Black hole evaporation time calculator
Double a black hole's mass and its Hawking evaporation time grows eight times, because lifetime scales with the cube of mass. Enter the mass in kilograms and get the idealized lifetime in seconds. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass
- 1,000,000,000,000
- Mass kg
- 1,000,000,000,000 seconds
- Lifetime seconds
- 84,114,779,048,559,820,000
This black hole evaporation time calculator estimates how long an ideal non-rotating, uncharged black hole takes to evaporate through Hawking radiation. The calculation uses fixed SI constants and makes the important mass-cubed scaling explicit: a modest change in mass creates a very large change in lifetime.
What Hawking evaporation lifetime means
Hawking radiation is the quantum-field-theory prediction that a black hole emits thermal radiation and consequently loses mass. In an idealized calculation, continued mass loss eventually causes the black hole to evaporate. This calculator estimates that total lifetime for a Schwarzschild black hole: an object described only by mass, with no rotation and no electric charge.
The returned lifetime is measured in seconds from the chosen starting mass to evaporation under the standard isolated-vacuum approximation. It is not the age of an observed black hole, the time since its formation, or a forecast of when a specific astronomical object will disappear. Real environments can feed matter and radiation into a black hole, while the simple formula assumes the evaporation model can be applied without tracking accretion or changing surroundings.
The lifetime also should not be confused with a light-crossing time, orbital period, collapse time, or the time experienced by an infalling observer. Those quantities answer different physical questions. Here the central feature is the cubic dependence on mass.
If one ideal black hole has twice the mass of another, its estimated evaporation lifetime is eight times longer. This steep scaling explains why stellar-mass and supermassive black holes have extraordinarily long theoretical lifetimes, while sufficiently small hypothetical black holes could evaporate far more quickly.
How the mass-cubed calculation is performed
Provide mass as a finite, strictly positive number in kilograms. Keeping the input and constants in SI units makes the output seconds without an additional conversion. The algorithm first forms a fixed coefficient from the constants and then multiplies it by the mass three times.
The response includes the normalized mass, lifetime in seconds, output unit, and formula label so that downstream users can identify the model. Missing values, non-numeric values, Infinity, NaN, zero, and negative values are rejected. Inputs so large that the cubic result exceeds finite JavaScript arithmetic are rejected too, rather than returning Infinity as though it were a physical answer.
The process uses no live database, random number, current date, remote service, or adjustable cosmological parameter. Consequently, identical valid input yields identical output. The displayed digits still come from standard floating-point arithmetic, so users should interpret precision according to the accuracy of the supplied mass and constants, not assume that every printed digit represents measurable certainty.
Interpreting the estimate and its limits
Use this result as a standard theoretical estimate for an isolated Schwarzschild black hole, especially in classroom exercises, order-of-magnitude comparisons, and deterministic software tests. It is well suited to demonstrating cubic scaling: multiplying mass by ten multiplies lifetime by one thousand. Developers can compare an independent implementation against the returned seconds, and educators can create examples that connect SI constants to the enormous timescales often discussed in black hole thermodynamics.
The formula is deliberately specific and does not constitute a complete history of a real black hole. Rotation and charge alter the physical description, and a black hole can gain mass from surrounding gas, stars, or background radiation. The semiclassical derivation also does not supply a settled theory of the final quantum-gravity stage of evaporation.
In some references, alternative particle-content assumptions, greybody factors, or simplified conventions lead to different coefficients even though the dominant mass-cubed relationship remains. This calculator uses the commonly quoted standard coefficient shown in its formula and does not add corrections for those effects. For observational work, state the assumed starting mass and model alongside the result.
For engineering or safety decisions involving speculative microscopic black holes, consult an appropriate specialist analysis rather than treating this one-equation estimate as a complete risk model.
What you can do with it
Check a black hole thermodynamics exercise
Turn a mass in kilograms into the standard Hawking lifetime in seconds and compare it with a hand calculation.
Explore cubic mass scaling
Compare hypothetical black holes and show how a mass ratio becomes the cube of that ratio in evaporation time.
FAQ
What unit should I use for mass?
Enter mass in kilograms. The returned evaporation lifetime is in seconds.
Why does lifetime scale with the cube of mass?
In the standard Hawking model, radiated power and mass loss lead to an integrated lifetime proportional to M³, so doubling mass increases lifetime eightfold.
Does this model include a rotating black hole?
No. It applies to an ideal non-rotating, uncharged Schwarzschild black hole and does not model spin, charge, or accretion.
Is the result the age of a real black hole?
No. It is the total time an isolated black hole would take to evaporate from the mass you enter. It is not its age or a forecast for a real object, since real surroundings can feed matter into it.
What happens if I enter zero or an enormous mass?
Zero, negative and non-numeric masses are rejected. A mass so large that the cubed result would no longer be a finite number is rejected too, instead of showing infinity as if it were a physical answer.
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/astro/black-hole-lifetime \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"mass":1.9885e+30}'const res = await fetch("https://api.kit.forhosting.com/astro/black-hole-lifetime", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"mass": 1.9885e+30
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/astro/black-hole-lifetime",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"mass": 1.9885e+30
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/astro/black-hole-lifetime", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"mass":1.9885e+30}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"mass":1.9885e+30}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/astro/black-hole-lifetime", 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": 1.9885e+30
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "astro.black_hole_lifetime",
"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
Enter a positive mass in kilograms and it applies the standard lifetime formula t = 5120πG²M³/(ℏc⁴), returning the result in seconds. It is deterministic, requires no network access, and produces the same output in the browser and API. Use the browser calculation free, or make a successful API request for $0.002 when you need repeatable results in software or coursework.
How the mass-cubed calculation is performed
The calculator evaluates t = 5120πG²M³/(ℏc⁴), where G is the gravitational constant, c is the speed of light, and ℏ is the reduced Planck constant. It uses G = 6.67430 × 10⁻¹¹ in SI units, c = 299792458 metres per second, and ℏ = 1.054571817 × 10⁻³⁴ joule-seconds.
Interpreting the estimate and its limits
A successful API calculation costs $0.002, while invalid mass is returned as invalid_input instead of a plausible-looking number.
Integration use cases
Create deterministic software fixtures
Generate stable reference outputs for astronomy lessons, scientific calculators, and tests of independent implementations.
Technical questions
What formula does the calculator use?
It uses the standard Schwarzschild evaporation lifetime t = 5120πG²M³/(ℏc⁴).
What happens if mass is zero or negative?
The calculation fails with invalid_input because mass must be finite and strictly positive.