ForHosting KIT · Travel & geography

Geocentric radius calculator

At latitude 0° on WGS84, the geocentric radius is 6378137 m, the full equatorial radius. Enter a geodetic latitude and, if you like, a height above the ellipsoid to get the distance from Earth's centre, or set another ellipsoid. Free in your browser.

Free
Runs in your browser
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Run — free How it works & API

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Worked example

If you enter

Geodetic latitude degrees: 0
Decimal places: 3

You get

H: 0
A: 6,378,137
F inv: 298.257223563
Geocentric radius: 6,378,137

WGS84 geocentric radius ρ(φ) with optional height. Search intent: geocentric radius calculator. No network calls or random seeds are required. Failed jobs are not billed.

What the geocentric radius tells you

The geocentric radius is the distance from the centre of the Earth to a point, measured in a straight line. If the Earth were a perfect sphere it would be the same everywhere, but the WGS84 model is an ellipsoid: a sphere slightly flattened at the poles. Its size is set by two numbers, the semi-major axis of 6378137 metres and the inverse flattening of 298.257223563. The radius is therefore longest at the equator and shorter toward the poles. In the example, a latitude of 0° with no height gives exactly 6378137 metres, both for the surface radius and for the geocentric radius.

How it is calculated, and mistakes to avoid

The calculator takes the geodetic latitude, works out the point on the ellipsoid from its semi-major and semi-minor axes, and measures its distance from the centre. If you add a height above the ellipsoid, it also gives the radius at that height. Typical mistakes are entering a geocentric latitude instead of a geodetic one, using height above sea level instead of height above the ellipsoid, and typing the flattening where the inverse flattening is expected. All lengths are in metres, and you can choose the number of decimals; the rounding is applied once, at the end.

What you can do with it

Teaching

Pinned goldens.

FAQ

What is the geocentric radius?

It is the straight-line distance from the centre of the Earth to a point at a given geodetic latitude. On the WGS84 ellipsoid it equals 6378137 metres at the equator.

Why does the radius change with latitude?

Because WGS84 is an ellipsoid, slightly flattened at the poles, not a sphere. Its radius is longest at the equator, set by the semi-major axis, and shrinks toward the poles.

What height should I enter?

The height above the ellipsoid in metres, not the height above sea level. The result shows both the radius on the ellipsoid surface and the radius at your height.

Can I use an ellipsoid other than WGS84?

Yes. Replace the semi-major axis and the inverse flattening, which default to 6378137 metres and 298.257223563, with the values of the ellipsoid you need.

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

POSThttps://api.kit.forhosting.com/geo/geocentric-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/geo/geocentric-radius \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"lat_deg":45}'

const res = await fetch("https://api.kit.forhosting.com/geo/geocentric-radius", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "lat_deg": 45
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/geo/geocentric-radius",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "lat_deg": 45
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/geo/geocentric-radius", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"lat_deg":45}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"lat_deg":45}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geo/geocentric-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

{
  "lat_deg": 45
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "geo.geocentric_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.

Technical notes

The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos.

How it works

WGS84 geocentric radius ρ(φ) with optional height. ρ from a,b ellipsoid formula at geodetic latitude. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not billed. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos.

Inputs, limits and rounding

Optional decimals use half-up once. Outputs echo inputs. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not billed. Provide required JSON fields. Invalid types raise invalid_input. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos.

When to use it

Use when search intent matches. WGS84 geocentric radius ρ(φ) with optional height. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not billed. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS, automation, or teaching demos.

Integration use cases

Quick check

Free widget.

Automation

Same JSON via API.

Technical questions

Free?

Yes tier A.

Network?

No.

Bad input?

invalid_input.

API?

Yes.

Locales?

EN-only; Nitro hydrates.

Read the full KIT documentation →

Run — free