Acceleration calculator
A speed gain of 20 m/s over 4 seconds is an average acceleration of 5 m/s²: enter the change in velocity and the time it took, and the calculator divides one by the other, keeping the sign when something brakes. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Change in velocity
- 20
- Time
- 4
- Acceleration
- 5 m/s^2
- Precision
- 10
This acceleration calculator finds the average acceleration of an object when you know how much its velocity changed and how long that change took. The definition is the closed form a equals delta-v over t, which is the mean rate of change of velocity over a finite interval and matches the slope of a velocity-versus-time graph between two points. When delta-v is given in metres per second and t in seconds, the result is reported in metres per second squared; any consistent unit pair works the same way. Negative delta-v yields a negative average acceleration, which is the usual signed description of slowing down along a chosen positive direction. The engine is fully deterministic arithmetic: no network calls, no sampling, and no date-dependent shortcuts.
What average acceleration tells you
In introductory mechanics, average acceleration over a time interval is the change in velocity divided by the duration of that interval. If an object goes from an initial velocity to a final velocity, delta-v is final minus initial, and a equals that difference over elapsed time t.
The quantity is a signed scalar along a chosen axis (or the magnitude when you supply only a speed change with an agreed sign convention): positive values mean the velocity component is increasing in the positive direction, and negative values mean it is decreasing. Instantaneous acceleration is the limit of this ratio as the interval shrinks to zero; this calculator answers the finite-interval form that students and engineers use for constant-acceleration segments and for mean values when the detailed profile is unknown.
Zero velocity change is valid and yields zero average acceleration when t is non-zero.
Where average acceleration fits in study, labs, and software
Students meet average acceleration when a textbook introduces constant-acceleration kinematics, when a lab measures speeds at two times with a photogate or video tracker, or when a contest problem gives a velocity change and a duration and asks for a without calculus. Teachers can pre-generate answer keys for modest delta-v and t values without trusting opaque calculator apps that silently switch units or drop the sign of deceleration.
Developers call the same contract from scripts to seed deterministic test vectors for game physics demos, to normalize user-entered speed changes before a visualization, or to satisfy programming-challenge statements that demand a rather than a hand-waved sketch. Vehicle and sports first-order checks use the mean definition when only start and end speeds and a stopwatch reading are known: average a equals delta-v over t for that interval, before drag curves or power limits are modeled.
What you can do with it
Homework and lab checks
Compute average acceleration from measured velocity change and elapsed time before grading worksheets or comparing to sensor data.
Tutoring and teaching software
Normalize user-entered Δv and t into average acceleration for interactive lessons and step helpers.
FAQ
What does the acceleration calculator cost?
It is free in your browser on this page.
What formula is used for average acceleration?
Average acceleration is a = Δv / t, where Δv is the change in velocity and t is the elapsed time. With SI inputs the unit is m/s².
What happens if time is zero?
Average acceleration is undefined when the elapsed time equals zero because division by zero has no finite value.
Is this instantaneous or average acceleration?
It is the average (mean) acceleration over the finite interval of length t. Instantaneous acceleration would require the limit as t approaches zero or a full a(t) profile.
Can the acceleration come out negative?
Yes. Enter a negative change in velocity, for example a car braking along the direction you call positive, and the average acceleration is negative. A change of zero gives zero, as long as the time is not zero.
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/acceleration \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"delta_v":20,"time":4}'const res = await fetch("https://api.kit.forhosting.com/mech/acceleration", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"delta_v": 20,
"time": 4
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/acceleration",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"delta_v": 20,
"time": 4
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/acceleration", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"delta_v":20,"time":4}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"delta_v":20,"time":4}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/acceleration", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"delta_v": 20,
"time": 4
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.acceleration",
"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_delta_v | 1000000000000000 |
max_abs_time | 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 average acceleration means and what the response contains
The response returns the normalized inputs delta_v and time, the computed acceleration, the precision used, a method tag average_acceleration, a short formula reminder, and a unit hint m/s squared for SI inputs. There is no numerical ODE integration and no Monte Carlo sampling of trajectories: the engine either evaluates the division inside the supported numeric range or rejects the input with invalid_input. Rejected cases include a missing delta_v or time, non-finite values, magnitudes above the documented ceilings, and any time that equals zero, because division by zero is undefined and there is no average rate of change over an empty interval.
How delta_v and time are read and how a stays reproducible
Delta_v may be positive or negative; only non-finite values and magnitudes above the documented ceiling are rejected. Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces and non-numeric tokens are rejected. The preferred field for the velocity change is delta_v, but aliases dv, velocity_change, change_in_velocity, and delta_velocity are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. The preferred field for duration is time, with aliases t, elapsed, elapsed_time, dt, and duration. Time must be finite and non-zero: a literal zero fails with invalid_input and a message that names the field and explains that a equals delta-v over t is undefined when elapsed time equals zero, so a bad cell does not become a silent infinity or NaN. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for the numeric outputs, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the average-acceleration formula yourself.
Where average acceleration fits in study, labs, and software
Product and education tools use the endpoint when a learner types a velocity change and a time and the UI must show metres per second squared. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with free-fall time or projectile max-height helpers when you need related kinematics, and with other math endpoints when you are building a small lab of free, deterministic physics calculators.
Integration use cases
Deterministic test fixtures
Generate reproducible acceleration values for unit tests, game-physics demos, and CI assertions on a = Δv/t.
Technical questions
Can delta_v be negative?
Yes. A negative change in velocity produces a negative average acceleration (deceleration along the chosen positive axis).