Free fall time calculator
Dropped from rest, an object falls 100 m in 4.5160075575 seconds under standard gravity of 9.80665 m/s². Enter the drop distance, change g for another planet or a textbook value, and get the time and impact speed. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Distance
- 100
- G
- 9.80665
- Time
- 4.5160075575
- Impact velocity
- 44.2869055139
- Precision
- 10
This free fall time calculator finds how long an object takes to reach the ground when dropped from rest through a known vertical distance under constant gravitational acceleration, with air resistance ignored. The closed-form identity is t equals the square root of two times distance over g, which follows directly from the kinematic relation distance equals one half g t squared when the initial speed is zero. The response also reports the ideal impact speed magnitude as the square root of two g d, equal to g times t. The engine is fully deterministic arithmetic: no network calls, no sampling, and no date-dependent shortcuts.
Fall time from rest and what you get
In introductory mechanics, free fall from rest means an object starts with zero initial velocity and accelerates only under constant gravitational acceleration g, with air drag and buoyancy neglected. Integrating constant acceleration gives the familiar distance equals one half g t squared, which rearranges to t equals the square root of two d over g for a non-negative drop distance d. Impact speed under the same ideal model is the square root of two g d, or equivalently g times the fall time.
Zero distance is valid and yields zero time and zero impact speed rather than a division singularity.
Where free-fall time fits in study, labs, and software
Students meet free-fall timing when a textbook introduces constant acceleration, when a lab drops a ball from a measured height and compares stopwatch data to theory, or when a contest problem asks for time without graphing velocity. Teachers can pre-generate answer keys for modest heights and g values without trusting opaque calculator apps that silently switch units or round g without saying so.
Developers call the same contract from scripts to seed deterministic test vectors for game physics demos, to normalize user-entered drop heights before a visualization, or to satisfy programming-challenge statements that demand t rather than a hand-waved sketch. Safety and engineering first-order checks use the ideal formula before drag matters: a short vertical drop estimate under constant g, or a comparison between Earth and lunar g for the same height.
What you can do with it
Homework and lab checks
Compute ideal free-fall time from drop height and g before comparing to stopwatch data or grading kinematics worksheets.
Tutoring and teaching software
Normalize user-entered height and g into fall duration and impact speed for interactive lessons and step helpers.
FAQ
What does the free fall time calculator cost?
It is free in your browser on this page.
What formula is used for free-fall time?
For motion from rest under constant g with no air resistance, t = √(2d/g). Impact speed magnitude is v = √(2gd) = g·t.
What happens if the fall distance is negative?
Distance must be a non-negative length; a negative value is not a valid free-fall drop from rest.
Can I change g for other planets or textbook problems?
The default is 9.80665 m/s². g must be strictly positive and within the documented magnitude limit.
Does this include a non-zero initial velocity?
No. This calculator models free fall from rest only. For launches with an initial vertical speed or an angle, use a dedicated projectile kinematics tool.
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-time \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"distance":100}'const res = await fetch("https://api.kit.forhosting.com/mech/free-fall-time", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"distance": 100
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/free-fall-time",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"distance": 100
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/free-fall-time", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"distance":100}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"distance":100}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/free-fall-time", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"distance": 100
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.free_fall_time",
"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_distance | 1000000000000000 |
max_abs_g | 1000000 |
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 free-fall time means and what the response contains
This calculator returns the normalized inputs distance and g, the fall time, the impact velocity magnitude, the precision used, a method tag free_fall_from_rest, and a short formula reminder. There is no numerical ODE integration and no Monte Carlo sampling of paths: the engine either evaluates the closed form inside the supported numeric range or rejects the input with invalid_input. Rejected cases include a missing distance, non-finite values, a non-positive g, magnitudes above the documented ceilings, and any negative fall distance, because a signed drop below the reference is not a valid free-fall length from rest.
How distance and g are read and how t stays reproducible
Zero distance is valid and yields zero time. 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. Gravitational acceleration g defaults to nine point eight zero six six five meters per second squared, the conventional standard gravity, and may be overridden for other planets or textbook problems that use g equals nine point eight or ten; g must be strictly positive and within the documented magnitude ceiling. Computation uses Math.sqrt on two d over g and on two g d for the companion impact speed. The preferred field is distance for the vertical fall length, but aliases d, h, height, fall_distance, and drop are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Distance must be finite and non-negative: a negative value fails with invalid_input and a message that names the field, so a bad cell does not become a silent absolute-value guess. 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 free-fall formulas yourself.
Where free-fall time fits in study, labs, and software
Product and education tools use the endpoint when a learner types a height and the UI must show fall time and impact speed. 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 projectile max-height or range 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 time and impact_velocity values for unit tests, game-physics demos, and CI assertions.