Centripetal force calculator
A 2 kg mass moving at 10 m/s on a 5 m radius needs a 40 N pull toward the centre. Use it to check string tension, the grip a car needs on a curve, or a homework answer. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass
- 2
- Speed
- 10
- Radius
- 5
- Force
- 40
Uniform circular motion always needs a net force pointed toward the center of the path—the centripetal force—whose magnitude is mass times speed squared over radius. Students checking homework, teachers building answer keys, engineers estimating banked-curve loads or tether tension, and game developers sanity-checking orbital or carousel physics all need the same three inputs and one clear number without reopening a textbook every time.
What centripetal force means and which three quantities you must send
In classical mechanics, an object of inertial mass m moving at constant tangential speed v on a circle of radius r has acceleration of magnitude v squared over r directed toward the center. Newton's second law then requires a net force of magnitude F equals m times v squared over r in that same radial direction.
That identity is the backbone of introductory circular-motion problem sets, free-body diagrams for cars on flat curves, satellite order-of-magnitude checks, and countless engineering estimates: how much tension a string must supply, how large a normal force a banked road needs, or what force a rotor arm experiences at a given spin rate. Search intent clusters around phrases such as centripetal force calculator, circular motion force, F equals m v squared over r, mass speed radius force, and centripetal force formula calculator.
People want a numeric answer they can check against a worksheet, embed in a simulation, or feed into a larger pipeline—not only a reminder that the formula exists. Units stay consistent with whatever mass, speed, and length basis you chose: kilograms with metres per second and metres yield newtons, or any coherent set you prefer.
Practical use, limits, pricing, and delivery channels
Use the browser tool when you want an immediate centripetal-force check while grading homework, verifying a lab carousel or whirling-mass run, sanity-checking a game orbit constant, or sketching string tension for a known mass and radius. Choose units consistently—if mass is in kilograms, speed in metres per second, and radius in metres, force comes out in newtons. Results are fully deterministic: the same three inputs always yield the same force and the same formula label.
There is no language model, no external physics service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible lesson materials.
What you can do with it
Homework and lab circular-motion drills
Students and graders confirm centripetal force for given mass, speed, and radius, with clear rejection when radius is zero or mass is non-positive.
Game, sim, and tether sanity checks
Quick structured numbers for string tension, rotor load, or orbital-scale force estimates without standing up a full dynamics stack.
FAQ
Which formula does the centripetal force calculator use?
Uniform circular motion: F = m v² / r, where m is mass, v is tangential speed, and r is the path radius. The force is the magnitude toward the center.
What happens if radius is zero?
Zero radius is not allowed for circular motion because F=mv²/r would divide by zero; those calls are not charged.
Is the centripetal force calculator free?
The browser tool runs free on your device.
Why can't the speed be negative?
Speed here is the size of the velocity along the circle, so a negative value is treated as an input mistake and rejected instead of being squared into a positive force. Enter zero or a positive number.
Does it account for banked curves or friction?
No. It gives the net inward force for ideal uniform circular motion from mass, speed and radius only. There is no banking angle, no friction and no unit conversion, so splitting that force into its sources is up to you.
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/mech/centripetal-force \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"mass":2,"speed":10,"radius":5}'const res = await fetch("https://api.kit.forhosting.com/mech/centripetal-force", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"mass": 2,
"speed": 10,
"radius": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/centripetal-force",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"mass": 2,
"speed": 10,
"radius": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/centripetal-force", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"mass":2,"speed":10,"radius":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"mass":2,"speed":10,"radius":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/centripetal-force", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"mass": 2,
"speed": 10,
"radius": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.centripetal_force",
"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
This capacity accepts mass, tangential speed, and path radius as finite numbers, rejects zero or non-positive radius with a clear invalid_input error (division by zero is never silent), rejects non-positive mass and negative speed, and returns the force plus the echoed inputs as structured JSON with formula and method labels.
What centripetal force means and which three quantities you must send
Delivering mass, speed, radius, force, formula, and method as JSON makes the result easy to paste into notes, diff in automated tests, or reuse across languages without reimplementing the arithmetic.
How this calculator validates input and applies F = m v² / r
Numeric strings that parse to finite numbers are accepted so forms and CSV-style pipelines can pass values without an extra cast. Mass must be strictly positive. Speed must be non-negative because the product treats it as the magnitude of tangential velocity; negative speed is rejected rather than silently squared into a positive force. After validation, force is computed as mass times speed times speed divided by radius. There is no banking-angle model, no friction, no torque, and no unit conversion; this is ideal uniform circular motion from the three known quantities. Send a JSON body with required fields mass, speed, and radius. Every field must be finite: missing fields, empty strings, non-numeric text, NaN, and Infinity all fail immediately with invalid_input before any result is returned, and failed validation is not charged. Radius must be strictly positive: a zero radius is explicitly invalid for circular motion and would divide by zero in the formula, so the engine returns invalid_input with a message that names radius and the division-by-zero risk. Results are rounded to a stable decimal precision so the same input always yields the same JSON across JavaScript engines. Aliases m, v or velocity, and r are accepted. The same pure function powers the free in-browser tool and the API path.
Practical use, limits, pricing, and delivery channels
Each successful request is one billable item at $0.002; failed validation does not consume balance. Wire the endpoint into mechanics drills, contest answer checkers, circular-motion worksheets, or preprocessing steps where you already prefer explicit domain errors—such as rejecting a zero radius—over opaque black-box widgets that cannot explain why a bad input was refused.
Integration use cases
Deterministic fixtures for physics tests
Pipelines that seed unit tests or interactive mechanics demos can call a pure F=mv²/r oracle instead of reimplementing circular motion force in every language.
Technical questions
How do I compute centripetal force with this API?
Send a JSON body with mass, speed, and radius to mech.centripetal_force. The response returns force plus the echoed inputs, formula F=mv^2/r, and method.
Can I pass velocity instead of speed?
Yes. The field aliases velocity and v are accepted for speed, and m and r for mass and radius. Speed must still be non-negative (magnitude).