ForHosting KIT · Developer Utilities

Circumference to Radius Calculator

The circumference to radius calculator takes the length of a circle's boundary and returns the distance from its centre to its edge, using the exact relationship r = C / (2 * pi).

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

You send one number, you get one number back, in the same unit you started with: give it millimetres and the answer is in millimetres, give it feet and the answer is in feet. This is the inverse of the familiar two pi r formula, solved for the radius so you never have to rearrange it by hand. There is no rounding policy to configure and no hidden approximation beyond the double-precision value of pi baked into every modern runtime, so the result is deterministic and reproducible anywhere. The same code that runs on our edge runs free in your browser, which means the free web tool and the paid API never disagree. Use it when the boundary is what you can measure — a rolled tape around a pipe, a wheel's rollout, a ring's inner length — and the radius is what the drawing or the machine actually needs.

Why start from the circumference

Geometry class teaches the radius first and derives everything else from it, but in the workshop and the field the circumference is often the only dimension you can actually touch. You wrap a tape around a barrel, you roll a wheel one full turn along the ground, you measure the inner length of a gasket or the strip that closes a ring. In all of those cases the boundary length is the measurement and the radius is the unknown, yet most calculators ask for the radius and give you the circumference, forcing you to invert the formula by hand with a division that is easy to misplace. The circumference to radius calculator is built around the measured reality: it accepts the circumference exactly as read and divides it by two pi, returning the radius in the same unit. If you happen to hold the diameter instead, halve it and you already have the radius; if you hold the circumference and want the diameter back, that sibling inverse problem belongs to a different capability. Keeping one input and one job makes the contract trivial to test: a positive finite number goes in, the radius comes out, and anything else — zero, a negative value, a missing field, a string that is not a number — is rejected as invalid input before any arithmetic happens.

How the number is computed

The computation is one division: the circumference, validated as a positive finite number, divided by two times Math.PI, the double-precision constant available in every JavaScript engine. There is no series expansion, no lookup table and no iterative approximation, so the answer cannot drift between runs, between servers or between the browser and the API. The result is then rounded to six decimal places before it is returned. That rounding is a deliberate stability choice, not a precision claim: raw floating-point division can produce a last-digit wobble across CPUs, and a stored golden example compared byte to byte would fail on a different machine for a reason that has nothing to do with correctness. Six decimals is far beyond what any physical measurement of a circumference justifies — a tape read to a tenth of a millimetre constrains the radius far more than pi does. Units pass through untouched: the tool never converts, so whatever unit your circumference carries is the unit of the answer, and converting units beforehand is your call. A numeric string such as "31.415927" is accepted and coerced, which keeps form submissions and CSV-driven pipelines simple without loosening validation.

Where it fits in real work

Single-value geometry sounds trivial until it sits inside a pipeline that consumes thousands of measurements. A rolling-line station that turns rollout distances into wheel radii, a machining planner that derives the turning radius from a measured part perimeter, a fit-check that compares a measured ring length against a tolerance band expressed as a radius — all of them call this endpoint as a deterministic step they never have to reimplement or re-test. Because the capability is a pure parse worker with no network calls, no secrets and no shared state, it behaves identically under one request or ten thousand, and its cost is a flat $0.002 per request with no per-unit surcharge. The free browser version runs the same module, so an engineer can sanity-check a value by hand before wiring the API into production and trust that both paths return the same number. Input that is not a positive finite number fails with an invalid input error and is not charged, which makes the endpoint safe to expose directly to untrusted form submissions, spreadsheets and scraped data feeds.

What you can do with it

Recover a wheel radius from rollout

Roll a wheel one full turn, measure the distance travelled, and get the effective rolling radius for a drivetrain or odometer calibration.

Size a bore from a ring's inner length

Turn the measured inner circumference of a gasket or seal into the radius a mating bore or shaft must match.

Feed geometry pipelines from tape readings

Convert thousands of wrap-around tape measurements into radii for quoting, nesting or tolerance checks without hand-written math.

FAQ

What does it cost?

$0.002 per request, with no per-unit surcharge. It is also free in the browser, running the exact same code.

What input does it accept?

A single field, circumference, as a positive finite number or a numeric string. Zero, negatives, non-numbers and missing values are rejected as invalid input.

What unit is the result in?

The same unit as the circumference you sent. The tool never converts units; it only divides by two pi.

How accurate is the result?

It uses the double-precision value of pi and rounds to six decimal places, far beyond the accuracy of any physical circumference measurement.

Can I get the diameter instead?

The radius is returned; double it for the diameter, or use a circle diameter calculator from the catalogue that outputs the diameter directly.

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

POSThttps://api.kit.forhosting.com/math/circumference-to-radius

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/circumference-to-radius \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"circumference":31.415927}'

const res = await fetch("https://api.kit.forhosting.com/math/circumference-to-radius", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "circumference": 31.415927
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/math/circumference-to-radius",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "circumference": 31.415927
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/circumference-to-radius", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"circumference":31.415927}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"circumference":31.415927}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/circumference-to-radius", 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": 31.415927
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "math.circumference_to_radius",
  "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

Per request$0.002

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.

Read the full KIT documentation →