Albers equal-area projection calculator
Enter Washington (38.9072, −77.0369) and standard parallels at 29.5° and 45.5°, and you get its X and Y in metres on an equal-area cone. Each region keeps its true relative size, so choropleth and density maps stay honest. 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
- 29.5
- Standard parallel 2
- 45.5
- Central meridian
- -96
- Latitude of origin
- 37.5
- Radius m
- 6,378,137
- N
- 0.6028370046
The Albers equal-area conic projection is the workhorse map projection for thematic maps of countries, states, and continents when area ratios must stay truthful. Cartographers, GIS students, and data journalists choose Albers whenever choropleth coloring or density comparisons would be distorted by Web Mercator or other conformal planes. 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 constant C, and the polar radii ρ and ρ0 from the classical spherical Albers formulas. Results are fully deterministic with no network calls, no sampling, and no date-dependent shortcuts.
What Albers equal-area returns and how the conic formulas work
Albers equal-area conic projects the sphere onto a cone that intersects the globe along two standard parallels φ1 and φ2. Along those parallels scale is true; between them and outside them the linear scale varies, but every region keeps its correct relative area on the map plane.
The spherical formulation used here follows Snyder: the cone constant n equals the average of the sines of the two standard parallels; the auxiliary constant C is cos squared of φ1 plus two n times sin of φ1; the polar radius of the latitude of origin is ρ0 equals R over n times the square root of C minus two n sin 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 Albers path and no datum shift: the model is the transparent spherical equal-area conic that textbooks and many lightweight GIS notebooks teach first.
What you can do with it
Thematic and choropleth basemaps
Project country or state pins to Albers X/Y so area-preserving maps keep density and share comparisons honest.
GIS homework and teaching demos
Check student work on spherical Albers formulas with known standard parallels without installing desktop GIS software.
FAQ
Why are two standard parallels required?
Albers equal-area 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.
What are the default central meridian and latitude of origin?
If you leave them empty, the central meridian is −96° and the latitude of origin is 37.5°, the common setting for maps of the contiguous United States. Change both when you project another country or continent.
Does this Albers calculator use the WGS84 ellipsoid?
No. It uses the spherical form of Albers that textbooks teach first, with a sphere radius of 6378137 m by default, the WGS84 semi-major axis. There is no ellipsoidal version and no datum shift.
Which pairs of standard parallels are rejected?
Pairs that cancel each other out, such as the same latitude north and south of the equator. Their sines add up to zero, the cone constant vanishes and no cone can be built, so the calculator refuses them instead of returning nonsense.
Why use Albers instead of Web Mercator for a choropleth map?
Because Albers keeps every region at its correct relative area, while Web Mercator and other conformal maps distort the sizes that the colours are compared across. When colour shows density or shares, equal area keeps the comparison honest.
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/albers-equal-area \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"latitude":38.9072,"longitude":-77.0369,"standard_parallel_1":29.5,"standard_parallel_2":45.5}'const res = await fetch("https://api.kit.forhosting.com/geo/albers-equal-area", {
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": 29.5,
"standard_parallel_2": 45.5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geo/albers-equal-area",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"latitude": 38.9072,
"longitude": -77.0369,
"standard_parallel_1": 29.5,
"standard_parallel_2": 45.5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geo/albers-equal-area", 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":29.5,"standard_parallel_2":45.5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"latitude":38.9072,"longitude":-77.0369,"standard_parallel_1":29.5,"standard_parallel_2":45.5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geo/albers-equal-area", 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": 29.5,
"standard_parallel_2": 45.5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geo.albers_equal_area",
"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 Albers equal-area returns and how the conic formulas work
This capability returns the echoed geographic inputs, the two standard parallels, central meridian, latitude of origin, radius in meters, n, C, ρ, ρ0, θ in radians, projected X and Y, the precision applied, a short formula string, and the method tag albers_equal_area_conic_spherical. Rejected cases include missing required fields, non-finite values, latitudes or longitudes outside their closed degree ranges, a non-positive radius, a cone constant n whose absolute value is effectively zero (standard parallels that cancel, for example equal-magnitude opposite latitudes), and configurations that would make a radicand under a square root negative.
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 Albers 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 thirty-seven point five 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 Albers parameter set so a quick check of a CONUS city pin needs only lat, lon, and the two standard parallels twenty-nine point five and forty-five point five. Failed validation returns invalid_input and is not billed; successful API calls use the published $0.002 base price.
Where equal-area conic coordinates earn their keep in maps and software
Thematic cartographers project country and state outlines with Albers whenever area-preserving statistics matter more than local shape, for example election maps, population density layers, and environmental inventories that would mislead under Mercator inflation near the poles. Contest and interview practice often needs a fast offline source of equal-area projected points so solutions can be checked without spinning up PROJ or a full spatial database under time pressure. Pair it with Web Mercator project or unproject tools when you need slippy-map meters, and with polygon area helpers when you are building a small lab of free, deterministic geospatial utilities around equal-area mapping. 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. Journalists and analysts who reproject sparse latitude-longitude tables before computing planar polygon areas 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 equal-area coordinates for CI tests, choropleth renderers, and projection unit tests.
Technical questions
How do I project lat/lon with Albers equal-area 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, C, ρ, and ρ0 from the spherical Albers formulas.
What defaults apply if I omit the central meridian or origin?
central_meridian defaults to -96°, latitude_of_origin to 37.5°, and radius_m to 6378137 m—a common CONUS Albers spherical parameter set.
When does the Albers projector reject input?
Missing or non-finite fields, out-of-range degrees, non-positive radius, standard parallels that make n≈0, or a negative radicand under ρ all fail with invalid_input and are not billed.
What does the Albers equal-area 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.