Newton's second law calculator
Give any two of mass, acceleration and net force and the third appears with its working: a 10 kg body accelerating at 2 m/s² needs a net force of 20 N. Enter all three to check a handwritten answer. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass
- 10
- Acceleration
- 2
- Mass
- 10
- Acceleration
- 2
- F
- 20
- Force
- 20
A Newton's second law calculator turns the classic equation F equals m times a into a practical solver for homework, labs, and quick engineering checks. Enter any two of mass m, acceleration a, and net force F in a consistent unit system, leave the unknown blank, and the tool returns the missing value together with a substituted equation, a short physics message, and ordered step strings you can paste into worksheets or automated tests. Mass must stay positive; acceleration and force may be signed for direction.
What F = m a means and which variable you can leave blank
Newton's second law relates the net force on a body to its mass and the acceleration that force produces along a chosen axis: net force F equals mass m times acceleration a. In introductory mechanics this is written F equals m a, with force in newtons when mass is in kilograms and acceleration in metres per second squared, or any other coherent triad that multiplies to a force unit.
Mass is a positive scalar property of the body in classical problems; acceleration and force are signed quantities that point along or against the positive direction you chose when you drew the free-body diagram. This calculator accepts any two of the three numbers and solves algebraically for the third: given m and a it returns F equals m times a; given F and a it returns m equals F divided by a when a is non-zero; given F and m it returns a equals F divided by m.
Leaving two fields blank is rejected because the equation cannot determine two free unknowns from a single product relation. Providing all three values is allowed only when they are consistent within a tight numerical tolerance, which is useful as a check against a handwritten answer. The tool never rearranges multi-force systems for you: if several forces act, sum them to a single net F first, then call the solver.
It also never converts units mid-equation, so mixing kilograms with feet per second squared will produce a nonsense force that the math cannot detect.
Practical tips, limits, and related searches
Use one consistent unit system end to end—for example kilograms, metres per second squared, and newtons—before calling; this landing does not perform unit conversion. When teaching free-body diagrams, reduce every multi-force problem to one net F along the axis of interest before using the calculator, and keep the sign of a and F aligned with that axis.
This page targets people searching for a Newton's second law calculator, F equals m a solver, or net force from mass and acceleration online; it is not a full dynamics suite that integrates trajectories, not a variable-mass rocket equation, and not a unit converter. Prefer this capability when you already know any two of mass, acceleration, and net force and only need the third; if your source problem gives weight on Earth instead of mass, convert weight to mass with local g first.
Round-trip checks are easy: recompute m times a by hand and confirm it equals the published F within the same twelve-decimal rounding used in the response.
What you can do with it
Homework checks for F = m a
Students enter any two of mass, acceleration, and net force from textbook second-law problems and compare the missing value and substitution steps against a deterministic result before submitting.
Lab pre-check before multi-body models
Pipelines validate net force from measured mass and acceleration first, then branch to multi-force or multi-axis models only when the single-axis F equals m a check matches lab notes.
FAQ
What formula does the Newton's second law calculator use?
It uses F = m a, where F is net force, m is mass, and a is acceleration. Leave any one field blank to solve for that variable.
What happens if two unknowns are left blank?
Newton's second law needs any two of m, a, and F; two blanks leave the equation underdetermined.
Can mass be negative or zero?
No. Classical F = m a requires a positive mass. Zero or negative m is rejected whether you provide it or solve for it as F / a.
Does this convert units for me?
No. Keep m, a, and F in one consistent unit system (for example kg, m/s², and N). The calculator only evaluates F = m a.
Is the Newton's second law calculator free?
The browser tool is free and runs locally.
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/newton-second-law \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"m":10,"mass":1e-15}'const res = await fetch("https://api.kit.forhosting.com/mech/newton-second-law", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"m": 10,
"mass": 1e-15
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/newton-second-law",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"m": 10,
"mass": 1e-15
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/newton-second-law", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"m":10,"mass":1e-15}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"m":10,"mass":1e-15}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/newton-second-law", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"m": 10,
"mass": 1e-15
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.newton_second_law",
"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
max_abs | 1000000000000 |
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
If two unknowns are left blank, validation fails with a clear invalid_input error so incomplete forms never silently invent a number. Pricing is a flat $0.002 per successful API request; failed validation is never charged.
How to call the API and what comes back
Absolute values must stay within the published limit of one trillion; mass, when present or when solved, must be strictly positive and at least one times ten to the minus fifteen. Send a JSON body with any two of the optional finite fields m (alias mass), a (aliases acceleration and accel), and F (aliases force, net_force, and f). Failed validation—two unknowns left blank, non-finite numbers, values outside absolute limits, non-positive mass, division by zero when solving m equals F over a with a equal to zero, an inconsistent triple, or a non-finite product—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price. Prefer JSON numbers when you control the client; string numbers are accepted only when they match a strict finite numeric pattern for homework-form paste paths.
Practical tips, limits, and related searches
Keep m, a, and F inside the published absolute range so products and quotients remain finite in IEEE double precision on the Worker and in the browser. Pair classroom examples deliberately: m equals ten and a equals two yields F equals twenty; F equals fifty and m equals five yields a equals ten; F equals twelve and a equals three yields m equals four; and a single field alone demonstrates the hard invalid_input path when two unknowns are left blank. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately omit two fields.
Integration use cases
Unit tests for dynamics helpers
Generate known-good force, mass, and acceleration cases plus deliberate two-blank rejections for coding kata expected values in games or simulators.