Particle velocity calculator
A particle with 9 J of kinetic energy and a mass of 2 kg moves at 3 m/s. Enter the energy in joules and the mass in kilograms to get the speed of anything from a dust grain to a hockey puck. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Energy
- 9
- Mass
- 2
- Velocity
- 3 m/s
A particle velocity calculator answers a search that kinetic-energy pages only invert in passing: given a particle's kinetic energy and its mass, what is its speed in metres per second? The classical identity that kinetic energy equals one-half mass times speed squared rearranges to velocity equal to the square root of twice the energy divided by the mass, which is a non-negative magnitude because energy is a scalar and cannot recover a direction. This capability requires two finite numbers — energy in joules and mass in kilograms — and returns that speed together with the formula string so worksheets and APIs stay aligned. Zero energy with a positive mass yields rest, velocity equal to zero.
What particle velocity from kinetic energy means
Classical translational kinetic energy of a particle is the scalar KE equals one-half times mass times the square of speed. Solving for speed is a single algebraic rearrangement: multiply both sides by two, divide by the mass, and take the principal non-negative square root, which yields v equals the square root of two E over m. That is the quantity this particle velocity calculator returns, in metres per second when energy is in joules and mass is in kilograms.
Direction is not recovered, because a scalar energy is compatible with motion along any axis; if a problem needs a signed velocity you must supply a direction from elsewhere. The same identity covers a dust grain in a lab, a proton treated classically, a hockey puck, or a spacecraft fragment, as long as the speed remains far below the speed of light so that the relativistic kinetic energy (gamma minus one) times rest energy is unnecessary. Negative mass is likewise rejected as unphysical in this model.
Negative kinetic energy cannot arise from one-half m v squared for a real speed, so it is rejected too. A particle at rest has zero kinetic energy and therefore zero speed, which is a valid success path rather than an error. Convert grams to kilograms and electron-volts to joules before calling; this landing does not convert units.
People looking for a kinetic energy calculator that starts from a known speed want a different page; this one is the inversion that starts from energy and mass and reports metres per second.
What you enter, what you get and the limits
Mass must be strictly greater than zero: zero mass and negative mass are both rejected because the classical square-root identity is not a finite unique speed in those cases. Energy must not be negative; kinetic energy of a real particle cannot be below zero in this model, while energy equal to zero with a positive mass is rest and returns velocity equal to zero.
On success the body echoes the rounded energy and mass, sets velocity to the non-negative speed in metres per second rounded to twelve decimal places for stable goldens, sets formula to the string v equals sqrt of two E over m, and sets unit to m/s. Example: energy equals nine joules and mass equals two kilograms yields velocity equals three metres per second, because the square root of two times nine over two is the square root of nine. Failed validation is never charged.
Pair the response with your own unit converter if the source data is not already in joules and kilograms.
What you can do with it
Homework checks for v = √(2E/m)
Students enter kinetic energy in joules and mass in kilograms from textbook particle problems and compare the returned metres-per-second speed against the square-root identity before submitting.
Lab and beam notebooks
Pipelines convert a measured or catalogued kinetic energy and a known particle mass into classical speed before comparing with time-of-flight data or plotting a non-relativistic trajectory.
FAQ
How do I calculate particle velocity from kinetic energy and mass?
Send finite energy E in joules (non-negative) and mass m in kilograms (strictly positive).
What happens if the mass is zero or negative?
Classical v = sqrt(2 E / m) is not a finite unique speed when mass is zero or negative, so those requests are not billed.
What units does the particle velocity calculator use?
Energy in joules, mass in kilograms, velocity in metres per second. Convert grams or electron-volts first; this tool does not convert units.
Does the result tell me which way the particle is moving?
No. Kinetic energy has no direction, so you get the speed only, which is zero or positive. If a problem needs a signed velocity, the direction has to come from another piece of information.
Can I use it for particles close to the speed of light?
No. The formula is the classical one and holds only while the speed stays far below the speed of light. Near that limit you need relativistic kinetic energy, which this calculation does not apply.
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/particles-velocity \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"energy":9,"mass":2}'const res = await fetch("https://api.kit.forhosting.com/phys/particles-velocity", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"energy": 9,
"mass": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/particles-velocity",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"energy": 9,
"mass": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/particles-velocity", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"energy":9,"mass":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"energy":9,"mass":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/particles-velocity", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"energy": 9,
"mass": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.particles_velocity",
"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
Zero or negative mass is rejected, as is negative kinetic energy; those failures return invalid_input and are not billed. Successful API calls cost $0.002.
What particle velocity from kinetic energy means
When mass is exactly zero the classical formula is not well posed: dividing by zero would claim an infinite speed, so the task fails with invalid_input instead of inventing a number.
Input contract, response shape, and error behaviour
POST a JSON body with two required finite numbers: energy, the particle kinetic energy in joules (aliases kinetic_energy, ke, and KE), and mass, the particle mass in kilograms (alias m). Each field may arrive as a JSON number or as a numeric string that matches a strict finite pattern; missing fields, empty strings, non-finite values, and magnitudes above the published absolute limit of one trillion fail with invalid_input naming the field. Pricing is a flat $0.002 per successful request with unit item. Prefer JSON numbers when you control the client; string numbers exist for homework-form paste paths.
Where a particle velocity API earns its keep
Classrooms and tutoring platforms use a particle velocity calculator so learners can check the inversion of one-half m v squared without flipping a square-root algebra error by hand. Exam generators need a deterministic oracle that marks zero mass and negative energy as invalid instead of silently returning infinity or NaN that a buggy grader might treat as success. Beam-line notebooks and tabletop labs often know deposited energy and particle mass from a data sheet and need metres per second before they plot a trajectory or compare to a time-of-flight measurement. Failed validation does not consume balance, which keeps exploratory scripts cheap when learners deliberately send zero mass. Keep energy and mass inside the published absolute range so the square root remains finite in IEEE double precision on the Worker and in the browser. This page is not a relativistic kinematics solver, not a drift-velocity calculator for charge carriers, and not a kinetic-energy page that starts from a known speed: prefer those landings when that is the actual search intent.
Integration use cases
Golden cases for simulators
Generate known-good energy-mass-speed triples plus deliberate zero-mass and negative-energy rejections for unit tests in games, notebooks, and coding kata.
Technical questions
Can kinetic energy be negative?
No. Negative energy is rejected. Kinetic energy ½ m v² cannot be negative for a real particle speed; energy equal to zero with positive mass is rest (v = 0).
What does the particle velocity calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.