Length of a degree of longitude
At the equator one degree of longitude spans about 111.32 km, and the same step shrinks toward the poles until it reaches zero. Enter a latitude to see the east-west length of one degree in metres, kilometres, miles 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 in decimal degrees
- 0
- Meters
- 111,319.490793
- Kilometers
- 111.319490793
- Miles
- 69.1707247135
- Nautical miles
- 60.1077164111
One degree of longitude does not cover a fixed ground distance. Along the equator a one-degree step spans roughly one hundred eleven point three kilometers, but the same angular step shrinks as you move toward the poles because the parallel circles of constant latitude get smaller until they collapse to a point. Surveyors, GIS developers, navigation textbooks, and map-scale designers constantly need the ground length of one degree of longitude at a stated latitude so they can convert angular deltas into meters, size east-west buffers, check textbook tables, or explain why a degree of longitude is shorter in London than in Singapore. This calculator uses the standard WGS84 ellipsoid formula: the prime vertical radius of curvature N at latitude phi times the cosine of phi, scaled by pi over one hundred eighty for a single degree. Latitudes outside negative ninety to positive ninety are rejected with a clear validation error instead of inventing a non-physical parallel.
How the length of one degree of longitude is computed
Start from the WGS84 reference ellipsoid used by GPS and almost every modern GIS stack: semi-major axis a equals six million three hundred seventy-eight thousand one hundred thirty-seven meters, and first eccentricity squared e squared is about six point six nine four times ten to the minus three. At geodetic latitude phi the prime vertical radius of curvature is N of phi equals a divided by the square root of one minus e squared times sin squared of phi.
That N is the radius of the ellipsoid section that contains the local vertical; multiplying by cos of phi gives the radius of the circle of latitude—the parallel you walk when you hold latitude fixed and change only longitude. One full revolution around that parallel is two pi times the parallel radius; one degree is therefore that circumference divided by three hundred sixty, which simplifies to pi over one hundred eighty times N of phi times cos of phi.
At the equator cos is one and N equals a, so you recover about one hundred eleven thousand three hundred nineteen meters per degree. At forty-five degrees the cosine factor dominates and the length falls near seventy-eight point eight kilometers. At the poles cosine vanishes, so the length of a degree of longitude is exactly zero—there is no east-west displacement left.
NaN and Infinity are rejected the same way.
What you send and what you get back
The field is required. Latitude outside the closed interval from negative ninety to positive ninety fails with an out-of-range message so clients can fix GPS glitches or form typos instead of guessing. Classic checks include latitude zero for the equatorial constant near one hundred eleven point three two kilometers, latitude forty-five for a mid-latitude table value, latitude sixty for a clearly shorter arc, and the poles where meters must be zero.
Wire the free browser form for homework and quick sanity checks when reading a chart scale, then call the identical contract from scripts when bulk-generating answer keys or validating coordinate math helpers.
Where degree-of-longitude length calculators show up in real work
Navigation and surveying courses assign tables of meters per degree of latitude and longitude at selected parallels; students need a trusted oracle that matches WGS84 rather than a flat mean-Earth rule of thumb that is wrong by kilometers at high latitude. GIS and mapping products convert a user-drawn east-west span in degrees into meters for distance labels, buffer widths, and “about N kilometers wide” copy that stays honest as the map center moves north or south.
Scientific notebooks that grid the globe at fixed degree spacing need the physical cell width of each longitude step to compute areas or flux integrals without re-deriving ellipsoid geometry. If you later need the length of one degree of latitude, Web Mercator meters per pixel, great-circle destination points, or tile indices from lat/lon, treat those as separate search intents and landings rather than overloading this page—the SEO intent here is specifically the ground length of one degree of longitude at a stated latitude.
What you can do with it
Convert degree deltas to ground meters
Turn an east-west longitude span in degrees into meters, kilometers, or miles at the map center latitude for distance labels and buffer widths.
Surveying and navigation tables
Generate WGS84 meters-per-degree-of-longitude values for textbook parallels and exam answer keys without hand-coding ellipsoid formulas.
Grid cell width for global models
Compute the physical width of fixed-degree longitude cells at each latitude for area, flux, or climate-grid post-processing notebooks.
FAQ
Why is a degree of longitude shorter at higher latitudes?
Parallels of constant latitude are smaller circles as you approach the poles. One degree is 1/360 of that circle, so ground length shrinks with cos(φ) (and a mild N(φ) correction on the ellipsoid).
What happens at the poles?
At latitude ±90°, cos(φ) is zero, so the length of one degree of longitude is zero. There is no east-west displacement left at a point pole.
What latitude range is accepted?
Any finite number in the closed interval [-90, 90] degrees.
What does it cost?
The browser tool is free and runs locally.
How long is a degree of longitude at 45° latitude?
About 78.8 km, compared with about 111.32 km at the equator. The parallel at 45° is a smaller circle than the equator, so each of its degrees covers less ground from west to east.
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-longitude \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"latitude":0}'const res = await fetch("https://api.kit.forhosting.com/geo/degree-length-longitude", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"latitude": 0
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geo/degree-length-longitude",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"latitude": 0
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geo/degree-length-longitude", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"latitude":0}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"latitude":0}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geo/degree-length-longitude", 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": 0
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geo.degree_length_longitude",
"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
How the length of one degree of longitude is computed
The pipeline is deterministic floating-point arithmetic: no random seeds, no wall-clock timestamps, no network calls, and no model drift, so identical latitudes always produce identical JSON. Latitude must be a finite number in the closed geographic interval from negative ninety to positive ninety degrees; values outside that range are not valid Earth latitudes and fail with invalid_input.
What you send and what you get back
Send one number under the field latitude: a finite decimal degree value with north positive and south negative. Missing fields, non-numeric strings, NaN, and Infinity fail with invalid_input and are not charged. On success the response echoes the cleaned latitude, the primary meters value for one degree of longitude, kilometers, statute miles, and international nautical miles for unit-friendly consumers, the prime_vertical_radius_m N of phi, parallel_radius_m as N times cos of phi, parallel_circumference_m for full three-hundred-sixty-degree rings, equatorial_meters as the reference length at latitude zero, earth_semi_major_m, eccentricity_squared, a model label set to WGS84, a method label, and a compact formula string. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where degree-of-longitude length calculators show up in real work
Aviation and maritime education still quote nautical miles per degree of longitude at a given latitude when explaining great-circle versus rhumb-line planning, and having statute miles and nautical miles in the same payload avoids unit mistakes. Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Technical questions
What formula does this calculator use?
WGS84 ellipsoid: L = (π/180) · N(φ) · cos(φ), where N(φ) = a / √(1 − e² sin²φ) is the prime vertical radius of curvature and a = 6378137 m.