Acceleration calculator
A force of 20 N on a 5 kg mass gives an acceleration of 4 m/s². Enter the net force in newtons and the mass in kilograms; a negative force returns a negative acceleration along your axis. Free in your browser.
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- Your data stays on your device
Run — free
Worked example
- Force
- 20
- Mass
- 5
- Acceleration
- 4 m/s^2
You send a force in newtons and a mass in kilograms, and you receive the acceleration in metres per second squared, computed deterministically with no rounding surprises. Zero or negative mass is rejected with a clear validation error instead of a meaningless number.
Newton's second law, reduced to one division
Every dynamics problem in classical mechanics starts from the same relationship: the net force on an object equals its mass times its acceleration, F = m·a. Rearranged, the acceleration produced by a known force on a known mass is simply a = F/m. That single division hides a remarkable amount of physics.
Double the force on the same object and the acceleration doubles; double the mass under the same force and the acceleration halves. This linearity is what makes the second law the workhorse of introductory physics, engineering estimates and simulation sanity checks. Send a force of 20 newtons and a mass of 5 kilograms and you receive 4 metres per second squared, every time, on any machine.
There is no model, no approximation and no hidden state between calls — the same input always produces byte-identical output, which is what lets you cache the answer, assert it in a test suite, or compare results across environments without tolerance bands.
Signed forces, positive mass, and the errors that matter
The force you send may be negative, and that is meaningful: a negative force simply points along the negative direction of your chosen axis, so the returned acceleration is negative too. Direction is first-class in the second law, and discarding the sign would throw away information a caller may depend on. Mass is different.
In classical mechanics mass is a strictly positive quantity, and a zero or negative value does not produce a special result — it produces a mistake. Dividing by zero mass would be undefined, and a negative mass would invert the relationship between force and motion in a way no physical object exhibits. Both fields must be finite numbers; numeric strings are accepted for convenience, but NaN, infinities and non-numeric values are rejected the same way.
What you can do with it
Generate exact worked examples
Produce physics exercises whose answers are guaranteed correct because they come from the same deterministic formula the students are taught.
Sanity-check a simulation
Compare your integrator's output against the analytic a = F/m value for a single step and catch unit or sign errors early.
FAQ
What units does it use?
Force in newtons, mass in kilograms, and the result in metres per second squared. Keep inputs in SI units for a correct result.
Can the force be negative?
Yes. A negative force points along the negative axis and produces a negative acceleration. Only mass is constrained to be positive.
Is my input stored?
No. The two numbers are processed and discarded; only the computed acceleration is returned.
What happens to the acceleration if I double the force or the mass?
Double the force on the same mass and the acceleration doubles; double the mass under the same force and it halves. With 20 N, a 5 kg mass gets 4 m/s², while a 10 kg mass gets 2 m/s².
How do I find the force from mass and acceleration instead?
This tool only divides force by mass. For the reverse, use the Newton's second law calculator, which solves for whichever of force, mass or acceleration you leave out.
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/phys/acceleration-using-force-and-mass \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"force":20,"mass":5}'const res = await fetch("https://api.kit.forhosting.com/phys/acceleration-using-force-and-mass", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"force": 20,
"mass": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/acceleration-using-force-and-mass",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"force": 20,
"mass": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/acceleration-using-force-and-mass", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"force":20,"mass":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"force":20,"mass":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/acceleration-using-force-and-mass", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"force": 20,
"mass": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.acceleration_using_force_and_mass",
"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 acceleration from force and mass API applies Newton's second law of motion in its most direct form: divide the net force acting on an object by the object's mass, and you get the acceleration that force produces. The same formula runs free in your browser on this page, so you can check a value by hand and only pay when you automate the call — $0.002 per request via the API.
Newton's second law, reduced to one division
The acceleration from force and mass endpoint performs exactly that division and nothing more, which is precisely its value: a deterministic, auditable result you can reproduce with a pocket calculator.
Signed forces, positive mass, and the errors that matter
For that reason the endpoint validates mass before dividing and rejects anything at or below zero with an invalid_input error that names the field and states the requirement, so your pipeline can fail fast and loudly instead of propagating a nonsense number downstream. Validation errors are never charged: a rejected request costs you nothing, which makes it safe to wire the endpoint into a form or a retry loop.
Where a force-and-mass acceleration lookup earns its place
The obvious user is the student checking homework, but the durable users are automated. If you need the inverse operation — force from mass and acceleration — pair this with the Newton's second law capability, which solves for whichever variable you leave out. Robotics and control software estimate expected acceleration from actuator force and payload mass before committing to a motion; game and simulation engines cross-check their integrators against the analytic value; educational platforms generate worked examples where the arithmetic must be exactly right; and engineering tools validate that a thrust curve and a vehicle mass budget stay inside structural acceleration limits. In all of these the calculation is trivial but the cost of getting it wrong is not, so it pays to centralise it behind one tested endpoint rather than re-implementing the division — and its validation — in every service. This capability runs on our global edge with no input retained after the response, and the identical code runs free in your browser on this page: paste a force and a mass, see the same number the API returns, and only pay when you automate it. The price is $0.002 per request, with no per-unit surcharge, so cost forecasting is a single multiplication.
Integration use cases
Check an actuator before motion
Estimate the acceleration a motor force will produce on a known payload and reject the move if it exceeds a safe limit.
Technical questions
What does it cost?
$0.002 per request. It is also free to run in your browser on this page.
Why was my mass rejected?
Mass must be strictly greater than zero. Zero would make the division undefined and negative mass is not physical, so both return an invalid_input error.
Is the result rounded?
Yes, to 12 decimal places, so the API and the free browser version return byte-identical output on any machine.