Length of a degree of latitude
At 45° of latitude, one degree from south to north covers about 111 km, close to 60 nautical miles. Enter any latitude and get the exact length on the WGS-84 ellipsoid in metres, kilometres, feet and nautical miles. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Latitude
- 45
- Meters per degree
- 111,131.7774141756
- Km per degree
- 111.1317774142
- Feet per degree
- 364,605.5689441457
- Nautical miles per degree
- 60.0063592949
How many metres does one degree of latitude span on the ground? On a perfect sphere the answer would be constant, but Earth is an oblate WGS-84 ellipsoid, so the meridional length of one degree grows slightly from the equator toward the poles as the meridional radius of curvature changes with latitude. Surveyors, GIS engineers, map-projection teachers, navigation students, and simulation pipelines need that local scale factor when converting grid cells, checking textbook tables, or sizing latitude bands without integrating a full geodesic. Latitudes outside the closed interval from minus ninety to ninety fail with a clear invalid input error.
What one degree of latitude measures and how to supply latitude
One degree of latitude is the north–south ground distance along a meridian between geodetic latitude phi and phi plus one degree, approximated locally by the meridional radius of curvature M of phi times pi over one hundred eighty. That formula is the standard differential meridian-arc length on an oblate spheroid: M equals a times one minus e squared, all over the three-halves power of one minus e squared times sin squared of phi, where a and e squared come from the WGS-84 ellipsoid.
Unlike a spherical mean-Earth model that freezes the degree length near one hundred eleven kilometres everywhere, this product reports the true latitude-dependent scale so tables at the equator, mid-latitudes, and poles stay consistent with modern geodesy references. Latitude must lie between minus ninety and ninety inclusive. Missing fields, non-finite numbers, and non-numeric strings fail the same way.
What you can do with it
Map grid and cell sizing
Convert a one-degree latitude band into metres or kilometres at a chosen latitude when building equal-angle grids, heatmaps, or regional sampling frames on WGS-84.
Navigation and chart scale checks
Pilots, mariners, and route planners verify how many nautical miles one degree of latitude spans at a given latitude without opening a desktop GIS.
FAQ
What happens if latitude is out of range?
Missing or non-finite latitude fails the same way.
Is the length the same at every latitude?
No. On WGS-84 the meridional radius of curvature varies with latitude, so one degree of latitude is slightly shorter near the equator and slightly longer near the poles than a spherical mean would suggest.
Is the length of a degree of latitude calculator free?
The browser tool runs free on your device.
How long is one degree of latitude at 45°?
About 111 km, or 111131.7774141756 metres to be exact, which is close to 60 nautical miles. It is the distance you cover along a meridian when your latitude changes by one degree there.
Which Earth model does the calculation use?
The WGS-84 ellipsoid, with its equatorial radius of 6378137 metres and its flattening. A simple sphere would give about 111 km for every degree; the ellipsoid gives the real value for each latitude.
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/geo/degree-length-latitude \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"latitude":45}'const res = await fetch("https://api.kit.forhosting.com/geo/degree-length-latitude", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"latitude": 45
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geo/degree-length-latitude",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"latitude": 45
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geo/degree-length-latitude", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"latitude":45}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"latitude":45}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geo/degree-length-latitude", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"latitude": 45
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geo.degree_length_latitude",
"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
This capability takes a single geodetic latitude in decimal degrees, evaluates the closed-form meridional radius of curvature with fixed WGS-84 semi-major axis and flattening, multiplies by pi over one hundred eighty, and returns metres, kilometres, feet, and nautical miles as deterministic JSON.
What one degree of latitude measures and how to supply latitude
Send the required field latitude as a JSON number or numeric string in decimal degrees; aliases lat and phi are accepted when your client already uses those names. Any value outside that range raises invalid_input with a message that names the field and the bound, so callers never silently clamp bad GPS noise into a fake degree length. Identical inputs always produce identical JSON because the path is pure closed-form arithmetic with fixed WGS-84 constants, no wall clock, no random seed, and no external map service.
Reading metres, kilometres, feet, nautical miles, and datum fields
Prefer metres for survey corridors and cadastral grid sizing; prefer kilometres for classroom tables; prefer nautical miles when cross-checking pilot or chart notes. On success the response echoes latitude, then reports meters_per_degree as the primary ground length of one degree of latitude in metres. km_per_degree divides that length by one thousand for regional and textbook work; feet_per_degree uses the international foot of zero point three zero four eight metres; nautical_miles_per_degree divides by one thousand eight hundred fifty-two so aviation and marine tables can compare against a degree of latitude in sea miles. meridional_radius_m is the intermediate M of phi in metres, useful when a projection or curvature notebook needs the radius itself rather than the degree scale. ellipsoid is always the string WGS-84, a_m is the semi-major axis six million three hundred seventy-eight thousand one hundred thirty-seven metres, f is the flattening one over two hundred ninety-eight point two five seven two two three five six three, and e2 is the first eccentricity squared derived from f, so downstream code can assert the datum without hard-coding constants in every client. method is always meridional_radius_of_curvature. Validation failures for out-of-range latitude, missing latitude, and non-finite values fail closed and are not charged under the prepaid API.
API usage, pricing, GIS workflows, and practical limits
Send a JSON body with the required latitude field, then call the free in-browser length of a degree of latitude calculator for homework checks, lecture demos, and quick map-scale verification without installing PROJ, GeographicLib, or a full GIS stack. Use the prepaid API when a mapping platform, curriculum generator, simulation harness, or coordinate-conversion pipeline needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Pair this endpoint with a longitude-degree length tool when you need both east–west and north–south local scales for a rectangular cell, or with Vincenty geodesic distance when the next question is the finite surface path between two distinct points rather than the local differential degree length. This product does not integrate a long meridian arc between distant latitudes; for multi-degree arcs use a geodesic library.
Integration use cases
Classroom geodesy and exam oracles
Students compare spherical approximations against the ellipsoidal degree length; graders pin deterministic meters_per_degree JSON from the same latitude used in the problem set.
Technical questions
How do I compute the length of one degree of latitude?
Send JSON with latitude set to a decimal degree value between −90 and 90. The response includes meters_per_degree, km_per_degree, feet_per_degree, and nautical_miles_per_degree on the WGS-84 ellipsoid.
Which datum and constants are used?
Always WGS-84: semi-major axis a = 6378137 m and flattening f = 1/298.257223563. The response echoes ellipsoid, a_m, f, and e2 on every success.