Schwarzschild radius calculator
A mass of 1.9885e+30 kg, about the Sun's, has a Schwarzschild radius of 2953.3839390285 m, roughly 2.95 km. Enter any mass in kilograms to compare stellar, planetary and supermassive horizons. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass
- 1,988,500,000,000,000,000,000,000,000,000
- Schwarzschild radius
- 2,953.3839390285 m
- Radius m
- 2,953.3839390285
- G
- 0.0000000001
- C
- 299,792,458
This Schwarzschild radius calculator returns the event-horizon radius of a non-rotating black hole from a single mass value. The closed form is fully deterministic: Rs equals two times G times M over c squared, using the CODATA 2018 gravitational constant G equals 6.67430 times ten to the minus eleven cubic metres per kilogram per second squared and the exact SI speed of light c equals 299792458 metres per second. With mass in kilograms the result is in metres, the natural SI length for comparing stellar, planetary, and supermassive horizons. Well-known checks include a solar-scale mass near 1.9885 times ten to the thirty kilograms, which yields about 2.95 kilometres, and an Earth-scale mass near 5.972 times ten to the twenty-four kilograms, which yields about 8.87 millimetres. The engine uses only finite arithmetic with no network calls, no sampling, and no date-dependent shortcuts.
Where Schwarzschild radius fits in study, astronomy, and software
Students meet the Schwarzschild radius when a textbook moves from Newtonian gravity to black-hole horizons, when a contest problem asks for the event-horizon size of a given stellar mass, or when they compare planetary and solar compact-object scales without full general-relativity machinery. Teachers can pre-generate answer keys for modest mass values without trusting opaque calculator apps that silently switch units or drop scientific notation.
Developers call the same contract from scripts to seed deterministic test vectors for astrophysics simulators, to normalize user-entered mass before mission or black-hole demos, or to satisfy programming-challenge statements that demand Rs rather than a hand-waved solar value. Contest practice often needs a fast, offline source of horizon radii so solutions can be checked without graphing calculators under time pressure.
Product and education tools use the formula when a learner types a mass in kilograms and the UI must show the Schwarzschild radius in metres next to comparisons with solar and terrestrial scales.
What you can do with it
Homework and black-hole horizon checks
Compute Rs from textbook stellar or planetary mass values and verify the event-horizon size before GR or compact-object problems.
Astronomy and education tools
Normalize user-entered mass into horizon radius for black-hole demos, mission planners, and interactive lessons.
FAQ
What does the Schwarzschild radius calculator cost?
It is free in your browser on this page.
Does this include rotating or charged black holes?
No. It only returns the Schwarzschild (non-rotating, uncharged) horizon radius. Kerr or Reissner–Nordström horizons need dedicated tools.
Why are results rounded to a precision?
Default precision is 10 decimal places; you can set precision from 0 to 15.
How big would Earth be as a black hole?
Compressed into a black hole, an Earth-scale mass of about 5.972e+24 kg would have a Schwarzschild radius of roughly 8.87 millimetres. The Sun's mass gives about 2.95 kilometres.
What does the Schwarzschild radius mean?
It is the size of the event horizon of a non-rotating, uncharged black hole. Any spherical mass squeezed inside that radius becomes a black hole, and light emitted from the horizon cannot reach distant observers.
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/schwarzschild-radius \
-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/schwarzschild-radius", {
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/schwarzschild-radius",
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/schwarzschild-radius", 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/schwarzschild-radius", 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.schwarzschild_radius",
"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_mass | 1e+40 |
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
What the Schwarzschild radius means and what the response contains
The Schwarzschild radius is the critical radial coordinate at which the event horizon of a non-rotating, uncharged black hole sits in general relativity. For a mass M the horizon radius is Rs equals two G M over c squared: any spherical mass compressed inside that radius becomes a black hole in the Schwarzschild solution, and light emitted from the horizon cannot reach distant observers. This calculator returns the normalized mass you supplied, the computed schwarzschild_radius and radius_m fields rounded to the requested precision, the fixed CODATA gravitational constant G and exact speed of light c used in the product, a unit string m, the method tag schwarzschild_radius, the precision used, and a short formula reminder. There is no approximate numerical integrator and no random sampling of multipole moments: the engine either builds exact floating-point Rs inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include missing mass, non-finite values, magnitudes above the documented ceiling, and any mass that is zero or negative, because the Schwarzschild radius is undefined or non-physical for non-positive mass in this model.
How mass is read and how Rs stays reproducible
Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong horizon size. The preferred field is mass for the body mass in kilograms, but aliases m, M, and body_mass are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Mass must be strictly positive: if mass is zero, negative, or negative zero, the request fails with invalid_input because Schwarzschild radius Rs equals two G M over c squared is undefined for a non-positive mass. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for mass and the radius fields, defaulting to ten and capped at fifteen so JSON goldens stay stable. 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 Schwarzschild formula yourself.
Where Schwarzschild radius fits in study, astronomy, and software
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 — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with surface-gravity or light-travel-time tools when you need related astronomy steps, and with other physics endpoints when you are building a small lab of free, deterministic science helpers.
Integration use cases
Deterministic test fixtures
Generate reproducible Schwarzschild radii for unit tests, property checks, and CI assertions on astrophysics modules.
Technical questions
How is the Schwarzschild radius defined here?
For a non-rotating black hole of mass M, Rs = 2·G·M/c² with G = 6.67430×10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA 2018) and c = 299792458 m/s. The SI unit is metres.
What happens if mass is zero or negative?
The input is rejected with invalid_input. Schwarzschild radius Rs = 2GM/c² is undefined for a non-positive mass.