Stopping distance calculator
At 20 m/s with a 1.5 s reaction time and 8 m/s² of braking, a car covers 30 m before braking starts and 25 m while braking, 55 m in all. Enter the speed, reaction time and deceleration to get both parts and the total. Free in your browser.
- Free
- Runs in your browser
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- Your data stays on your device
Run — free
Worked example
- Speed
- 20
- Reaction time
- 1.5
- Deceleration
- 8
- Reaction distance m
- 30 m
- Braking distance m
- 25
- Stopping distance m
- 55
This stopping distance calculator finds the total distance a vehicle travels from the instant a hazard appears until it comes to a complete stop. The total is the sum of two segments: thinking distance at constant speed during the driver's reaction time, then braking distance under constant deceleration. The closed-form identity is d = v t + v squared over 2 a. Given speed in metres per second, a non-negative driver reaction time in seconds, and a strictly positive braking deceleration in metres per second squared, the engine returns the distance in metres. Highway-code tables, fleet trainers, physics homework, and safety simulators all need that combined number rather than a braking-only or reaction-only fragment. Zero deceleration is rejected because the braking term would be undefined. The arithmetic is fully deterministic: no network calls, no sampling, and no date-dependent shortcuts.
What total stopping distance means and which quantities determine the answer
In highway safety and vehicle kinematics, total stopping distance is the length of road a vehicle covers from the moment a hazard appears until the vehicle is fully at rest. It is the sum of two physically different segments that happen in sequence. First comes thinking distance, also called reaction or perception-reaction distance: while the driver is still seeing, deciding, and moving a foot to the pedal, speed is treated as constant, so that length is speed times reaction time.
Second comes braking distance: after the brakes apply a constant deceleration of magnitude a, the SUVAT or work-energy identity with final speed zero rearranges to speed squared over twice the deceleration. Adding those two lengths is the closed-form total: d equals v t plus v squared over two a. Search intent for this page clusters around phrases such as stopping distance calculator, total stopping distance from speed and reaction time, thinking distance plus braking, driver reaction and deceleration, and how far a car travels before it stops.
People want the combined metre figure they can check against a highway-code table, a fleet briefing, or a simulation, not a braking-only or reaction-only fragment. Zero deceleration is invalid because the braking term would be undefined; missing or non-numeric fields fail the same way so a bad cell never becomes a silent zero distance.
Keep units consistent: convert kilometres per hour to metres per second by dividing by 3.6 before calling, otherwise both the linear term and the squared term are dimensionally wrong and the metre result cannot be trusted against a worksheet.
Where total stopping distance fits in training, study, and software
Use the browser tool when you want an immediate total stopping distance while checking a highway-code worksheet, comparing a one-second alert driver with a two-and-a-half-second design value at the same speed, briefing a fleet on wet-night hazards that change both reaction time and available deceleration, or sanity-checking a game-physics constant for the delay before brakes apply plus the stop that follows.
Choose units consistently — if speed is still in kilometres per hour, convert before calling so time in seconds, deceleration in metres per second squared, and distance in metres 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 a braking-only tool reports v squared over two a, and a reaction-distance tool reports v times t; those are different search intents and different numbers.
This calculator is the combined highway-code stopping distance, which is the figure most people mean when they ask how far a car travels before it stops, and the three inputs exist so that thinking time and brake strength can be varied independently in the same request.
What you can do with it
Highway-code and classroom total-stop drills
Students and graders confirm how far a vehicle travels from hazard to rest for given speed, reaction time, and deceleration, with clear rejection when deceleration is zero, negative, missing, or non-numeric.
Fleet and driver-training scenarios
Compare alert versus delayed reaction times and dry versus wet deceleration at the same speed so briefings show how thinking distance and braking distance both grow before the vehicle stops.
FAQ
Which formula does the stopping distance calculator use?
Variable speed during thinking, ABS modulation, and tire-road friction tables are not modeled.
What happens if deceleration is zero?
