Equidistant conic projection
With standard parallels at 33° and 45°, scale stays true along both parallels and along every meridian. Enter a point and the two parallels to get projected X and Y, plus the cone constants, for regional atlases or GIS homework. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Latitude
- 38.9072
- Longitude
- -77.0369
- Standard parallel 1
- 33
- Standard parallel 2
- 45
- Central meridian
- -96
- Latitude of origin
- 0
- Radius m
- 6,378,137
- N
- 0.6281708098
The equidistant conic projection is the classic cone-based map projection that keeps scale true along every meridian and along two chosen standard parallels. Cartographers, GIS students, and regional planners choose it for mid-latitude countries and continents when north–south distances must stay trustworthy on the map plane while a simple cone geometry remains easy to teach and implement. This calculator accepts a geographic latitude and longitude together with two required standard parallels, optional central meridian and latitude of origin, and an optional sphere radius, then returns projected X and Y along with the intermediate cone constant n, the auxiliary constant G, and the polar radii ρ and ρ0 from the classical spherical Snyder formulas. Results are fully deterministic with no network calls, no sampling, and no date-dependent shortcuts.
What equidistant conic returns and how the Snyder formulas work
Equidistant conic projects the sphere onto a cone that intersects the globe along two standard parallels φ1 and φ2. Along those parallels linear scale is true; along every meridian distances from the apex-related polar radius stay true as well, which is why the projection is called equidistant. Between the standard parallels and outside them the east–west scale varies, and shapes are not conformal, but the contract is simple enough for textbooks and lightweight GIS notebooks.
The spherical formulation used here follows Snyder: when the two standard parallels differ, the cone constant n equals the difference of their cosines divided by the difference of the parallels in radians; when the parallels coincide, n reduces to the sine of that single parallel. The auxiliary constant G is cosine of φ1 over n plus φ1 itself.
The polar radius of the latitude of origin is ρ0 equals R times G minus φ0; the polar radius of the input latitude is the same expression with φ; the angular coordinate θ is n times the difference of longitude from the central meridian; finally X equals ρ sin θ and Y equals ρ0 minus ρ cos θ, so the origin sits on the central meridian at the latitude of origin with Y increasing northward in the usual map sense for northern cones.
There is no ellipsoidal equidistant-conic path and no datum shift: the model is the transparent spherical form that PROJ-style eqdc tutorials and many exam problems teach first.
What you can do with it
Regional atlas and planning basemaps
Project country or state pins to equidistant-conic X/Y so mid-latitude maps keep true scale along meridians and two standard parallels.
GIS homework and teaching demos
Check student work on spherical Snyder equidistant-conic formulas with known standard parallels without installing desktop GIS software.
FAQ
Why are two standard parallels required?
Equidistant conic is defined by two standard parallels that set the cone constant n. Both must be supplied explicitly so the projection parameters are never ambiguous; when they are equal the single-parallel limit n = sin φ1 is used.
What are the default central meridian and latitude of origin?
If you leave them out, the central meridian is -96° and the latitude of origin is 0°, with a sphere radius of 6378137 m. You can change all three to fit your own region.
When is the equidistant conic projection a good choice?
For mid-latitude countries, states and continents where north-south distances must stay trustworthy on the map, such as regional atlases and planning basemaps. Its simple cone geometry also makes it a favourite in GIS teaching.
When is the input refused?
When a required value is missing, a latitude or longitude is out of range, the radius is not positive, or both standard parallels sit at the equator, which leaves no usable cone.
Does the calculation use an ellipsoid?
No. It uses the classic spherical formulas by Snyder, with no ellipsoid and no datum shift. The default sphere radius is 6378137 m, and you can set your own.
