Orthographic projection calculator
Viewed from far out in space above 0, 0, the point 40.7128, -74.006 lands at x -0.7286473179 and y 0.6522677564 on a globe disk of radius 1, on the visible side. Far-side points still get coordinates, marked hidden for clipping. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Latitude
- 40.7128
- Longitude
- -74.006
- Center latitude
- 0
- Center longitude
- 0
- X
- -0.7286473179
- Y
- 0.6522677564
This orthographic projection calculator turns WGS84 latitude and longitude into plane coordinates that match the classic view of the Earth as seen from infinite distance — the round globe disk used in atlases, planetary science figures, and 3D-to-2D teaching demos. You supply a point and optionally the projection center (the spot on the sphere facing the viewer) plus a scale radius; the engine applies the standard azimuthal orthographic formulas with pure trigonometry, then reports X, Y, whether the point lies on the near hemisphere, and the cosine of the angular distance from the center. Results are fully deterministic: no network calls, no sampling, and no date-dependent shortcuts.
What orthographic projection returns and how the deep-space view is defined
The orthographic map projection is an azimuthal projection that places the observer at infinite distance along a ray through the chosen center of projection, so parallel light rays cast the sphere onto a plane. On that plane X increases to the right (east of the center meridian when the center is on the equator) and Y increases upward (toward the local north of the center).
The origin is the projected image of the center itself: latitude and longitude equal to the center project to X equals zero and Y equals zero. There is no ellipsoidal flattening step and no datum shift: the path is the unit-sphere (or scaled-sphere) model used in textbooks and most globe illustrations. Far-side points are not rejected: they still receive finite X and Y from the formulas, with visible set to false so callers can clip them when drawing a solid globe.
Where orthographic coordinates fit in globes, teaching, and software
Developers meet orthographic projection when a canvas globe, a planetary texture overlay, or a textbook figure expects plane coordinates that look like a photograph of a sphere from deep space rather than a rectangular map. GIS and cartography students use it when a lab asks for the projected position of a city relative to a chosen viewing center, when comparing limb geometry, or when checking that a pin is on the near side before drawing it.
Teachers can pre-generate answer keys for modest lat-lon pairs without trusting opaque calculator apps that silently switch to stereographic or Mercator formulas. Product teams call the same contract from scripts to seed deterministic test vectors for globe renderers, to normalize user-entered coordinates before clipping the far hemisphere, or to satisfy programming-challenge statements that demand orthographic X and Y rather than a hand-waved sketch.
Contest and interview practice often needs a fast, offline source of projected points so solutions can be checked without spinning up a full 3D stack under time pressure.
What you can do with it
Globe UI and canvas overlays
Convert a lat/lon pin to orthographic X/Y for drawing cities, flight paths, and markers on a deep-space globe disk.
Teaching and homework keys
Project textbook city coordinates into orthographic plane space for labs, answer keys, and classroom demos without a full GIS suite.
FAQ
What does the orthographic projection calculator cost?
It is free in your browser on this page.
Which formulas define X and Y?
With radius R, x = R · cos(φ) · sin(Δλ) and y = R · (cos(φ0) · sin(φ) − sin(φ0) · cos(φ) · cos(Δλ)), where (φ, λ) is the point and (φ0, λ0) is the center.
What does the visible flag mean?
visible is true when cos c ≥ 0, i.e. the point lies on the near hemisphere facing the viewer. Far-side points still get X and Y but visible is false.
Is this the same as Web Mercator or Gall–Peters?
No. Web Mercator maps the sphere to an unbounded rectangular plane for web tiles; Gall–Peters is equal-area cylindrical. Orthographic is azimuthal and shows a round globe disk.
Why are results rounded to a precision?
Default precision is 10 decimal places; you can set precision from 0 to 15.
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/orthographic-project \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"latitude":40.7128,"longitude":-74.006}'const res = await fetch("https://api.kit.forhosting.com/geo/orthographic-project", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"latitude": 40.7128,
"longitude": -74.006
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geo/orthographic-project",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"latitude": 40.7128,
"longitude": -74.006
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geo/orthographic-project", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"latitude":40.7128,"longitude":-74.006}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"latitude":40.7128,"longitude":-74.006}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geo/orthographic-project", 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": 40.7128,
"longitude": -74.006
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geo.orthographic_project",
"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.
Limits
min_latitude | -90 |
max_latitude | 90 |
min_longitude | -180 |
max_longitude | 180 |
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 orthographic projection returns and how the deep-space view is defined
This calculator returns the input latitude and longitude (echoed and rounded), the center latitude and longitude, the projected X and Y, the radius used as the disk scale, a boolean visible flag for the near hemisphere, the cosine of the angular distance c from the center, the precision applied, a short formula reminder, and the method tag orthographic_project. Rejected cases include missing latitude or longitude, non-finite values, latitude or center latitude outside the closed interval from negative ninety to positive ninety degrees, longitude or center longitude outside negative one hundred eighty to positive one hundred eighty, and a non-positive radius.
How latitude, longitude, and center are read and how X and Y stay reproducible
Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong plane coordinate. The preferred fields are latitude and longitude in decimal degrees for the point to project, with aliases lat and phi for latitude and lon, lng, long, and lambda for longitude so spreadsheets, query strings, and typed forms can reuse the same contract. Optional center_latitude and center_longitude, with aliases center_lat, lat0, phi0 and center_lon, lon0, lambda0, choose which hemisphere faces the viewer; both default to zero, which centers the disk on the equator and prime meridian. Optional radius, with aliases r, R, and scale, multiplies the unit-sphere coordinates into whatever drawing units you need, defaulting to one so the projected disk has radius one. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for numeric outputs, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the projection yourself.
Where orthographic coordinates fit in globes, teaching, and software
On this page the work runs entirely in your browser; through the API each successful lookup 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 mathematical result. Pair it with Web Mercator or equal-area converters when you need related coordinate tools, and with other geo endpoints when you are building a small lab of free, deterministic geospatial helpers.
Integration use cases
Deterministic cartography fixtures
Generate reproducible plane coordinates and visibility flags for unit tests, CI assertions, and renderer property checks.