Sin degrees calculator
The sine of 30 degrees is 0.5, but the sine of 30 radians is about −0.988: this calculator always converts your degrees first. Enter any angle in degrees, negative or above 360°, and get its sine between −1 and 1. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Angle
- 30
- Radians
- 0.5235987756
- Sine
- 0.5
- Expression
- sin(30°)
The sine of an angle given in degrees is the vertical coordinate of that angle on the unit circle, after the measure is converted to radians. Most programming libraries expose only a sine of radians, so a student, surveyor, CNC script, or waveform generator that thinks in degrees must apply theta times pi over 180 first or every opposite-over-hypotenuse ratio comes out wrong. This calculator accepts a single finite angle in degrees, converts it to radians, and returns the sine in the closed interval from minus one to one. Identities you can pin in tests include sine of zero degrees equals zero, sine of thirty degrees equals one half, and sine of ninety degrees equals one.
What sine of degrees means and why the conversion to radians comes first
Sine is the odd, three-hundred-sixty-degree-periodic function that maps an angle to the signed height of the corresponding point on the unit circle. When the angle is written in degrees, that height is not the library sine of the raw number: every mainstream runtime implements the analytic sine of a real argument in radians, so thirty must become pi over six before the series or the hardware instruction runs.
Forgetting the conversion is the most common classroom bug — sine of thirty radians is about minus zero point nine eight eight, not one half. The conversion is the exact identity that radians equal degrees times pi over one hundred eighty. After conversion the value always lands in the closed interval from minus one to one; a result outside that interval is floating-point noise and this implementation clamps it.
Special angles have textbook exact values that students expect without a trail of nines: sine of zero and one hundred eighty degrees is zero, sine of ninety degrees is one, sine of two hundred seventy degrees is minus one, sine of thirty and one hundred fifty degrees is one half, sine of forty-five and one hundred thirty-five degrees is root two over two, and sine of sixty and one hundred twenty degrees is root three over two.
Negative degrees are legal and use oddness: sine of minus theta equals minus sine of theta. Angles larger than a full turn remain valid; they are reduced modulo three hundred sixty degrees only when matching those special values, while the echoed input keeps the original measure. Related searches such as a six-function sine-cosine-tangent calculator, an arcsine that returns degrees, or a degrees-to-radians converter that never evaluates sine, are different intents.
Here the contract is the scalar sine of one finite degree measure.
What you enter, what comes back, and errors
There is no extra unit switch: this landing is the degrees path on purpose, so a caller who already holds radians should convert them or use a radians-first calculator instead of hoping a hidden flag will reinterpret the number. On success the body echoes the cleaned angle in degrees, returns radians as the converted argument, and returns sine as the primary result in the closed interval from minus one to one.
Example: angle thirty yields sine one half, because thirty degrees is pi over six radians and the sine of that argument is exactly one half. Example: angle ninety yields sine one. Example: angle zero yields sine zero.
Example: angle minus thirty yields sine minus one half by oddness. For all six trigonometric functions, or for converting a degree measure without evaluating sine, use the dedicated pages that match those searches.
Where a sine-of-degrees calculator earns its keep
Classrooms and tutoring platforms use a sin degrees calculator so learners can check sine of an arbitrary classroom angle without mixing degrees and radians or copying a calculator mode they cannot see. Exam generators need a deterministic oracle that marks non-finite tokens as invalid instead of silently returning NaN, which many language runtimes do and which a buggy grader might treat as a number. Failed validation does not consume balance.
Keep requests small, pin the rounded sine in tests, and you get a reproducible sine of degrees for homework, LMS plugins, and edge workers without standing up symbolic math infrastructure of your own. Related searches such as inverse sine in degrees, a unit-circle explorer, or a full sine-cosine-tangent table are different problems and are served by other pages; this contract stays on sine of one finite degree measure so the landing matches what a student actually types when the question is simply sin of this many degrees.
What you can do with it
Classroom and homework checks
Let students submit an angle in degrees and verify sin(θ°), including the identities sin(0°)=0, sin(30°)=1/2, and sin(90°)=1, against textbook methods.
Exam and LMS auto-grading
Mark sine-in-degrees items with a deterministic oracle that rejects non-finite angles and never invents NaN as a successful sine.
Headings, sprites, and resolved components
Convert a degree heading to the opposite-over-hypotenuse ratio in robotics, surveying, or game scripts without importing a full computer-algebra library.
FAQ
Why convert to radians first instead of calling sine on the degree number?
Library sine implements the analytic function of a real argument in radians. Sine of 30 radians is about -0.988, not 1/2. This calculator always converts first so a degree input cannot be misread as radians.
What happens if the angle is not a finite number?
Missing fields, empty strings, non-numeric text, NaN, and Infinity are rejected and are not billed.
Is sine defined at 0°, 90°, and 180°?
Yes. Sine of 0° and 180° is 0, and sine of 90° is 1. Unlike a six-function calculator that must refuse those angles because tangent or cosecant blows up, this page returns the sine at every finite degree measure.
Can I use negative angles or angles above 360°?
Yes. A negative angle gives the opposite sine, since sin(−θ) equals −sin θ, and an angle larger than a full turn is still valid; the angle you typed is shown back exactly as entered.
Which angles give exact textbook values?
30° and 150° give one half, 45° and 135° give √2/2, 60° and 120° give √3/2, 90° gives 1 and 270° gives −1. They come out clean, without a trail of nines.
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-degrees \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"angle":30}'const res = await fetch("https://api.kit.forhosting.com/math/sin-degrees", {
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-degrees",
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-degrees", 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-degrees", 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_degrees",
"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.
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
Non-finite tokens such as NaN and Infinity fail with invalid_input so a homework script never treats a missing sine as a successful zero.
What sine of degrees means and why the conversion to radians comes first
This page exists for the search that says sin degrees or sine of an angle in degrees: convert first, then evaluate.
Input contract, response shape, and error behaviour
POST a JSON body with the required field angle, a finite real number of degrees. The field may arrive as a JSON number or as a numeric string in decimal or scientific notation; aliases degrees, deg, theta, and x are accepted when angle is omitted. Missing fields, empty strings, non-numeric text, NaN, and Infinity fail with invalid_input naming the field and are not billed. A formula string restates sin of theta degrees equals sin of theta times pi over one hundred eighty, a compact expression such as sin(30°), and a one-line message complete the payload. Pair the payload with your own labels; this endpoint does not emit plots, a cosine or tangent companion, or a step-by-step lesson beyond the formula field.
Where a sine-of-degrees calculator earns its keep
Surveying, robotics, and game scripts store headings in degrees and still need the opposite-over-hypotenuse ratio for a rise, a sprite offset, or a resolved force; calling a tiny parse API avoids pulling a computer-algebra system for one conversion and one sine.
Technical questions
How do I compute the sine of an angle in degrees?
Send a finite number in the field angle (aliases degrees, deg, theta, x). The API converts degrees to radians with θ × π / 180 and returns sine in the closed interval from -1 to 1.
What does the sin degrees calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.