Sine of an angle in radians calculator
Get the sine of an angle given in radians: π/2 returns exactly 1, a quarter turn to the top of the unit circle. Negative values, decimals and large angles are all accepted, with no degree step in between. Free in your browser.
- Free
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- Your data stays on your device
Run — free
Worked example
- Angle
- 1.5707963268
- Angle radians
- 1.5707963268
- Sine
- 1
This sine of an angle in radians calculator evaluates one finite real angle and returns its sine as a decimal from minus one to one. Enter the angle directly in radians, including a negative value, a decimal, zero, or scientific notation. The calculator validates missing and nonnumeric input instead of silently inventing a value. It uses a deterministic trigonometric operation with no network calls, randomness, stored state, or clock dependency, making the same input reproducible.
Enter an angle in radians and interpret the result
Provide one angle measured in radians, and the calculator returns the sine as a unitless decimal between minus one and one. Radians measure rotation by comparing arc length with radius: one complete turn is two pi radians, half a turn is pi radians, and a quarter turn is pi divided by two radians. Familiar checkpoints make the result easy to verify.
Zero radians has sine zero, pi divided by two has sine one, pi has a value mathematically equal to zero, and three pi divided by two has sine minus one. Because computers store pi and most decimal values with finite precision, a calculation entered as a decimal approximation of pi may return a tiny residual such as 1.2246467991473532e-16 instead of exact zero. That is normal floating-point behavior, not a different trigonometric rule.
Do not append a degree symbol or the word radians to the field. Supply only the number. Positive and negative inputs are both valid, and there is no artificial restriction to one revolution because sine is defined for every finite real angle.
Understand validation and numeric input rules
Decimal notation, a leading plus or minus sign, and scientific notation are supported. The calculator therefore requires the complete string to describe one finite real number. It does not convert degrees into radians automatically.
If the source angle is in degrees, convert it first by multiplying degrees by pi and dividing by 180, then submit that radian value. Keeping conversion outside this capability makes the unit contract explicit and prevents a caller from accidentally converting an angle twice. Very large finite angles are accepted, although floating-point range reduction can reduce accuracy when an angle is enormous.
For ordinary scientific, engineering, educational, and geometry values, the platform sine operation provides the expected deterministic double-precision result.
Use sine results in geometry, waves, and software
Sine connects an angle to the vertical coordinate of the unit circle, so it appears throughout geometry, physics, signal processing, animation, navigation, and numerical software. In a right triangle, multiply a hypotenuse length by the sine of an acute angle to obtain the side opposite that angle. In a waveform, multiply the sine result by an amplitude and add any vertical offset to calculate a sample.
In two-dimensional graphics, sine often supplies the vertical component of a rotation while cosine supplies the horizontal component. The result itself has no angle unit and always remains within the closed interval from minus one to one, apart from the exact representation choices of floating-point arithmetic. Sine is periodic: adding or subtracting any whole multiple of two pi gives the same mathematical value.
It is also an odd function, meaning the sine of a negative angle is the negative of the sine of the corresponding positive angle. These properties are useful for checking outputs and simplifying test cases.
What you can do with it
Resolve a triangle component
Multiply a known length by the returned sine to calculate its component opposite a radian angle.
Sample a periodic waveform
Evaluate sine at a radian phase before applying amplitude, frequency, or vertical-offset terms.
Check application calculations
Create deterministic expected values for code that passes radian angles to a trigonometric function.
FAQ
What unit should the input use?
Enter the angle in radians. The calculator does not interpret the value as degrees or convert units automatically.
What range can the sine result have?
The result is a unitless decimal in the closed interval from minus one to one.
Why is the sine of a pi approximation not exactly zero?
Computers store decimal approximations with finite precision, so expected exact zeros can appear as extremely small residual values.
Which inputs are rejected?
Missing, empty, nonnumeric, NaN, and infinite values are rejected. The angle must be one finite real number.
What is the sine of pi over two?
The sine of π/2 is 1. A quarter turn places the point at the top of the unit circle, where the vertical coordinate, which is the sine, reaches its highest value.
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/trig/sin-radians \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"angle":1.5707963267948966}'const res = await fetch("https://api.kit.forhosting.com/trig/sin-radians", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"angle": 1.5707963267948966
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/trig/sin-radians",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"angle": 1.5707963267948966
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/trig/sin-radians", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"angle":1.5707963267948966}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"angle":1.5707963267948966}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/trig/sin-radians", 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": 1.5707963267948966
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "trig.sin_radians",
"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
Automated API requests cost $0.002 each and process one angle per request.
Enter an angle in radians and interpret the result
The response includes the parsed angle in `angle_radians` and the computed decimal in `sine`, so an automated caller can confirm which numeric value was evaluated.
Understand validation and numeric input rules
The required field is `angle`. A JSON number is the clearest input for API use, while a strict numeric string is also accepted to support text-oriented forms. Missing values, empty strings, labels, unit suffixes, NaN, positive infinity, and negative infinity are rejected with an `invalid_input` error. This matters because silently converting an empty field to zero would return a plausible sine of zero and hide incomplete data. Likewise, loosely parsing a value such as `1.2 radians` could discard the suffix and make inconsistent input appear valid.
Use sine results in geometry, waves, and software
The capability performs one calculation per request for $0.002. It has no remote dependencies and does not retain input, so it is suitable for reproducible examples, spreadsheet replacements, server-side validation, classroom checks, and lightweight computation pipelines where a narrowly defined radians-only operation is preferable to a broader multi-function trigonometry tool.
Technical questions
How much does an API request cost?
Each request costs $0.002 and evaluates one angle as one item.