Circle perimeter calculator
Find the length of a circle's edge from its radius alone, so a radius of 5 gives a perimeter of 31.415927, in the same unit you measured in. Ready for edging strip, gaskets, a round rug or weatherstripping a round window. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Radius
- 5
- Perimeter
- 31.415927
You send one number, you get one number back, with controlled rounding so the result is stable across machines.
What the perimeter of a circle actually is
The perimeter of a circle is the distance you would travel if you walked all the way around its edge once. Mathematicians usually call it the circumference, but the word perimeter means the same thing here: the total length of the closed curve that bounds the shape. It is not the area, which measures the surface enclosed inside, and it is not the diameter, which is the straight line across the middle.
Because a circle is perfectly symmetric, its perimeter depends on a single measurement: the radius, the distance from the center to any point on the edge. Double the radius, multiply by π, and you have the perimeter. That relationship, written 2·π·r, is exact — π is the same constant for every circle that exists, from a coin to a planet's orbit.
The circle perimeter calculator on this page applies that formula directly, so there is no estimation, no lookup table and no approximation beyond the rounding you choose for the final figure.
How the calculation is done
You send the radius as a positive number, in whatever unit you are working in — millimeters, inches, meters — and the result comes back in that same unit, because the formula multiplies a length by a dimensionless constant. The radius must be a real, finite number greater than zero; a missing value, text, zero or a negative number is rejected with a clear error before any calculation happens, and rejected requests are not charged.
Internally the perimeter is computed as 2·π·r with double-precision arithmetic and then rounded half-up to the number of decimal places you request — six by default, configurable from zero to twelve. Rounding half-up rather than leaving the raw float matters for one practical reason: the same input produces byte-for-byte the same output on any machine, which is what lets you store the result, compare it in tests, or print it on a specification sheet without surprises.
If you need more precision for a later computation, ask for more decimals instead of rounding twice.
When you will reach for it
Any time a round object meets a linear material, you need this number. How much edging strip does a circular rug need? That is the perimeter.
How many times does a wheel of a given radius turn over a known distance? Distance divided by perimeter. How long a belt drives two pulleys, how much weatherstripping seals a round window, how much ribbon wraps a cake — all the same formula.
If what you have is the diameter rather than the radius, halve it first; if you also need the area or work from other givens, see the companion circle capabilities in the catalog.
What you can do with it
Material edging for round pieces
Work out how much trim, piping or veneer strip a circular table top, rug or mirror needs before ordering material.
Wheel and pulley rotations
Convert between distance traveled and number of turns by dividing the distance by the wheel's perimeter.
FAQ
Is the perimeter the same as the circumference?
Yes. Circumference is simply the traditional name for the perimeter of a circle; both are computed as 2·π·r.
Which unit is the result in?
The same unit as the radius you sent. The formula multiplies a length by a constant, so no unit conversion happens.
Can I control the precision of the result?
Yes. The optional decimals field sets the number of decimal places, from 0 to 12; it defaults to 6 and uses half-up rounding.
What if I know the diameter instead of the radius?
Divide it by two and send that as the radius — the perimeter is then π times the diameter you started with.
How many times does a wheel turn over a given distance?
Divide the distance by the wheel's perimeter. Each full turn covers exactly one perimeter, so a wheel with a radius of 5 moves 31.415927 per turn, in whatever unit the radius was measured in.
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/circle-perimeter \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"radius":5}'const res = await fetch("https://api.kit.forhosting.com/math/circle-perimeter", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"radius": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/circle-perimeter",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"radius": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/circle-perimeter", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"radius":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"radius":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/circle-perimeter", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"radius": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.circle_perimeter",
"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
The circle perimeter API takes the radius of a circle and returns its perimeter — the length of the boundary, also known as the circumference — using the exact formula 2·π·r. It is the measurement you need when you have to fence a round garden, trim a circular table, wrap a cable around a drum or size a rubber gasket. It runs free in your browser on this page with exactly the same code that serves the paid API.
When you will reach for it
In software, the endpoint fits naturally into quoting tools, cut-list generators and educational apps: one POST with the radius, one JSON field back. It runs on our edge network with nothing stored after the response, and the identical code runs free in your browser here, so you can verify a figure by hand and only pay — $0.002 per request — when you automate the call inside your own system.
Integration use cases
Quoting and cut-list tools
Embed the call in a pricing app so perimeter-based materials are costed automatically from a single radius input.
Technical questions
What does it cost?
$0.002 per request. It is also free to run in your browser on this page with the same code.
What happens if the radius is zero, negative or missing?
The request is rejected with an invalid_input error explaining that the radius must be a positive finite number, and it is not charged.