Free fall height calculator
If a stopwatch shows a 2-second drop under 9.8 m/s² of gravity, the object was released 19.6 metres up. Enter the fall time, and a different gravity if needed, to recover the height of the drop and the speed at impact. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Fall time
- 2
- Gravity
- 9.8
- Height
- 19.6
- Impact velocity
- 19.6
This free fall height calculator recovers the vertical drop of an object released from rest when you already know the elapsed fall time and the gravitational acceleration that acted during the drop. The closed-form identity is height equals one half times g times fall time squared, which is the inverse of the more common square-root formula that yields time from a known height. When time is in seconds and g is in metres per second squared, height is in metres. Optional gravity defaults to standard Earth g so homework sheets can omit it.
Drop height from a fall time, 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 that constant acceleration twice yields the textbook identity that drop height h equals one half g t squared, which this calculator evaluates for a known elapsed fall time.
The response reports the validated fall time, the gravitational acceleration actually used, the drop height in metres when g is in metres per second squared and time is in seconds, and the ideal impact speed magnitude g times t as a companion kinematic quantity. Zero time is a legitimate edge: the object has not left the release point, so height and impact speed are both zero rather than a division singularity.
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 fails with a field-named error. If you already know the height and want the clock reading, use a free-fall time tool; this page answers the inverse search people type when a stopwatch is known and the drop is not.
Where drop height from fall time fits in study, labs, and software
Students meet drop-height-from-time when a lab records a photogate or stopwatch interval and asks how far the mass fell, when a contest problem gives duration instead of a tape measure, or when a video-analysis worksheet reports frames and frame rate but not a calibrated metre stick. 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 convert a captured duration into a spawn height, or to satisfy programming-challenge statements that demand height 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 from a measured delay, or a comparison between Earth and lunar g for the same fall time.
Pair it with free-fall time or projectile helpers when you need the inverse or angled kinematics, and keep requests inside the documented magnitude ceilings so the half-g-t-squared product stays finite.
What you can do with it
Lab photogate and stopwatch checks
Convert a measured free-fall duration and known g into an ideal drop height before comparing it to a tape measure or photogate spacing.
Homework and answer keys
Grade kinematics worksheets that give fall time instead of height, including textbook g equals 9.8 or 10, without rounding surprises.
FAQ
What happens if fall time is negative?
Elapsed free-fall time cannot be less than zero, so a negative duration is rejected and is not billed.
Does the free fall height calculator include air resistance?
No. The model is from-rest free fall under constant g with drag neglected: h = ½ g t². Use a dedicated drag or terminal-velocity tool when air resistance matters.
How do I find the height of a drop from a stopwatch reading?
Enter the measured fall time in seconds and leave gravity at its default. The height is half of gravity times the time squared, so a time from a photogate, a stopwatch or counted video frames turns straight into metres.
Which gravity is used if I leave it blank?
The standard Earth value of 9.80665 metres per second squared. You can replace it with another planet's gravity or a textbook value such as 9.8, as long as the time is in seconds.
Why is a fall time of zero accepted?
Because it is a genuine edge case: the object has not yet left the release point. Height and impact speed are then both zero, and no error is raised.
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-height \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"fall_time":2}'const res = await fetch("https://api.kit.forhosting.com/phys/free-fall-height", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"fall_time": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/free-fall-height",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"fall_time": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/free-fall-height", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"fall_time":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"fall_time":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/free-fall-height", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"fall_time": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.free_fall_height",
"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_fall_time | 1000000000000000 |
max_abs_gravity | 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
Negative fall time is rejected as invalid_input rather than silently folded into an absolute value. The same deterministic arithmetic powers the free browser tool and the API at $0.002 per successful call, with no network, no sampling, and no date-dependent shortcuts.
What free-fall height means and what the response contains
Negative time is not a duration, so it is rejected with invalid_input instead of being folded into an absolute value that would invent a drop that never happened.
How fall time and gravity are read and how height stays reproducible
Zero is valid and yields zero height. 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. Gravity must be strictly positive and within the documented magnitude ceiling. The preferred field is fall_time for the elapsed free-fall duration from rest, but aliases t and time are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Fall time must be finite and non-negative: a missing field, an empty string, Infinity, NaN, or a non-numeric token fails with invalid_input naming fall_time. A negative fall_time fails with a clear message that elapsed free-fall time cannot be less than zero, and that failure is not billed. Gravitational acceleration gravity defaults to nine point eight zero six six five metres per second squared, the conventional standard Earth gravity, and may be overridden for other planets or textbook problems that use g equals nine point eight or ten; aliases g and gravity_accel are accepted. Computation uses one half times gravity times fall time squared for height and gravity times fall time for impact speed, then rounds to ten decimal places so JSON goldens stay stable across JavaScript 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 drop height from fall time fits in study, labs, and software
Product and education tools use the endpoint when a learner types a duration and the UI must show height in metres. 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 — lets you move from a classroom demo to an automated pipeline without changing the mathematical result.
Integration use cases
Deterministic test fixtures
Generate reproducible height and impact_velocity values for unit tests, game-physics demos, and CI assertions from a known duration.
Technical questions
How do I compute free-fall drop height from fall time?
Send a finite non-negative fall_time in seconds and optional gravity in m/s² (default 9.80665). The API returns height h = 0.5·g·t² in metres and impact speed g·t.
Which value of g is used if I omit gravity?
Standard Earth gravity 9.80665 m/s². Override gravity (aliases g, gravity_accel) for other planets or textbook values such as 9.8 or 10; g must be strictly positive.
What does the free fall height calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.