when it is defined.
Worked Example
A painter in Jaipur leans a 5 m ladder against a wall at 30 degrees. The sine of 30° is exactly 0.5, so the top of the ladder reaches 5 × 0.5 = 2.5 m up the wall. In radians, the same angle is π/6, and entering that confirms sin(π/6) = 0.5. For a 45-degree angle the sine is about 0.7071, meaning a 5 m ladder reaches about 3.54 m. The calculator's sine of 90° returns 1, the maximum possible value, which matches a ladder stood vertically against the wall.
Tips and Common Mistakes
- •Tip 1: Degrees and radians are different units — sin(30) in radians is about −0.988, so keep the unit selector consistent.
- •Tip 2: For height problems, multiply the ladder or rod length by sin(angle) — the tool gives you the ratio.
- •Tip 3: Sine repeats every 360°, so sin(390°) equals sin(30°), both 0.5.
- ✗Mistake 1: Entering degrees while the calculator is set to radians, which silently changes the answer.
- ✗Mistake 2: Expecting a sine above 1 — the function never exceeds 1 for any real angle.
Frequently Asked Questions
What is the sine of an angle?
In a right triangle, sine is the ratio of the side opposite the angle to the hypotenuse. sin(30°) = 0.5 means the opposite side is exactly half the hypotenuse.
How do I convert degrees to radians for sine?
Multiply the degree value by π/180. So 30° becomes π/6 radians, and sin(π/6) = sin(30°) = 0.5. The calculator does this conversion automatically when you select radians.
What is the range of the sine function?
Sine always returns a value between −1 and 1 for any angle. It reaches 1 at 90°, 0 at 0° and 180°, and −1 at 270°, repeating every 360°.
When would I use sine in real life?
For heights and distances: a 5 m ladder leaning at 30° reaches 5 × sin(30°) = 2.5 m up the wall. It is also used for waves, sound, AC electricity and satellite geometry.
What is cosecant?
Cosecant is the reciprocal of sine: 1/sin(θ). Since sin(30°) = 0.5, cosecant is 2. It is undefined when sine is 0, such as at 0° and 180°, because division by zero has no meaning.
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