E=mc² calculator
One kilogram at rest holds nearly 9 × 10¹⁶ joules, its mass times the speed of light squared. Enter a rest mass in kilograms to get its rest energy in joules, worked out with the exact value of c. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass
- 1
- Energy
- 89,875,517,873,681,760 J
- Energy j
- 89,875,517,873,681,760
- C
- 299,792,458
- C squared
- 89,875,517,873,681,760
Einstein's mass–energy relation E = mc² states that a body at rest still stores an enormous energy equal to its rest mass times the square of the speed of light. This E=mc² calculator accepts a rest mass in kilograms and returns that rest energy in joules using the exact SI value of c, 299792458 metres per second, not a rounded three-times-ten-to-the-eight estimate from a poster. Students, nuclear-engineering notes, science explainers, and automation scripts all need the same closed-form product so homework, articles, and pipelines never disagree on a famous constant. Zero mass yields zero energy.
What E = mc² means and why rest energy is so large
The equation E equals m c squared is the rest-energy form of Einstein's mass–energy equivalence: rest mass m is an invariant property of a body, and the vacuum speed of light c is an exact SI constant equal to 299792458 metres per second, not a measured laboratory estimate you have to look up for each problem. Multiplying mass in kilograms by c squared yields energy in joules, because a joule is defined as a kilogram metre-squared per second-squared.
The numerical size of that product is why a single kilogram of matter corresponds to nearly nine times ten to the sixteen joules if the entire rest mass were converted, which is why nuclear binding, pair production, and particle rest masses are often quoted in electronvolts while the SI rest energy remains in joules. This capability computes only that SI rest energy.
It does not convert the result into kilowatt-hours, calories, or megaelectronvolts, it does not multiply by a relativistic Lorentz factor gamma, and it does not model a nuclear reaction Q-value or a fission yield. Those are different search intents served by other tools. What you send is a rest mass; what you get is E equals m times c squared in joules.
Input contract, units, and what happens when mass is invalid
Negative mass is likewise rejected: rest energy E equals m c squared is defined for a non-negative rest mass, and a negative kilogram is not a physical input for this identity. Zero mass is allowed and returns zero joules, which is the consistent limit of the product. Keep units SI: if you weighed a sample in grams, divide by one thousand before calling; the engine never converts slugs, solar masses, or atomic mass units.
Pair the joule figure with conv.energy if you later need kilowatt-hours or electronvolts. Extremely large masses that overflow to Infinity are rejected rather than returned as a non-finite energy.
Where an E=mc² calculator earns its keep, and what it costs
Classrooms and tutoring platforms use an E=mc² calculator so learners can check the rest energy of one kilogram, one gram, or a stated particle mass without dropping a digit in c or writing 3e8 by habit. Exam generators and LMS plugins need a deterministic oracle that rejects a negative mass instead of silently returning a negative energy that a buggy grader might treat as success. Engineering notebooks that compare chemical, nuclear, and rest-mass energy scales call a tiny parse step instead of pulling a computer-algebra system for a one-line product.
Failed validation does not consume balance. Pin the returned joule value in tests, keep requests small, and you get reproducible rest energies for homework, explainers, and edge workers without standing up symbolic math infrastructure of your own.
What you can do with it
Classroom rest-energy checks
Let students submit a rest mass in kilograms and verify E = mc² in joules against textbook methods, including a clear error when mass is negative.
Explainer pages and science CMS widgets
Embed a live E=mc² calculator on a mass–energy article so readers see the SI joule figure for one kilogram or one gram using the exact speed of light.
Exam generators and energy-scale notebooks
Mark rest-energy items with a deterministic oracle, or compare rest-mass energy with chemical and nuclear scales in a pipeline without a computer-algebra library.
FAQ
What happens if mass is negative?
Rest energy E=mc² requires a non-negative finite mass; a negative kilogram is rejected and is not billed.
Which value of the speed of light does the calculator use?
Energy is SI joules when mass is kilograms.
Does this include kinetic energy or a Lorentz factor?
No. This capability returns rest energy only. Relativistic total energy γmc² and classical kinetic energy ½mv² are different problems and different tools.
What if my mass is in grams?
Divide it by 1000 first, because the calculator expects kilograms and never converts units. The same goes for atomic mass units or solar masses: turn them into kilograms before you enter them.
Does it give the energy released by fission or another nuclear reaction?
No. It returns only the rest energy of the mass you enter, in joules. The energy a fission or another nuclear reaction releases is a different calculation that this tool does not model.
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/emc2 \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"mass":1}'const res = await fetch("https://api.kit.forhosting.com/phys/emc2", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"mass": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/emc2",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"mass": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/emc2", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"mass":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"mass":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/emc2", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"mass": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.emc2",
"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.
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 mass is unphysical for this rest-energy identity and is rejected as invalid_input; a value that is not a finite number is rejected the same way. Successful API calls cost $0.002; failed validation is not billed.
Input contract, units, and what happens when mass is invalid
POST a JSON body with one required field, mass, the rest mass in kilograms. The value must be a finite number; it may arrive as a JSON number or as a numeric string such as 0.001 or 1e-3. Aliases m and mass_kg are accepted so existing lab or notebook payloads map without renaming the key. Missing mass, an empty string, NaN, plus or minus Infinity, and any non-numeric token fail with invalid_input naming the field and are not billed. On success the body echoes mass, returns energy and energy_j as the same joule value, reports c as 299792458 and c_squared as the IEEE product of that constant with itself, and includes formula, unit equal to J, and method equal to mass_energy_equivalence so clients can branch without sniffing shapes.
Where an E=mc² calculator earns its keep, and what it costs
Use the on-page tool for a single mass at the desk; use the API when a grader, CMS plugin, or data pipeline needs the same contract under KIT balance. Do not send a relativistic total energy problem and expect gamma m c squared; this endpoint is rest energy only.
Technical questions
How do I calculate energy from mass with E = mc²?
Send a finite non-negative rest mass in kilograms as mass (aliases m, mass_kg). The API returns rest energy in joules as E = m c² with c = 299792458 m/s exact.
What does the E=mc² calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.