Coefficient of friction calculator
A friction force of 20 N against a normal force of 50 N gives a coefficient of friction of 0.4. Enter both forces in the same unit and get the dimensionless ratio with the substituted equation and each step. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Friction force magnitude
- 20
- Normal force
- 50
- Friction force
- 20
- Friction
- 20
- Normal force
- 50
- Normal
- 50
A coefficient of friction calculator turns the elementary contact-mechanics ratio into a practical tool for homework, lab books, and quick engineering checks. Enter the friction force Ff along the surface and the normal force N perpendicular to it in the same force unit system, and the tool returns the dimensionless coefficient mu equals Ff divided by N, together with a substituted equation, a short physics message, and ordered step strings you can paste into worksheets or automated tests. Missing either force, non-finite values, and out-of-range magnitudes are likewise rejected before any ratio is published.
What μ = Ff / N means and when the normal force must not be zero
The coefficient of friction is defined as the ratio of the friction force parallel to a contact surface to the normal force pressing the two bodies together. In symbols, mu equals Ff over N. The result is dimensionless when both forces share the same unit—newtons over newtons, pounds-force over pounds-force, or any other consistent force pair—so you never convert the answer into a force unit after the division.
Positive normal force is the usual laboratory case of weight or clamping load; a negative N is still accepted as a signed component if your free-body diagram orients the normal axis opposite to convention, because the algebra is still a single division. Friction force may likewise be signed when your problem resolves a surface component along a chosen axis; many textbook problems simply pass magnitudes so that mu comes out non-negative.
Practical tips, limits, and related searches
Use one consistent force unit end to end—for example both forces in newtons—before calling; this landing does not perform unit conversion between SI and imperial. When teaching Coulomb friction, treat this tool as the ratio step only: if the source problem gives mass and local g, compute N equals m g yourself, then pass that normal force here.
This page targets people searching for a coefficient of friction calculator, mu from friction and normal force, or Ff over N online; it is not a material handbook lookup for rubber-on-concrete tables, not a full multibody contact solver, and not a unit converter. Prefer this capability when you already know both force magnitudes and only need the dimensionless ratio; if your lab reports limiting friction force and contact load, this is the one-line check before you write mu into a report.
Round-trip checks are easy: recompute Ff divided by N by hand and confirm it equals the published mu within the same twelve-decimal rounding used in the response.
What you can do with it
Homework checks for μ = Ff / N
Students enter friction force and normal force from textbook contact problems and compare the dimensionless coefficient and substitution steps against a deterministic result before submitting.
Lab pre-check before material tables
Pipelines validate measured sliding force over measured normal load first, then compare the experimental mu against handbook ranges for the surface pair only after the ratio check matches the lab notes.
FAQ
What formula does the coefficient of friction calculator use?
It uses mu = Ff / N, where Ff is the friction force and N is the normal force. The result is dimensionless when both forces use the same unit.
Do I need the same units for both forces?
Yes. Keep Ff and N in one consistent force unit (for example both newtons). The calculator does not convert units.
Is mu static or kinetic?
The calculator returns the ratio of the forces you supply. Label the result static or kinetic according to your experiment; the math path is the same division.
Is the coefficient of friction calculator free?
The browser tool is free and runs locally.
What if I only know the object's mass?
Work out the normal force first. When a problem gives mass and gravity, multiply them to get the normal force and enter that value here; this tool only performs the ratio of friction force to normal force.
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/coefficient-of-friction \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"Ff":20,"N":50}'const res = await fetch("https://api.kit.forhosting.com/mech/coefficient-of-friction", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"Ff": 20,
"N": 50
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/coefficient-of-friction",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"Ff": 20,
"N": 50
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/coefficient-of-friction", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"Ff":20,"N":50}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"Ff":20,"N":50}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/coefficient-of-friction", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"Ff": 20,
"N": 50
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.coefficient_of_friction",
"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 the normal force is zero, validation fails with a clear invalid_input error so incomplete or singular forms never silently invent a number. Pricing is a flat $0.002 per successful API request; failed validation is never charged.
What μ = Ff / N means and when the normal force must not be zero
Physically, a zero normal force means there is no contact pressure, so the classical Coulomb ratio is undefined and this calculator rejects N equal to zero with invalid_input rather than returning infinity or a quiet NaN. This tool does not invent static versus kinetic labels from material tables: when you supply measured sliding force and measured normal load, the ratio is the operative coefficient for that trial, whether you later call it mu_s at the verge of slip or mu_k during steady sliding. It also does not integrate multi-body contacts, deforming surfaces, or velocity-dependent friction laws—reduce those problems to a single effective Ff and N pair before calling the solver.
How to call the API and what comes back
Absolute values must stay within the published limit of one trillion, and N must not be zero within a tiny numerical epsilon used to catch exact and near-zero singular cases. Send a JSON body with the required finite fields Ff (aliases friction_force, friction, F_f, ff, and f_friction) and N (aliases normal_force, normal, Fn, F_n, and fn). Failed validation—missing force, non-finite numbers, values outside absolute limits, or zero normal force—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 Ff and N inside the published absolute range so the quotient remains finite in IEEE double precision on the Worker and in the browser. Pair classroom examples deliberately: Ff equals twenty and N equals fifty yields mu equals zero point four; Ff equals fifteen and N equals twenty-five yields mu equals zero point six; and N equal to zero demonstrates the hard invalid_input path required by the product brief. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set N to zero.
Integration use cases
Unit tests for game and sim friction helpers
Generate known-good force pairs and deliberate zero-normal rejections for coding kata expected values in physics engines and sliding contact stubs.
Technical questions
What happens if the normal force is zero?
The tool returns invalid_input. Division by zero is rejected because the coefficient of friction is undefined when N = 0.