Force calculator
A 5 kg mass accelerating at 4 m/s² needs a net force of 20 N: give any two of force, mass and acceleration and the calculator solves the third with Newton's second law. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass m
- 5
- Acceleration a
- 4
- Force
- 20
- Solved
- force
Newton's second law is the shortest path from a free-body sketch to a number you can check: net force equals mass times acceleration. Students verifying homework, teachers building answer keys, engineers sizing thrusters or braking loads, and game developers sanity-checking physics constants all need the same triad—force, mass, acceleration—without reopening a textbook every time.
What F = ma means and which two quantities you need to send
In classical mechanics along a chosen axis, the net force F on a rigid body of inertial mass m produces acceleration a according to F equals m times a. That identity is the backbone of introductory problem sets, free-body diagrams, and countless engineering estimates: how hard must a thruster push to reach a target acceleration, what acceleration does a known load produce on a known mass, or what effective mass is implied by a measured force and acceleration pair.
Search intent clusters around phrases such as force calculator, F equals m a calculator, mass from force and acceleration, acceleration from force and mass, and Newton's second law 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, force, and acceleration basis you chose: kilograms with newtons and metres per second squared, or any coherent set you prefer.
How this calculator validates input and applies F = ma
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 whether you supply it or the solver computes it as force divided by acceleration; zero or negative mass is always rejected. When mass is the unknown, acceleration must be non-zero to avoid division by zero.
After validation, the missing quantity is computed as force equals mass times acceleration, or acceleration equals force over mass, or mass equals force over acceleration. Signed force and acceleration are allowed: negative values simply reverse the sense of the motion axis. There is no friction model, no multi-body system, and no unit conversion; this is ideal one-dimensional F equals m a from the two known quantities.
Practical use, limits, pricing, and delivery channels
Use the browser tool when you want an immediate F equals m a check while grading homework, verifying a lab force plate run, sanity-checking a game physics constant, or sketching how hard a thruster must push for a short burn. Choose units consistently—if force is in newtons and mass is in kilograms, acceleration comes out in metres per second squared. Results are fully deterministic: the same two inputs always yield the same triad and the same solved field 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 F=ma drills
Students and graders confirm force, mass, or acceleration for given pairs, with clear rejection when mass is non-positive or a field count is wrong.
Game, sim, and thruster sanity checks
Quick structured numbers for net force under known mass and acceleration without standing up a full dynamics stack.
FAQ
Which formula does the force calculator use?
Newton's second law in one dimension: F = m a. Given mass and acceleration it returns force; given force and mass it returns acceleration; given force and acceleration it returns mass.
What happens if mass is zero or negative?
Non-positive mass is rejected whether you supply it or it would be computed as force divided by acceleration, and those calls are not charged.
Is the force calculator free?
The browser tool runs free on your device.
Can force or acceleration be negative?
Yes. Finite signed force and acceleration are accepted; they reverse the sense of your chosen axis. Mass must still be strictly positive.
How do I find mass from force and acceleration?
Enter the force and the acceleration and leave mass empty; the calculator divides force by acceleration. Acceleration cannot be zero in that case, and a mass that comes out zero or negative is rejected.
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/force-mass-accel \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"force":20,"mass":5}'const res = await fetch("https://api.kit.forhosting.com/mech/force-mass-accel", {
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/mech/force-mass-accel",
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/mech/force-mass-accel", 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/mech/force-mass-accel", 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": "mech.force_mass_accel",
"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 exactly two of those three quantities as finite numbers, rejects non-positive mass and malformed input with a clear invalid_input error, and returns the complete F=ma triad as structured JSON including which field was solved.
What F = ma means and which two quantities you need to send
Delivering force, mass, acceleration, solved, 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 = ma
Send a JSON body with exactly two of force, mass, and acceleration. Every provided field must be finite: missing all three, only one field, all three at once, 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. Results are rounded to a stable decimal precision so the same input always yields the same JSON across JavaScript engines. 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, free-body worksheets, or preprocessing steps where you already prefer explicit domain errors—such as rejecting a non-positive mass—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=ma oracle instead of reimplementing Newton's second law in every language.
Technical questions
How do I compute force, mass, or acceleration with this API?
Send a JSON body with exactly two of force, mass, and acceleration to mech.force_mass_accel. The response returns the full triad plus solved, formula, and method.