Radius of a circle
Get the radius of a circle from the distance around it: a circumference of 2π gives a radius of 1 and a diameter of 2, and one of 10π gives a radius of 5. Handy right after wrapping a tape measure around something round. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Circumference
- 6.2831853072
- Circumference
- 6.2831853072
- Radius
- 1
- Diameter
- 2
The radius of a circle is the fixed distance from the center to every point on the rim. When the number you already have is the circumference—the full path length around that rim—this calculator recovers the radius with the exact rearrangement r equals circumference over two π. No network calls, no random sampling, and no wall-clock dependence—just r = C / (2π) on the number you provide.
What the radius of a circle is and the formula r = C / (2π)
The radius of a circle is the single length that places every point of the boundary at a fixed distance from the center. Circumference is the one-dimensional measure of that closed boundary: the distance you travel if you walk once around the edge and return to the start. In Euclidean plane geometry the ratio of circumference to diameter is the constant π, so C equals π times the diameter, or equivalently C equals two times π times the radius.
Solving that identity for the unknown radius is a single division: r equals C over two π. The inversion is exact for a perfect circle; it is not an approximation, not a numerical root finder, and it does not depend on the location of the center or on a general-form equation. Double the circumference and you double the radius.
Classic checks include a circumference of two π, which yields radius one (the unit circle); a circumference of ten π, which yields radius five; and a circumference of ten, which yields radius five over π after ordinary floating arithmetic. This capability requires a strictly positive circumference, so a missing placeholder zero is never silently turned into radius zero, and a negative path length is never folded into an absolute value that would hide a data-entry bug.
Diameter is always twice the recovered radius; the response includes that companion so a single call covers the two linear sizes most homework and design forms ask for after a tape measure. Because the formula is a single division by a known constant, there is no iteration, no sampling, no mesh, and no dependence on coordinate frames: you do not need three points on the circle, a central angle, or the enclosed area. When you need radius from area, use the dedicated radius-from-area tool.
When you already know the radius and want the full circumference, use the inverse C equals two π r landing. This page is for people who measured or were given the circumference and want the radius of a circle with a reproducible contract.
Where a radius-of-a-circle calculator earns its keep
Secondary-school and college plane-geometry courses constantly ask for the radius of a circle given the circumference, often as the inverse of the two-π-r product on the same problem set; a trusted calculator with a strict positive-circumference gate speeds homework grading and removes spreadsheet mistakes where someone divides by π instead of two π or confuses radius with diameter.
Construction, civil engineering, and landscaping workflows often start from a measured tape wrap around a tank, planter, fountain, or circular pad, then need the radius for formwork, radial set-out, and material estimates; the same division feeds layout when only the perimeter is on the plan. Game, graphics, and CAD libraries store path lengths or ring perimeters and need radii for drawing disks and collision circles; deterministic radius recovery supports layout math and proxies without a full computational-geometry stack.
Prefer this tool when you already know the circumference and need the radius. Prefer the circumference-from-radius landing when the known quantity is r, and the radius-from-area landing when only enclosed area is known. A general multi-field circle converter answers a different keyword.
What you can do with it
Tape-wrap set-out on site
Turn a measured circular perimeter into radius for formwork, radial layout, fencing arcs, and material lists without a separate spreadsheet formula.
FAQ
How do I find the radius of a circle from its circumference?
Divide the circumference by two π: r = C / (2π).
Why are zero and negative circumferences rejected?
A geometric circumference is a strictly positive path length.
How is this different from radius from area?
Radius from area uses r = √(A/π). This tool uses r = C / (2π) from circumference. Send the quantity you actually know; the two landings do not accept each other's primary field.
What does the radius-of-a-circle calculator cost?
The browser tool is free and runs locally.
What is the radius of a circle with a circumference of 10?
About 1.591549430919. You divide 10 by two times π, the same single step used for any circumference. The diameter, twice that radius, is shown next to it so you do not have to work it out.
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/radius-of-a-circle \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"circumference":6.283185307179586}'const res = await fetch("https://api.kit.forhosting.com/math/radius-of-a-circle", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"circumference": 6.283185307179586
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/radius-of-a-circle",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"circumference": 6.283185307179586
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/radius-of-a-circle", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"circumference":6.283185307179586}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"circumference":6.283185307179586}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/radius-of-a-circle", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"circumference": 6.283185307179586
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.radius_of_a_circle",
"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
A missing, non-finite, or non-positive circumference is rejected with a clear invalid_input error instead of a silent nonsense radius.
What the radius of a circle is and the formula r = C / (2π)
Units of length are whatever you pass—metres, inches, millimetres, or game units—as long as you interpret radius in that same unit; the API does not convert linear units for you.
How to call the API and what comes back
Example: circumference equal to two π yields radius one and diameter two. Missing circumference likewise fails without billing. Keep circumference finite so the quotient stays representable; extremely large values that overflow double precision surface as a non-finite result and are rejected with a clear error. POST a JSON body with the required field circumference—a finite number strictly greater than zero. Numeric strings such as "10" or "6.283185307179586" are coerced when they parse as finite numbers; empty strings, non-numeric text, Infinity, and NaN fail with invalid_input naming the field. On success the response echoes circumference after stable twelve-decimal rounding; returns radius as the primary result from r equals C over two π; and includes diameter as two r plus a formula string r = C / (2π) so clients can log which closed form was used. Circumference ten yields radius about 1.591549430919 after twelve-decimal rounding, matching hand calculation with π from IEEE double precision. A non-positive circumference—for instance zero or negative three—returns invalid_input with a message that circumference must be a positive number; those validation failures are never charged against prepaid balance. Pricing is a flat $0.002 per successful request with unit item. Use the endpoint from geometry homework pipelines, CNC and packaging takeoff scripts, sports-field and track layout helpers, interview-prep sandboxes, or any workflow that needs a reproducible radius of a circle from a measured perimeter without installing a computer-algebra package on every machine. Pair the numeric result with your own unit labels; this endpoint solves for radius only and does not emit plots or convert metres to inches.
Where a radius-of-a-circle calculator earns its keep
Because this capability is a pure parse engine, failed validation does not consume balance and successful runs stay at $0.002 per item. This landing is not a full circle-equation solver from general-form coefficients, not an arc-length tool from a central angle, and not a great-circle distance calculator on the Earth. Pin the rounded JSON fields in tests so Worker and browser goldens stay byte-stable across runtimes.
Integration use cases
Homework checks for r = C / (2π)
Give students a circumference; compare their hand-computed radius (and optional diameter) against a deterministic API or free browser result.
Disks in games and CAD
Convert a stored ring perimeter into radius (and diameter) for drawing, packing, and collision proxies in the browser or via API.
Technical questions
Is this the same as a circle circumference calculator?
No. That inverse landing takes radius and returns C = 2πr. This page takes circumference and returns the radius of a circle. Different search intent, different contract.