Deceleration must be a positive number greater than zero; a zero value would make the braking term undefined, is not billed, and returns no distance.
How is total stopping distance different from braking distance or reaction distance alone?
Reaction distance is v t while the driver is still reacting. Braking distance is v²/(2a) while the vehicle is decelerating. Total stopping distance is the sum of both segments, which is the number this calculator returns.
How do I use a speed in km/h?
Divide it by 3.6 to get metres per second before you enter it. If you skip that step, both the reaction part and the braking part come out wrong, and the total no longer matches a highway-code table.
Does the calculator account for the road surface or the tyres?
Not directly. There is no friction model or tyre table: you enter the braking deceleration yourself, so a wet or icy road means typing a smaller deceleration. Alcohol and fatigue are not modelled either.
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/phys/stopping-distance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"speed":20,"reaction_time":1.5,"deceleration":8}'const res = await fetch("https://api.kit.forhosting.com/phys/stopping-distance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"speed": 20,
"reaction_time": 1.5,
"deceleration": 8
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/stopping-distance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"speed": 20,
"reaction_time": 1.5,
"deceleration": 8
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/stopping-distance", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"speed":20,"reaction_time":1.5,"deceleration":8}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"speed":20,"reaction_time":1.5,"deceleration":8}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/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,
"reaction_time": 1.5,
"deceleration": 8
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.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.
Limits
max_abs | 1000000000000000 |
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
What total stopping distance means and which quantities determine the answer
This engine returns the validated speed, reaction_time, and deceleration, the two segment lengths reaction_distance_m and braking_distance_m, the total stopping_distance_m, a formula tag d=v*t+v^2/(2a), a method tag stopping_distance, and the unit m. There is no tire-road lookup and no numerical integration: the engine either evaluates that identity inside the supported range or rejects the input with invalid_input.
How this calculator validates input and applies d = v t + v² / (2 a)
Numeric strings that parse to finite numbers are allowed so forms and CSV-style pipelines can pass values without an extra cast. After validation, deceleration must be strictly positive. Zero deceleration would imply an infinite braking term because of division by two a; a negative value would mean acceleration rather than braking, so both cases are rejected with a message that names the field and states that deceleration must be a positive number greater than zero. Reaction time must be non-negative: zero reaction time yields a total equal to the braking segment alone, which is physically consistent with an instantaneous response. Speed must be non-negative: zero speed yields zero stopping distance, consistent with a parked vehicle. Magnitudes above the documented ceiling are refused so overflow cannot masquerade as a huge road length. There is no friction model, no alcohol or fatigue table, and no numerical integration of a time-varying brake force; this is the ideal one-dimensional highway-code identity from the three known inputs. Send a JSON body with required speed, reaction_time, and deceleration. The preferred field for the interval is reaction_time, but aliases time, t, reaction, thinking_time, and perception_time are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Speed accepts aliases v, velocity, and vehicle_speed. Deceleration accepts aliases a, braking, braking_deceleration, and decel. 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 engine then computes reaction_distance_m as speed times reaction_time, braking_distance_m as speed times speed divided by two times deceleration, and stopping_distance_m as the sum of those two segments. Results are rounded to a stable ten-decimal grid so the same input always yields the same JSON across JavaScript engines.
Where total stopping distance fits in training, study, and software
Each successful request is one billable item at $0.002; failed validation does not consume balance. Results are fully deterministic: the same speed, reaction time, 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 a zero deceleration — over opaque widgets that cannot explain why a bad input was refused.
Integration use cases
Deterministic fixtures for safety tests
Pipelines that seed unit tests or interactive driving demos can call a pure total-stopping-distance oracle instead of reimplementing d=v t + v²/(2a) in every language.
Technical questions
How do I compute total stopping distance from speed, reaction time, and deceleration?
Send a JSON body with speed in metres per second (non-negative), reaction_time in seconds (non-negative), and deceleration in metres per second squared (must be positive). The response returns stopping_distance_m plus the two segment lengths, the validated inputs, formula, method, and unit.
What does the stopping distance calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.