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/equidistant-conic \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"latitude":38.9072,"longitude":-77.0369,"standard_parallel_1":33,"standard_parallel_2":45}'const res = await fetch("https://api.kit.forhosting.com/geo/equidistant-conic", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"latitude": 38.9072,
"longitude": -77.0369,
"standard_parallel_1": 33,
"standard_parallel_2": 45
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geo/equidistant-conic",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"latitude": 38.9072,
"longitude": -77.0369,
"standard_parallel_1": 33,
"standard_parallel_2": 45
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geo/equidistant-conic", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"latitude":38.9072,"longitude":-77.0369,"standard_parallel_1":33,"standard_parallel_2":45}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"latitude":38.9072,"longitude":-77.0369,"standard_parallel_1":33,"standard_parallel_2":45}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geo/equidistant-conic", 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": 38.9072,
"longitude": -77.0369,
"standard_parallel_1": 33,
"standard_parallel_2": 45
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geo.equidistant_conic",
"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
What equidistant conic returns and how the Snyder formulas work
This capability returns the echoed geographic inputs, the two standard parallels, central meridian, latitude of origin, radius in meters, n, G, ρ, ρ0, θ in radians, projected X and Y, the precision applied, a short formula string, and the method tag equidistant_conic_spherical. Rejected cases include missing required fields, non-finite values, latitudes or longitudes outside their closed degree ranges, a non-positive radius, and a cone constant n whose absolute value is effectively zero, for example both standard parallels at the equator.
Input contract, defaults, aliases, and stable numeric output
Latitude must lie in the closed interval from negative ninety through positive ninety; longitude and the optional central meridian must lie in the closed interval from negative one hundred eighty through positive one hundred eighty. Standard parallels and latitude of origin share the latitude range. The required fields are latitude and longitude in decimal degrees, plus standard_parallel_1 and standard_parallel_2 for the two equidistant-conic standard parallels. Aliases exist so spreadsheets and typed forms can reuse familiar names: lat and phi for latitude; lon, lng, long, and lambda for longitude; phi1, sp1, and lat1 for the first parallel; phi2, sp2, and lat2 for the second; lon0, lambda0, and cm for the central meridian; lat0, phi0, and origin_lat for the latitude of origin; R and radius for radius_m; decimals and dp for precision. When central_meridian is omitted the default is negative ninety-six degrees; when latitude_of_origin is omitted the default is zero degrees; when radius_m is omitted the default is six million three hundred seventy-eight thousand one hundred thirty-seven meters, the WGS84 semi-major axis used as a spherical map radius. Those defaults match a common continental United States equidistant-conic style parameter set when you also supply the classic thirty-three and forty-five degree standard parallels, so a quick check of a CONUS city pin needs only lat, lon, and those two parallels. Failed validation returns invalid_input and is not billed; successful API calls use the published $0.002 base price.
Where equidistant conic coordinates earn their keep in maps and software
Regional cartographers project country and state outlines with equidistant conic whenever true scale along meridians and along two carefully chosen parallels matters more than area preservation or local angles, for example atlas plates of mid-latitude nations, distance-aware planning maps, and classroom basemaps that must not stretch north–south distances the way Web Mercator does. Contest and interview practice often needs a fast offline source of equidistant projected points so solutions can be checked without spinning up a full spatial database under time pressure. Pair it with the Albers equal-area projector when area ratios matter more than meridional scale, and with Web Mercator project or unproject tools when you need slippy-map meters around a small lab of free, deterministic geospatial utilities. GIS coursework asks students to compute X and Y for a city under given standard parallels so they can compare hand algebra against a trusted oracle; this endpoint supplies that oracle without installing a desktop GIS stack or linking PROJ. Journalists and analysts who reproject sparse latitude-longitude tables before measuring planar north–south separations can batch through the API while keeping the mathematical contract identical to the interactive page. On this page the work runs entirely in your browser; through the API each successful projection costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split—free interactive exploration and a priced, identical API—matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the projected result.
Integration use cases
Deterministic projection fixtures
Generate reproducible equidistant-conic coordinates for CI tests, map renderers, and projection unit tests.
Technical questions
How do I project lat/lon with equidistant conic?
Send latitude, longitude, standard_parallel_1, and standard_parallel_2 in degrees. Optionally set central_meridian, latitude_of_origin, radius_m, and precision. The API returns X and Y plus n, G, ρ, and ρ0 from the spherical Snyder formulas.
What defaults apply if I omit the central meridian or origin?
central_meridian defaults to -96°, latitude_of_origin to 0°, and radius_m to 6378137 m—a common CONUS-style spherical parameter set when paired with standard parallels such as 33° and 45°.
When does the equidistant conic projector reject input?
Missing or non-finite fields, out-of-range degrees, non-positive radius, or standard parallels that make n≈0 (for example both at the equator) all fail with invalid_input and are not billed.
What does the equidistant conic projection calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.