Sine calculator
sin(30°) is 0.5 and sin(90°) is 1: enter an angle in degrees or radians and get its sine, plus the radian measure actually used, so you can check the conversion. Degrees are the default. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Angle
- 30
- Angle unit
- Degrees
- Angle radians
- 0.5235987756
- Sine
- 0.5
Sine is the trigonometric function that maps an angle to the vertical coordinate of the matching point on the unit circle, and to opposite over hypotenuse in a right triangle. People search for a dedicated sine calculator when they need only sin(θ), not a six-function panel that also emits cosine, tangent, and the reciprocal ratios. This capability accepts a finite angle in degrees or radians, converts a degree measure through θ·π/180, evaluates sine, and returns that value together with the radian measure used internally so a client can audit the conversion. Failed validation is not billed.
What sine means on the unit circle and in a triangle
On the unit circle an angle θ is measured from the positive x-axis, counterclockwise for positive values. The point where the terminal ray meets the circle has coordinates (cos θ, sin θ), so sine is exactly the signed height of that point. That geometric reading is why sine is positive in the first and second quadrants, negative in the third and fourth, zero at 0° and 180° (and at every integer multiple of π radians), and equal to plus or minus one at 90° and 270°.
In a right triangle the same number is opposite over hypotenuse for an acute angle, which is how most school courses first meet the word sine before they meet the circle. Radians are the natural parameter for calculus: the derivative of sin θ is cos θ only when θ is in radians, and the arc length on the unit circle is θ itself.
Degrees remain the default in many classrooms, CAD drawings, and navigation problems, so a calculator that cannot accept both units forces a conversion that is easy to get backwards. Sine is defined for every finite real angle — unlike tangent, it has no vertical asymptote — so the only reason a well-formed finite angle would fail is that it exceeds the published absolute-magnitude limit meant to keep floating-point argument reduction meaningful.
Where a dedicated sine calculator earns its keep
Classrooms and tutoring platforms use a sine calculator so learners can check opposite-over-hypotenuse and unit-circle values for arbitrary degree or radian inputs without flipping a calculator into the wrong mode. Content sites that rank for sine calculator and for the terse query sin benefit from a dedicated landing whose free browser path matches the paid automation path byte-for-byte on the same pure module — distinct search intent from a six-function sine-cosine-tangent tool, from a sine-wave modeller, and from an inverse-sine (arcsine) solver. Failed validation does not consume balance.
Keep requests small, pin the rounded sine field in tests, and you get reproducible sine values for homework, LMS plugins, and edge workers without standing up symbolic math infrastructure of your own.
What you can do with it
Classroom and homework checks
Let students submit θ in degrees or radians and verify sin(θ), including textbook values such as sin(30°)=1/2 and sin(π/2)=1.
Headings in scripts and notebooks
Evaluate sine of a stored degree or radian heading in automation without importing a full CAS library or guessing calculator mode.
FAQ
Does this accept degrees and radians?
Yes. Degrees are the default. Degrees are converted with θ·π/180.
What happens if the angle is not a finite number?
Missing, empty, non-numeric, NaN, and infinite angles are rejected and the failure is not billed.
What are sin(30°) and sin(π/2)?
sin(30°) is 1/2. sin(π/2 radians) is 1. sin(0) is 0 and sin(90°) is 1. Residuals from floating-point π collapse to exact zero at 180° and π.
Why is the sine negative for some angles?
Because sine is the height of the matching point on the unit circle. It is positive in the first and second quadrants and negative in the third and fourth, so 270° gives −1 while 90° gives 1.
Does sin(180°) come out as exactly zero?
Yes. Tiny leftovers from the arithmetic are cleaned up, so sin(180°) shows 0 rather than a long decimal that is almost, but not quite, zero.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/math/sin \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"angle":30}'const res = await fetch("https://api.kit.forhosting.com/math/sin", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"angle": 30
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/sin",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"angle": 30
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/sin", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"angle":30}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"angle":30}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/sin", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"angle": 30
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.sin",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_abs_angle | 1000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
An angle that is missing, empty, non-numeric, NaN, or infinite fails with invalid_input instead of leaking a silent NaN that a homework grader might treat as success.
What sine means on the unit circle and in a triangle
This endpoint treats degrees as the default, multiplies a degree input by π/180 before evaluating sine, and leaves a radian input unchanged.
Input contract, units, response shape, and error behaviour
An angle whose absolute value exceeds one trillion is rejected so that a huge wrap-around does not pretend to be a precise sine. POST a JSON body with one required finite number named angle: the measure of θ. Aliases theta and x are accepted so homework scripts and science notebooks can keep a familiar field name without remapping. The optional field angle_unit selects degrees or radians; the default is degrees. Aliases unit and angle_mode are accepted for that field, and the short tokens deg, d, rad, and r also resolve. Each numeric field may arrive as a JSON number or as a numeric string; missing fields, empty strings, booleans, objects, NaN, and Infinity fail with invalid_input naming the field. On success the body echoes angle rounded to twelve decimal places for stable goldens across runtimes, sets angle_unit to the resolved literal degrees or radians, returns angle_radians as the measure actually passed to sine, returns sine as the numeric value (also rounded, with residuals smaller than 1e-15 collapsed to zero so sin(180°) and sin(π) compare as exact zero), and includes formula as a short identity that records the degree-to-radian conversion. Classic checks: angle 30 with the default unit yields sine 0.5; angle π/2 with angle_unit radians yields sine 1; angle 90 degrees yields sine 1; angle 0 yields sine 0. Validation failures do not consume prepaid balance. This endpoint never returns cosine, tangent, or the reciprocal ratios — those belong to a multi-function tool — and it never inverts sine; for an angle from a ratio, use an arcsine calculator.
Where a dedicated sine calculator earns its keep
Exam generators and LMS auto-graders need a deterministic oracle that rejects a non-finite angle as invalid_input instead of writing NaN into a markbook. Physics, robotics, and game-loop notebooks already store headings in one unit or the other; calling a tiny parse API documents the conversion next to the number and avoids pulling a full computer-algebra system for a single sine evaluation.
Integration use cases
Exam and LMS auto-grading
Mark sine items with a deterministic oracle that rejects missing or non-finite angles as invalid_input rather than writing NaN.
Technical questions
How do I compute the sine of an angle?
Send a finite number angle. Optional angle_unit is degrees (default) or radians. The API returns sine, the radian measure used, and a short formula string.
What does the sine calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.