Braking distance calculator
At 20 m/s with a steady deceleration of 5 m/s², a vehicle needs 40 m to stop. Enter speed and deceleration to get the braking distance in metres for safety checks or homework. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Speed
- 20
- Deceleration
- 5
- Stopping distance m
- 40 m
Braking distance is the distance a vehicle or sliding body travels while decelerating from an initial speed down to a full stop under constant deceleration. Drivers studying highway safety, physics students checking homework, fleet trainers comparing wet-road and dry-road scenarios, and engineers sizing emergency stop zones all need the same closed-form number: distance equals speed squared divided by twice the deceleration magnitude.
What braking distance means and which quantities determine the answer
Under constant deceleration, kinematics reduces the stopping problem to a single algebraic identity. Search intent clusters around phrases such as braking distance calculator, stopping distance from speed and deceleration, v squared over two a, emergency stop distance, and vehicle braking distance formula. People want a numeric length they can check against a worksheet, embed in a fleet safety brief, or feed into a simulation—not only a reminder that the formula exists.
Keep units consistent: metres per second for speed and metres per second squared for deceleration yield metres of distance. If your source data is in kilometres per hour, convert speed to metres per second first (divide by 3.6) so the squared term remains dimensionally correct.
How this calculator validates input and applies d = v² / (2a)
Numeric strings that parse to finite numbers are accepted so forms and CSV-style pipelines can pass values without an extra cast. After validation, deceleration must be strictly positive. Zero deceleration would imply infinite stopping distance (division by zero); negative deceleration would mean acceleration rather than braking and would not produce a meaningful stop under this model, so both cases are rejected with a message that names the field and states that deceleration must be greater than zero.
Speed may be zero (distance is then zero) or negative in the algebraic sense; the squared term removes the sign so distance is non-negative. There is no friction model, no tire-road lookup table, no reaction-time add-on, and no multi-axis composition; this is the ideal one-dimensional constant-deceleration stop from the two known inputs.
Practical use, limits, pricing, and delivery channels
Use the browser tool when you want an immediate stopping distance while checking homework, comparing dry-road versus wet-road deceleration magnitudes, sizing a short emergency stop zone, or sanity-checking a game physics constant for vehicle brakes. Choose units consistently—if speed is still in kilometres per hour, convert before calling so deceleration and distance share the SI metre-second basis. There is no language model, no external traffic or weather service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible lesson materials.
Remember that real-world total stopping distance often adds a reaction-distance term of speed times reaction time; this calculator isolates the pure braking segment only.
What you can do with it
Homework and lab braking drills
Students and graders confirm stopping distance for given speed and deceleration pairs, with clear rejection when deceleration is zero, negative, missing, or non-numeric.
FAQ
Which formula does the braking distance calculator use?
Constant deceleration to a stop in one dimension: d = v² / (2a), where v is speed and a is positive deceleration. Reaction time, variable friction, and multi-axis paths are not modeled.
Is the braking distance calculator free?
The browser tool runs free on your device.
What units does the stopping distance use?
Convert from km/h by dividing speed by 3.6 before calling.
What happens if the deceleration is zero or negative?
You get an error instead of a distance. Deceleration must be greater than zero, because without braking the vehicle would never come to a stop in this model.
How do I use a speed in km/h?
Divide it by 3.6 first to get metres per second, then enter it with the deceleration in metres per second squared. The braking distance then comes out in metres.
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/stopping-distance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"speed":20,"deceleration":5}'const res = await fetch("https://api.kit.forhosting.com/mech/stopping-distance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"speed": 20,
"deceleration": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/stopping-distance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"speed": 20,
"deceleration": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/stopping-distance", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"speed":20,"deceleration":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"speed":20,"deceleration":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/stopping-distance", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"speed": 20,
"deceleration": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.stopping_distance",
"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 braking distance calculator accepts finite speed in metres per second and a strictly positive deceleration in metres per second squared, rejects zero or negative deceleration with a clear invalid_input error, and returns the stopping distance in metres as structured JSON.
What braking distance means and which quantities determine the answer
If a body starts at speed v and comes to rest under constant deceleration of magnitude a, the work-energy relation or the SUVAT equation v_final squared equals v_initial squared plus two a s with final speed zero both rearrange to s equals v squared over two a. That distance is the pure braking (stopping) distance: it does not include reaction time or free-rolling coast, only the distance covered while the brakes are actively applying the stated deceleration. Delivering speed, deceleration, stopping_distance_m, formula, method, and unit 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 d = v² / (2a)
Send a JSON body with required speed and deceleration. Every field must be present and finite: missing keys, empty strings, non-numeric text, NaN, and Infinity all fail immediately with invalid_input before any distance is returned, and failed validation is not charged. The stopping distance is computed as speed times speed divided by two times deceleration, then rounded to a stable decimal precision so the same input always yields the same JSON across JavaScript engines.
Practical use, limits, pricing, and delivery channels
Each successful request is one billable item at $0.002; failed validation does not consume balance. Results are fully deterministic: the same speed and deceleration always yield the same stopping_distance_m field. Wire the endpoint into safety drills, contest answer checkers, highway engineering worksheets, or preprocessing steps where you already prefer explicit domain errors—such as rejecting zero deceleration—over opaque black-box widgets that cannot explain why a bad input was refused.
Integration use cases
Fleet and safety training scenarios
Compare how stopping distance grows with speed squared when dry-road and wet-road decelerations differ, using stable JSON for lesson decks and quizzes.
Deterministic fixtures for physics tests
Pipelines that seed unit tests or interactive kinematics demos can call a pure braking-distance oracle instead of reimplementing d=v²/(2a) in every language.
Technical questions
How do I compute braking distance with this API?
Send a JSON body with speed (m/s) and deceleration (m/s², must be positive) to mech.stopping_distance. The response returns stopping_distance_m plus the validated inputs, formula, method, and unit.
What happens if deceleration is zero or negative?
The request fails with invalid_input. Zero or negative deceleration is not a valid braking magnitude for this formula, so no distance is returned and the call is not charged.