Action-reaction force calculator
Enter the push one body gives another and get the push it receives back: 50 N to the right returns 50 N to the left, written as minus 50. Each component flips the same way. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Force
- 50
- Action force
- 50
- F
- 50
- Reaction force
- -50
- Magnitude
- 50
Newton's third law of motion states that forces between two interacting bodies always come in pairs: if body A exerts a force on body B, then body B exerts a force on body A that is equal in magnitude and opposite in direction. Enter the action force one body exerts on another—as a signed scalar along a chosen axis, or as optional Cartesian components—and receive the reaction force, magnitude, formula string, law statement, and step lines you can paste into homework, labs, or automated tests.
What Newton's third law means for an action–reaction pair
Newton's third law says that whenever two bodies interact, the mutual forces they exert are equal in magnitude and opposite in direction. In symbols, if F_AB is the force that body A exerts on body B, then the force that body B exerts on body A is F_BA equals the negative of F_AB. The two forces form a single interaction pair: they act on different free-body diagrams, never cancel on the same body, and always appear together.
Magnitude equality means the size of the push or pull is the same; opposite direction means the vectors point along the same line of action but reverse sense. A person pushing a wall with fifty newtons to the right experiences fifty newtons from the wall to the left; a book resting on a table has the book's weight paired with the table's normal force only when those are truly mutual contact forces between book and table—not when other forces act on the same object.
This calculator implements the map F maps to negative F for a signed scalar force and for each provided Cartesian component. Zero force is allowed and yields a zero reaction. The tool does not invent friction coefficients, does not solve multi-body equilibrium, and does not replace free-body diagram reasoning: it only returns the third-law partner of the force you already identified as the action of A on B.
Practical tips, limits, and related searches
Use one consistent force unit end to end—for example newtons throughout a SI homework set—before calling; this landing does not perform unit conversion. When teaching free-body diagrams, remind learners that the third-law partner acts on the other body: the reaction of the ground on a walker is not cancelled by the walker's push on the ground on the same diagram.
This page targets people searching for an action reaction force calculator, Newton's third law pair tool, or equal and opposite force online; it is not a full multi-body dynamics suite, not a second-law F equals m a solver, and not a statics equilibrium balancer for concurrent forces on one object. Prefer this capability when you already know the force of A on B and only need F_BA; prefer a second-law calculator when you need net force from mass and acceleration on a single body.
Round-trip checks are easy: negate the reaction and confirm you recover the original action within the same twelve-decimal rounding used in the response.
What you can do with it
Homework checks for action–reaction pairs
Students enter the force of A on B from textbook third-law problems and compare the equal-and-opposite reaction, magnitude, and step lines against a deterministic result before submitting.
Lab pre-check of mutual interaction labels
Pipelines validate that labeled contact forces between two instruments are third-law consistent before folding measurements into a multi-body model.
FAQ
What formula does the action-reaction force calculator use?
It uses F_BA = −F_AB from Newton's third law: the reaction is the negation of the action force (equal magnitude, opposite direction).
Do the two forces cancel each other?
Not on the same free-body diagram. They act on different bodies. Each body still needs its own net force for F = m a.
Does this convert force units for me?
No. Keep action and reaction in one consistent unit (for example newtons). The calculator only applies F maps to −F.
Is the action-reaction force calculator free?
The browser tool is free and runs locally.
Can I enter a force as separate components?
Yes. Besides a single signed value along one axis, you can give optional Cartesian components, and each comes back with its sign reversed. A zero action is accepted too and simply returns a zero reaction.
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-third-law-pair \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"force":50}'const res = await fetch("https://api.kit.forhosting.com/mech/newton-third-law-pair", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"force": 50
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/newton-third-law-pair",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"force": 50
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/newton-third-law-pair", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"force":50}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"force":50}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/newton-third-law-pair", 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": 50
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.newton_third_law_pair",
"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 action-reaction force calculator turns that principle into a deterministic API and free browser tool. Non-numeric or missing force input fails with a clear invalid_input error and is never charged. Pricing is a flat $0.002 per successful API request.
What Newton's third law means for an action–reaction pair
Units of force are whatever you pass—newtons, kilonewtons, pounds-force, or game units—as long as you interpret the reaction in that same unit; the API does not convert force units for you.
How to call the API and what comes back
Absolute values must stay within the published limit of one trillion so products of rounding stay representable. POST a JSON body with the required finite field force—the action force F_AB along your chosen axis—or provide at least one of the optional components force_x, force_y, and force_z. Aliases F, action_force, and f map to the scalar force; Fx, Fy, Fz and lowercase variants map to components. Numeric strings such as "50" or "-12.5" are coerced when they match a strict finite numeric pattern; empty strings, bare signs, Infinity, NaN, and non-numeric text fail with invalid_input naming the field. When components are supplied, the response also includes force_x through force_z as provided, reaction_force_x through reaction_force_z, action_vector and reaction_vector objects, and vector_magnitude as the Euclidean norm of the provided component subset. Example: force fifty yields reaction_force negative fifty and magnitude fifty. Missing force with no components, or a non-numeric value such as the string "heavy", returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item.
Practical tips, limits, and related searches
Keep the action force inside the published absolute range so negation and magnitude remain finite in IEEE double precision on the Worker and in the browser. Pair classroom examples deliberately: force equals fifty for a classic equal-and-opposite check; force equals negative twelve to show that sign simply reverses again under the map; force_x equals three and force_y equals negative four for a 3-4-5 vector magnitude of five; and a non-numeric force to demonstrate the hard invalid_input path that protects automated graders. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send bad input.
Integration use cases
Unit tests for contact-force helpers
Generate known-good reaction pairs and deliberate non-numeric rejections for coding kata expected values in games, simulators, or physics engines that enforce mutual forces.
Technical questions
What happens if force is missing or not a number?
The tool returns invalid_input. Provide a finite number for force and/or at least one of force_x, force_y, force_z. Failed validation is never charged.