Kinetic energy calculator
A 2 kg mass moving at 3 m/s carries 9 J of kinetic energy. Enter any two of mass, speed and energy and get the third from KE = ½mv², or all three to check a hand calculation. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass
- 2
- Voltage (V)
- 3
- Mass
- 2
- Speed
- 3
- Velocity
- 3
- KE
- 9
A kinetic energy calculator turns the classic formula KE equals one-half mass times speed squared into a practical solver for homework, labs, and quick engineering checks. Enter any two of mass m, speed v, and kinetic energy KE in a consistent unit system, leave the unknown blank, and the tool returns the missing value in joules when mass is in kilograms and speed in metres per second, together with a substituted equation, a short physics message, and ordered step strings you can paste into worksheets or automated tests. Negative mass is rejected; kinetic energy must stay non-negative when provided.
What KE = ½mv² means and which variable you can leave blank
In SI units this yields joules when mass is in kilograms and speed in metres per second; any other coherent triad that multiplies the same way is fine as long as you never mix unit systems mid-equation. Mass is a non-negative scalar in classical problems; negative mass is physically rejected by this calculator. Speed may be entered signed when you already know velocity along an axis, because only v squared enters the formula, so direction does not change energy.
When speed is the unknown, the solver returns the non-negative magnitude equal to the square root of two KE over m, because energy alone cannot recover a sign.
This calculator accepts any two of the three numbers and solves algebraically for the third: given m and v it returns KE equals one-half m v squared; given KE and v it returns m equals two KE over v squared when v is non-zero; given KE and m it returns v equals the square root of two KE over m when m is positive. Leaving two fields blank is rejected because a single product relation cannot determine two free unknowns.
Providing all three values is allowed only when they are consistent within a tight numerical tolerance, which is useful as a check against a handwritten answer. The tool does not model rotational kinetic energy, relativistic corrections, or multi-body systems: sum or reduce those problems yourself before calling the solver.
Practical tips, limits, and related searches
Use one consistent unit system end to end—for example kilograms, metres per second, and joules—before calling; this landing does not perform unit conversion. When teaching energy conservation, treat this tool as the translational KE step only: add gravitational or elastic potential elsewhere, then compare total mechanical energy. This page targets people searching for a kinetic energy calculator, half m v squared solver, or joules from mass and speed online; it is not a full dynamics suite that integrates trajectories, not a rotational inertia calculator, and not a unit converter.
Prefer this capability when you already know any two of mass, speed, and kinetic energy and only need the third; if your source problem gives weight on Earth instead of mass, convert weight to mass with local g first. Round-trip checks are easy: recompute one-half m v squared by hand and confirm it equals the published KE within the same twelve-decimal rounding used in the response.
What you can do with it
Homework checks for KE = ½mv²
Students enter any two of mass, speed, and kinetic energy from textbook mechanics problems and compare the missing value and substitution steps against a deterministic result before submitting.
Lab pre-check before multi-body energy models
Pipelines validate translational kinetic energy from measured mass and speed first, then branch to rotational or multi-particle models only when the single-body KE check matches lab notes.
FAQ
What formula does the kinetic energy calculator use?
Leave any one field blank to solve for that variable.
What happens if two unknowns are left blank?
Kinetic energy needs any two of m, v, and KE; two blanks leave the equation underdetermined.
Can mass be negative?
No. Negative mass is rejected whether you provide it or would solve for it. Classical kinetic energy requires m ≥ 0.
In what units is the result?
When mass is in kilograms and speed in metres per second, KE is in joules. Keep m, v, and KE in one consistent unit system; the calculator does not convert units.
Is the kinetic energy calculator free?
The browser tool is free and runs locally.
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/kinetic-energy \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"m":2,"mass":0}'const res = await fetch("https://api.kit.forhosting.com/mech/kinetic-energy", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"m": 2,
"mass": 0
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/kinetic-energy",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"m": 2,
"mass": 0
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/kinetic-energy", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"m":2,"mass":0}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"m":2,"mass":0}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/kinetic-energy", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"m": 2,
"mass": 0
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.kinetic_energy",
"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 | 1000000000000 |
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
If two unknowns are left blank, validation fails with a clear invalid_input error so incomplete forms never silently invent a number. Pricing is a flat $0.002 per successful API request; failed validation is never charged.
What KE = ½mv² means and which variable you can leave blank
Classical translational kinetic energy relates the energy of motion of a point mass to its mass and speed: kinetic energy KE equals one-half times mass m times the square of speed v.
How to call the API and what comes back
Absolute values must stay within the published limit of one trillion; mass, when present or when solved, must not be negative; kinetic energy, when present, must not be negative. Send a JSON body with any two of the optional finite fields m (alias mass), v (aliases speed, velocity, and vel), and KE (aliases ke, energy, kinetic_energy, E_k, and Ek). Failed validation—two unknowns left blank, non-finite numbers, values outside absolute limits, negative mass, negative energy, division by zero when solving m equals two KE over v squared with v equal to zero, an inconsistent triple, or a non-finite product—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price. Prefer JSON numbers when you control the client; string numbers are accepted only when they match a strict finite numeric pattern for homework-form paste paths.
Practical tips, limits, and related searches
Keep m, v, and KE inside the published absolute range so products, quotients, and square roots remain finite in IEEE double precision on the Worker and in the browser. Pair classroom examples deliberately: m equals two and v equals three yields KE equals nine; KE equals fifty and m equals four yields v equals five; KE equals eighteen and v equals three yields m equals four; and a single field alone, or a negative mass, demonstrates the hard invalid_input path. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately omit two fields or try negative mass.
Integration use cases
Unit tests for game and sim energy helpers
Generate known-good mass, speed, and joule cases plus deliberate negative-mass and two-blank rejections for coding kata expected values in physics engines.