Free fall calculator
Drop something from 19.62 m with gravity at 9.81 m/s² and it lands after 2 seconds at 19.62 m/s: enter any height to get both the fall time and the impact speed. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Height
- 19.62
- Gravitational acceleration
- 9.81
- Fall time
- 2
- Impact velocity
- 19.62
- Initial velocity
- 0
Free fall from rest is the classic first problem in constant-acceleration kinematics: an object is released with zero initial velocity and drops under a fixed gravitational field until it reaches a lower surface a known height below the release point. Students, teachers, engineers, and game authors all need the same two numbers—how long the fall lasts and how fast the object is moving at impact—without reopening a textbook for the square-root formulas every time.
What free fall from rest means and which quantities determine the answer
In introductory mechanics, free fall under constant gravity means the only acceleration acting on the object is a constant downward vector of magnitude g. When the object is dropped from rest, its initial velocity is exactly zero at the release height. With that initial condition, the kinematic equation for displacement along the fall direction reduces to height equals one half times g times time squared.
Solving for time gives the familiar square root of two times height over g. The impact speed follows either by multiplying g by that time or by applying the work–energy style identity that speed squared equals two times g times height. Search intent clusters around phrases such as free fall calculator, time to fall from height, impact velocity from drop, and gravity free fall equation.
People want a numeric pair they can check against a worksheet, a safety estimate for a dropped tool, a game physics sanity check, or a lab report—not only a derivation that the motion is determined.
How this calculator validates input and applies the free-fall formulas
Height must be a finite number that is not negative; zero height is allowed and yields zero fall time and zero impact velocity, which is the correct limiting case of a drop with no distance to travel. Gravity, when provided, must be a positive finite number; when omitted, the engine uses the default standard Earth gravitational acceleration nine point eight zero six six five in SI-style units.
After validation, fall time is the square root of two times height divided by gravity, and impact velocity is the square root of two times gravity times height. Edge cases are explicit: missing height, non-numeric strings, non-finite values, zero or negative gravity, and oversized magnitudes all fail before any kinematic result is returned. There is no air resistance, no variable g with altitude, and no horizontal motion—this is the ideal one-dimensional drop from rest.
What you can do with it
Homework and lab free-fall drills
Students and graders confirm fall time and impact speed for given heights and g values, including clear rejection when height is negative.
Safety estimates and game or sim sanity checks
Quick structured numbers for drop height scenarios, prototype simulators, or briefing notes that need impact velocity without a full dynamics stack.
FAQ
Which formulas does the free fall calculator use?
From rest under constant g: fall time t = sqrt(2h/g) and impact velocity v = sqrt(2gh). Air resistance and variable gravity are not modeled.
What happens if height is negative?
Free-fall drop height must be non-negative; those calls are not charged.
Is the free fall calculator free?
The browser tool runs free on your device.
What gravity value is used by default?
If you omit gravity, the engine uses 9.80665 (standard Earth gravitational acceleration in m/s²-style units). Pass a positive custom gravity for other bodies or problem-set conventions.
Can I use it for the Moon or another planet?
Yes. Enter that body's gravitational acceleration instead of the default Earth value of 9.80665 m/s². Keep the height in the same length unit as the gravity value, and the time comes out in seconds.
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/free-fall \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"height":19.62}'const res = await fetch("https://api.kit.forhosting.com/mech/free-fall", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"height": 19.62
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/free-fall",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"height": 19.62
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/free-fall", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"height":19.62}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"height":19.62}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/free-fall", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"height": 19.62
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.free_fall",
"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 capacity accepts a non-negative drop height and an optional positive gravity (defaulting to standard Earth g), rejects negative heights with a clear invalid_input error, and returns fall time, impact velocity, and the gravity actually used as structured JSON.
What free fall from rest means and which quantities determine the answer
Delivering height, gravity, fall_time, impact_velocity, initial_velocity, and method as JSON makes the result easy to paste into notes, diff in automated tests, or feed into a larger pipeline without reimplementing square roots in every language you teach or deploy. Units stay consistent with whatever length and time basis you chose for height and gravity: metres with metres per second squared yield seconds and metres per second.
How this calculator validates input and applies the free-fall formulas
Send a JSON body with required height and optional gravity. A negative height fails immediately with invalid_input because a free-fall drop height cannot point the wrong way on the vertical axis used by this model. Both results are rounded to a stable decimal precision so the same input always yields the same JSON across engines.
Practical use, limits, pricing, and delivery channels
Use the browser tool when you want an immediate free-fall time and impact speed while checking homework, estimating how long a sensor package falls in a lab drop tower, verifying a game physics constant, or sanity-checking a safety briefing about objects dropped from a known height. Choose gravity to match your planet, moon, or classroom convention—Earth default, lunar about one point six two, or any positive constant you already use in a problem set. There is no language model, no external physics service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible lesson materials. Each successful request is one billable item at $0.002; failed validation does not consume balance. Results are fully deterministic: the same height and gravity always yield the same fall_time and impact_velocity fields. Wire the endpoint into free-fall drills, contest answer checkers, drop-test worksheets, or preprocessing steps where you already prefer explicit domain errors—such as rejecting a negative height—over opaque black-box widgets that cannot explain why a bad input was refused.
Integration use cases
Deterministic fixtures for physics tests
Pipelines that seed unit tests or interactive kinematics demos can call a pure free-fall oracle instead of reimplementing square roots in every language.
Technical questions
How do I compute free-fall time and impact velocity with this API?
Send a JSON body with height (required) and optional gravity to mech.free_fall. The response returns fall_time, impact_velocity, the gravity used, and initial_velocity 0.