Angle converter
180 degrees are π radians, or 3.14159265359. Convert angles between degrees, radians, gradians, arcminutes, arcseconds and turns, with the value in radians and each step shown for homework, surveying or astronomy. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Value
- 180
- From
- Deg
- To
- Rad
- Result
- 3.1415926536 rad
- Converted
- 3.1415926536
- Value rad
- 3.1415926536
- Factor
- 0.0174532925
A plane angle converter turns one angular magnitude into another unit without memorizing π factors or spreadsheet conversion chains. Enter a finite value plus a source unit and a target unit among degrees, radians, gradians, arcminutes, arcseconds, and turns; the tool returns the converted angle, the intermediate value in radians, the exact unit factor applied, and step-by-step substitution lines you can paste into a lab notebook or homework check. Students moving between calculus radians and geometry degrees, surveyors reading centesimal gradians, astronomers working in arcminutes and arcseconds, and engineers expressing full revolutions as turns all need the same deterministic path.
Which plane-angle units are supported and how conversion works
This capability converts among six plane-angle units that dominate classroom trigonometry, surveying, astronomy, robotics, and mechanical design. Radians are the SI coherent unit and the internal hub: every conversion multiplies the input by how many radians equal one source unit, then divides by how many radians equal one target unit. Degrees use the exact ratio pi over one hundred eighty.
Gradians, also called gons or grades, use pi over two hundred so that a full circle is four hundred gradians—the centesimal system still common on European theodolites. Arcminutes are one sixtieth of a degree; arcseconds are one three thousand six hundredth of a degree, matching catalog angular sizes and telescope plate scales. A turn is one full revolution, equal to two pi radians or three hundred sixty degrees.
Same-unit requests succeed and return the input magnitude with a short message that no change of unit was required.
Practical tips, limits, and when to use this landing
Prefer sending bare numbers for value when you control the client; string numbers are accepted only when they match a strict finite numeric pattern without degree symbols glued to the digits—put the unit in the from field instead. Round-trip checks are straightforward: convert A to B and B back to A and confirm you recover the original within the published twelve-decimal rounding.
When teaching unit analysis, pair classic examples such as one hundred eighty degrees to pi radians, one turn to three hundred sixty degrees, one hundred gradians to ninety degrees, and sixty arcminutes to one degree. Stay inside the absolute range so intermediate radian values cannot overflow. This landing targets people searching for an angle converter, degrees to radians, gradians to degrees, arcseconds to degrees, or turns to radians online; it is not a DMS composite parser, not a solid-angle steradian tool, and not an angular-velocity converter.
What you can do with it
Trigonometry homework and exam checks
Students convert degrees to radians (and back) for calculus identities, then compare deterministic step strings against hand-written π factors before submission.
Surveying and theodolite gradians
Field crews convert gon/gradian instrument readings into degrees or radians for GIS import, CAD plans, and mixed-unit client reports.
Astronomy catalogs and plate scales
Observers convert arcminutes and arcseconds of angular size into degrees or radians for small-angle approximations and instrument FOV planning.
FAQ
How many gradians are in a full circle?
Exactly 400 gradians (gons) equal one turn, 360 degrees, or 2π radians. This tool uses that exact ratio via π/200 radians per gradian.
Is the angle converter free?
The browser tool is free and runs locally.
How do I convert degrees to radians?
Multiply the degrees by π/180. That is why 180 degrees come out as π radians, which the converter shows as 3.14159265359, and why a full turn of 360 degrees is 2π.
How many arcseconds are in one degree?
There are 3,600. An arcminute is one sixtieth of a degree and an arcsecond is one sixtieth of an arcminute, the scale astronomers use for angular sizes and telescope plate scales.
Can I type degrees, minutes and seconds together?
No. The converter takes one number in one unit, so it does not read a combined degrees-minutes-seconds reading. Enter the arcminutes or arcseconds as their own unit instead.
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/conv/angle \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"value":180,"from":"deg","to":"rad"}'const res = await fetch("https://api.kit.forhosting.com/conv/angle", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"value": 180,
"from": "deg",
"to": "rad"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/conv/angle",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"value": 180,
"from": "deg",
"to": "rad"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/conv/angle", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"value":180,"from":"deg","to":"rad"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"value":180,"from":"deg","to":"rad"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/conv/angle", 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,
"from": "deg",
"to": "rad"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "conv.angle",
"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 | 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
Unknown unit names fail with a clear invalid_input error instead of inventing silent wrong factors.
Which plane-angle units are supported and how conversion works
Common aliases are accepted case-insensitively: degree and degrees for deg, radian and radians for rad, gon grade and gradians for grad, arc minute and minute of arc for arcmin, arc second and second of arc for arcsec, and rev revolution cycle or full circle for turn. If the name is not on that list the solver rejects the request with invalid_input naming the bad field and listing supported units, so clients never guess whether a typo produced a wrong number. Negative angles are allowed for directed orientation contexts; absolute magnitude must stay within the published one-trillion limit so intermediate products remain finite in IEEE double precision on the Worker and in the browser.
How to call the API and read the response
Value must be a finite number or a strict numeric string within absolute limits of one trillion. Wire this into dashboards, mobile clients, CAD helpers, or batch jobs that already hold an angle reading and only need a second unit for display, standards compliance, or mixed-unit comparison without shipping floating conversion tables in every app binary. Send a JSON body with three required fields: value (aliases angle, amount, and n), from (aliases from_unit, unit_from, and source), and to (aliases to_unit, unit_to, and target). From and to must resolve to supported unit names after alias normalization. On success the response echoes the rounded input value, canonical from and to labels, result and converted set to the same rounded target magnitude, value_rad as the radian intermediate, unit as the target label, factor as the from-to multiplier, formula as the short equation string, message as an English summary, steps as ordered substitution lines, and supported_units as the six canonical identifiers. Failed validation—missing fields, non-finite numbers, values outside absolute limits, or an unknown unit name—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, limits, and when to use this landing
Normalize display labels on your side if you need locale-specific spellings; this API always returns the short canonical tokens deg, rad, grad, arcmin, arcsec, and turn so automated tests stay stable. Prefer this capability when both endpoints are among the six supported plane-angle units and you need deterministic factors and step strings; if you need degrees-minutes-seconds structured fields, use a DMS converter instead. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when clients deliberately probe unknown unit names.
Technical questions
Which angle units can I convert?
Degrees (deg), radians (rad), gradians (grad/gon), arcminutes (arcmin), arcseconds (arcsec), and turns (turn/rev), including common aliases such as degrees, gon, and revolution.
What happens if I send an unknown unit name?
The API returns invalid_input, names the bad field, and lists the supported units. The failed task is not charged.
Are results deterministic across browser and API?
Yes. Handler and widget share the same lib.js solve path with fixed radian factors and twelve-decimal rounding, so golden examples match production.