Coriolis parameter calculator
Turn a latitude into the Coriolis parameter: at 45° north, f is 0.000103126079 per second with Earth's rotation rate. Southern latitudes come out negative and are labelled, so the sign never trips you up. Free in your browser.
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Worked example
- Latitude
- 45
- Latitude rad
- 0.7853981634
- Omega
- 0.0000729212
- Coriolis parameter
- 0.0001031261
- F
- 0.0001031261
Meteorologists, oceanographers, and students of geophysical fluid dynamics constantly need the local Coriolis parameter when they set up f-plane models, check textbook problems, or convert a station latitude into the coefficient that multiplies horizontal velocity in the momentum equations. Optional omega overrides the default Earth sidereal rate when you model another rotating planet or a classroom problem that pins a custom value.
What the Coriolis parameter tells you
In an inertial frame, free motion on a rotating planet looks curved when viewed in Earth-fixed coordinates. Projecting the planetary angular velocity vector onto the local vertical yields an effective vertical vorticity that multiplies horizontal velocity in the momentum equations. That factor is the Coriolis parameter f equals two omega sine of geographic latitude phi.
At the equator sine phi is zero, so f vanishes and the classic f-plane approximation must be replaced by equatorial beta-plane or full spherical dynamics. At the poles sine phi is plus or minus one, so the magnitude of f reaches its maximum of two omega. In the Northern Hemisphere f is positive; in the Southern Hemisphere it is negative, which reverses the sense of geostrophic circulation around highs and lows.
Mid-latitude weather models often hold f fixed at a reference latitude (the f-plane) or let it vary linearly with northward distance (the beta-plane). Ocean basin models, inertial oscillation analyses, and Rossby radius estimates all start from a numerical f taken from the latitude of interest. This capability implements the elementary trigonometric definition only: it does not solve the full vector Coriolis acceleration, does not include centrifugal terms, and does not integrate trajectories.
What you can do with it
Classroom and exam verification
Let students verify northern, southern, equatorial, and polar f values against the two-omega-sine-phi formula with deterministic rounding.
FAQ
How do I compute the Coriolis parameter from latitude?
Send latitude φ in degrees (−90 to 90). Optional omega Ω defaults to 7.292115×10⁻⁵ rad/s.
Why is f zero at the equator and maximum at the poles?
sin(0°) = 0 so f vanishes on the equator; |sin(±90°)| = 1 so |f| reaches 2Ω at the poles. The sign of f follows the hemisphere.
Can I override Earth's rotation rate Ω?
If omitted, Earth's mean sidereal rate 7.292115×10⁻⁵ rad/s is used.
What is the Coriolis parameter at 45 degrees latitude?
About 0.000103126079 per second, using Earth's default rotation rate of 0.00007292115 radians per second. The value is positive because 45 degrees north lies in the Northern Hemisphere; at 45 degrees south it has the same size with a negative sign.
Why is the Coriolis parameter negative in the Southern Hemisphere?
Because the sine of a southern latitude is negative. A negative f reverses the sense of the circulation around highs and lows compared with the north, and the result names the hemisphere so the sign is never ambiguous.
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/earth/coriolis-parameter \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"latitude":45}'const res = await fetch("https://api.kit.forhosting.com/earth/coriolis-parameter", {
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/earth/coriolis-parameter",
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/earth/coriolis-parameter", 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/earth/coriolis-parameter", 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": "earth.coriolis_parameter",
"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
The Coriolis parameter is twice Earth's angular rotation rate times the sine of geographic latitude: f equals two omega sine phi. This Coriolis parameter from latitude calculator applies that identity deterministically, echoes the latitude and omega used, returns f in inverse seconds, and labels the hemisphere so northern and southern signs stay obvious. Latitudes outside minus ninety to plus ninety degrees fail with invalid_input instead of producing a silent NaN.
What the Coriolis parameter means and where f = 2Ω sin(φ) comes from
Provide latitude in degrees, optionally override omega, and receive f in inverse seconds ready for textbooks, notebooks, and API clients that need a reproducible number rather than an ad-hoc constant hard-coded at forty-five degrees.
Input contract, response shape, and error behaviour
Values strictly below minus ninety or strictly above ninety are rejected with a clear message that the Coriolis parameter is undefined outside that range—those failures are not billed. Example: latitude equals forty-five degrees with default omega yields f approximately one point zero three one three times ten to the minus four per second, half the polar maximum, because sine of forty-five degrees is the square root of one half. Values are rounded to twelve decimal places for stable goldens across runtimes. POST a JSON body with required field latitude, the geographic latitude phi in degrees between minus ninety and plus ninety inclusive. Accept aliases lat, phi, the Greek letter phi, and latitude_deg. Latitude may be a JSON number or a numeric string; missing, empty, non-finite, and non-numeric values fail with invalid_input naming the field. Optional omega, or Ω, omega_rad_s, or earth_omega, overrides the default Earth mean sidereal angular rate of seven point two nine two one one five times ten to the minus five radians per second; when provided it must be a strictly positive finite number. On success the body includes latitude and latitude_rad as used, omega, coriolis_parameter and f as identical aliases for the computed value in inverse seconds, unit labels, hemisphere as northern, southern, or equator, formula and equation strings for display, method f_plane_coriolis, and a short steps array. Pair the response with your own beta equals two omega cosine phi over Earth radius if you need the meridional gradient; this endpoint returns f only and does not emit beta, Rossby number, or inertial period, though the inertial period is simply two pi over the absolute value of f when f is nonzero.
Where a Coriolis parameter API earns its keep
Atmospheric and oceanography courses use a Coriolis parameter from latitude calculator so learners can check textbook answers for mid-latitude and polar cases without a full GCM stack. Multi-planet teaching demos pass a custom omega to explore how faster rotation raises f at the same latitude. Invalid latitude or omega does not consume balance. Forecast desks and research notebooks convert station or grid latitudes into local f before estimating geostrophic wind, inertial periods, or Rossby radii; a tiny parse API avoids embedding conflicting omega constants and degree-versus-radian mistakes in every script. Keep requests small, pin the rounded coriolis_parameter in tests, and you get reproducible f values for homework, dashboards, and edge workers without standing up a geophysical fluid dynamics library of your own.
Integration use cases
f-plane model setup
Convert a reference latitude into local Coriolis parameter f = 2Ω sin(φ) before running shallow-water or quasigeostrophic notebooks.
Inertial period and Rossby radius checks
Obtain f from station latitude so follow-on scripts can compute T = 2π/|f| or the baroclinic Rossby radius without hard-coding mid-latitude defaults.
Technical questions
What happens if latitude is outside −90 to 90?
The task fails with invalid_input. Geographic latitude outside that range is invalid for f = 2·Ω·sin(φ); the failure is not billed.
What does the Coriolis parameter calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.