Free fall distance calculator
An object dropped from rest falls 19.6 metres in 2 seconds when gravity is 9.8 m/s², with air resistance ignored. Enter the elapsed time, and another gravity if you need it, to get the distance 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
- Time
- 2
- Gravity
- 9.8
- Distance
- 19.6
- Impact velocity
- 19.6
This free fall distance calculator finds how far an object drops from rest during a known elapsed time under constant gravitational acceleration, with air resistance ignored. The closed-form identity is distance equals one half g t squared, which follows directly from constant-acceleration kinematics when the initial vertical speed is zero. The response also reports the ideal impact speed as g times t, equal to the square root of two g d. Optional gravity lets you use Earth standard g, another planet, or a textbook value. The engine is fully deterministic arithmetic: no network calls, no sampling, and no date-dependent shortcuts.
How far a dropped object falls, 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 from a standing start gives the familiar distance equals one half g t squared, so a known clock interval maps directly to a vertical drop. Impact speed under the same ideal model is g times t, or equivalently the square root of two g d.
Search intent clusters around phrases such as free fall distance calculator, how far does something fall in t seconds, drop distance from elapsed time, and d equals one half g t squared. People want a numeric fall length they can check against a worksheet, a safety estimate for a timed drop, a game-physics sanity check, or a lab report—not only a symbolic derivation. Zero time is valid and yields zero distance and zero impact speed.
Where free-fall distance fits in study, labs, and software
Students meet free-fall distance when a textbook introduces constant acceleration, when a lab times a drop and asks how far the object should have fallen, or when a contest problem gives t and g instead of a measured height. Teachers can pre-generate answer keys for modest times 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 fall times before a visualization, or to satisfy programming-challenge statements that demand distance rather than a hand-waved sketch. Safety and engineering first-order checks use the ideal formula before drag matters: a short timed-drop estimate under constant g, or a comparison between Earth and lunar g for the same clock interval.
What you can do with it
Homework and lab timed-drop checks
Compute ideal free-fall distance from elapsed time and g before comparing to tape-measure data or grading kinematics worksheets that give t instead of height.
Safety estimates and planet-g comparisons
First-order timed-drop lengths under Earth, lunar, or classroom g before drag, buoyancy, or variable gravity matter.
FAQ
Which formula does the free fall distance calculator use?
From rest under constant g with no drag: distance d = ½·g·t² and impact speed v = g·t. Air resistance and variable gravity are not modeled.
What happens if time is negative?
Elapsed time for free-fall distance from rest must be non-negative; those calls are not charged.
How is this different from a free-fall time calculator?
Free-fall time tools take a known height and solve t = √(2d/g). This page takes a known elapsed time and returns how far the object falls: the inverse search intent.
How far does an object fall in the same time on the Moon or another planet?
Enter that body's gravity instead of the standard Earth value of 9.80665 m/s². The distance is proportional to gravity, so weaker gravity gives a shorter drop for the same clock interval.
How fast is the object moving when it lands?
In the same ideal model the impact speed is gravity times the elapsed time, which also equals the square root of twice gravity times the distance. The calculator gives it next to the distance.
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/free-fall-distance \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"time":2}'const res = await fetch("https://api.kit.forhosting.com/phys/free-fall-distance", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"time": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/free-fall-distance",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"time": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/free-fall-distance", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"time":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"time":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/free-fall-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
{
"time": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.free_fall_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_time | 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 distance means and what the response contains
This calculator returns the normalized inputs time and gravity, the fall distance, the impact velocity magnitude, a method tag free_fall_distance, 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 time, non-finite values, a non-positive g, magnitudes above the documented ceilings, and any negative elapsed time, because a signed interval before the clock starts is not a valid free-fall duration from rest.
How time and gravity are read and how distance stays reproducible
Zero time is valid and yields zero distance. 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. Computation uses one half times gravity times time squared for distance and gravity times time for the companion impact speed. There is no air resistance, no variable g with altitude, and no horizontal component—this is ideal one-dimensional free fall from rest under constant gravity for a chosen clock interval. The preferred field is time for the elapsed free-fall interval, but aliases t, elapsed, elapsed_time, and fall_time are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Time 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. Gravitational acceleration gravity defaults to nine point eight zero six six five meters per second squared, the conventional standard gravity, and may be overridden with aliases g and gravity_accel for other planets or textbook problems that use g equals nine point eight or ten; gravity must be strictly positive and within the documented magnitude ceiling. Both results and the echoed inputs are rounded to a stable ten-decimal grid so the same request always yields the same JSON across engines. 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 distance fits in study, labs, and software
Product and education tools use the endpoint when a learner types a time and the UI must show fall distance 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 free-fall time or thrown-downward helpers when you need the inverse or a nonzero initial speed, 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 distance and impact_velocity values for unit tests, game-physics demos, and CI assertions that pin d = ½gt².
Technical questions
How do I compute free-fall distance from elapsed time?
Send a JSON body with required time (non-negative) and optional gravity (default 9.80665). The API returns distance d = ½·g·t², impact_velocity, formula, method, and the validated inputs.
What does the free fall 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.