Degrees to radians converter
180 degrees is exactly π radians, about 3.1415926536, and the converter shows both the decimal and the π form. It also works in reverse, from radians to degrees, including negative angles and angles beyond a full turn. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Value
- 180
- Input value
- 180
- Input unit
- degrees
- Degrees
- 180
- Radians
- 3.1415926536
The degrees to radians converter answers a core trigonometry need with one deterministic contract: given a finite real angle and its unit, what is the matching measure in the other unit, and can the radian form be written as a clean multiple of π? Everyday checkpoints include zero staying zero, thirty degrees becoming π over six, forty-five becoming π over four, sixty becoming π over three, ninety becoming π over two, one hundred eighty becoming π, and three hundred sixty becoming two π. The reverse path recovers degrees from a radian input with the same formulas inverted. The engine never samples randomness, never reads the clock, and never calls the network.
Why degrees and radians coexist and how the formulas relate
Degrees divide a full turn into three hundred sixty equal parts, a convention that grew from astronomy and surveying and still dominates classroom protractors, maps, and many engineering drawings. Radians measure an angle by the arc length it subtends on the unit circle, so a full turn is two π and a right angle is π over two. That arc definition is the natural unit for calculus, series expansions, complex exponentials, and almost every programming language math library: Math.sin, Math.cos, and friends expect radians unless a library explicitly documents degrees.
Converting both ways therefore shows up whenever a human-facing diagram meets machine code. The exact linear maps are simple and deterministic: radians equal degrees times π over one hundred eighty, and degrees equal radians times one hundred eighty over π. Because the factors are constants, the conversion is bijective on the reals: every finite degree value has exactly one radian image and back again, including negatives and angles larger than a full turn.
This tool applies those formulas without mode switches that calculators sometimes hide.
Where degree–radian conversion fits in study, design, and automation
Students meet this conversion when unit-circle tables list both columns, when physics problems switch between elevation in degrees and angular velocity in radians per second, and when programming exercises insist that trigonometric functions receive radians. Teachers can generate answer keys that show degrees, radians, and the textbook π form without trusting opaque calculator apps that stay stuck in the wrong mode.
Game developers, CAD users, and robotics hobbyists often store orientations in degrees for human editing but feed radians into engines and solvers; converting in one place with a shared contract reduces silent off-by-π bugs. Surveyors and architects still annotate drawings in degrees while analysis scripts prefer radians for arc length and small-angle approximations. Data pipelines that normalize sensor headings sometimes need both representations and a stable rejection path for non-numeric cells before a downstream step assumes a float.
Pair it with inverse trigonometric helpers when you need angles from ratios, with triangle solvers when you need full side-angle completions, and with other analytic tools when your workflow mixes pure math with document or data steps.
What you can do with it
Homework and exam unit conversion
Convert worksheet angles between degrees and radians and match textbook multiples of π without guessing calculator mode.
Teaching unit circle and code libraries
Show students how the same angle appears in degrees, radians, and π form while they change inputs live in the browser at no cost.
FAQ
What does the degrees to radians converter cost?
It is free in your browser on this page.
Can I convert radians back to degrees?
Yes. Set from to radians (or rad). The response always includes both degrees and radians for either direction.
What happens if value is not a number?
Missing fields, non-numeric strings, Infinity, and NaN are rejected rather than coerced.
Is the algorithm randomized?
No. It uses deterministic multiplies by π constants and a fixed rationalization pass. The same value, from, and precision always yield the same result.
How many radians are in 180 degrees?
Exactly π, which is about 3.1415926536. To get radians from any degree value, multiply it by π and divide by 180; the result also shows the clean π form when the angle allows it.
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/deg-to-rad \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"value":180}'const res = await fetch("https://api.kit.forhosting.com/trig/deg-to-rad", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"value": 180
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/trig/deg-to-rad",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"value": 180
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/trig/deg-to-rad", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"value":180}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"value":180}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/trig/deg-to-rad", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"value": 180
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "trig.deg_to_rad",
"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-numeric values, missing fields, Infinity, and NaN fail with invalid_input instead of inventing a number. Explore free in the browser for homework, CAD checks, and teaching demos, or call the API at $0.002 per successful request when scripts and pipelines need reproducible unit conversions.
Why degrees and radians coexist and how the formulas relate
When the degree measure yields a simple rational multiple of π, the response also labels the angle as a compact as_pi string such as π over six or three π over two, so students and reviewers can match textbook answers without rounding noise. When the ratio is not a short rational, as_pi may be null while degrees and radians still report the precise floating-point conversion at the requested precision. That honesty keeps automated tests stable and prevents fake exactness on ugly angles.
How inputs are read and how the multiple-of-π form is built
Internally the engine multiplies by π over one hundred eighty or one hundred eighty over π, rounds degrees and radians to the requested precision, and attempts to express the radian measure as a reduced fraction times π by rationalizing the coefficient degrees over one hundred eighty with a bounded denominator search. The required field is value as a JSON number, with aliases angle, x, and number so forms, query strings, and spreadsheet columns can reuse one contract. Optional from, with aliases unit and input_unit, accepts degrees, radians, deg, or rad and defaults to degrees so the primary SEO journey is degrees to radians without extra fields. Decimal strings such as "180" or "-45.5" are accepted after trim; hex prefixes, empty strings, and non-numeric tokens are rejected with invalid_input because the specification forbids inventing angles from garbage. Optional precision, with aliases decimals and dp, is an integer from zero through fifteen that defaults to ten decimal places on the numeric fields in the response. Classic school angles therefore print as_pi equal to π over six, π over four, π over three, π over two, π, three π over two, or two π rather than a long decimal alone. The response always echoes input_value and input_unit, returns both degrees and radians, includes pi_coefficient when available, and attaches the formula string for the direction used.
Where degree–radian conversion fits in study, design, and automation
On this page the work runs entirely in your browser; through the API each successful conversion costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.
Integration use cases
Deterministic library and CI fixtures
Generate reproducible degree–radian checkpoints for unit tests, property checks, and CI assertions without static tables.
Technical questions
What is the as_pi field?
When the angle is a simple rational multiple of π, as_pi is a compact label such as π/6 or 3π/2. Otherwise it may be null while degrees and radians still report the conversion.