Stellar surface escape velocity calculator
Find the minimum speed needed to leave a star from its visible surface: the Sun, with 1.98847 × 10³⁰ kg and a radius of 695700000 m, gives 617684.0394130623 m/s. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass kg
- 1,988,470,000,000,000,000,000,000,000,000
- Radius m
- 695,700,000
- Escape velocity m s
- 617,684.0394130623
- Gravitational constant m3 kg s2
- 0.0000000001
The stellar surface escape velocity calculator finds the minimum ideal speed an object needs at a star's photosphere to escape its gravitational field without further propulsion. Enter stellar mass in kilograms and photospheric radius in metres, and the calculator applies the standard Newtonian escape-velocity equation to return metres per second. It is useful for comparing stars, checking astronomy exercises, and supplying a reproducible value to simulations. The calculation is deterministic, uses no network service, and rejects a zero or negative radius instead of producing an undefined result.
What stellar surface escape velocity represents
Surface escape velocity is the initial speed required for a small test object to leave a star's gravitational field and approach infinite distance with zero speed remaining. Here, surface means the stellar photosphere: the visible layer whose reported radius is commonly used as a star's radius. The result comes from balancing kinetic energy against Newtonian gravitational potential energy.
It does not depend on the mass of the escaping object because that mass cancels from both sides of the energy equation. A more massive star raises the escape speed, while a larger photospheric radius lowers it when mass stays fixed. This value is an ideal physical threshold, not a complete launch or outflow model.
The calculation assumes spherical symmetry, ignores atmospheric or plasma drag, neglects stellar rotation, and treats the escaping object as too small to affect the star. It also assumes no additional propulsion after the object begins at the photosphere. These simplifications make the result appropriate for classroom problems, first-pass stellar comparisons, and controlled software tests.
They do not describe every process that accelerates real stellar winds, jets, or mass ejections.
Formula, interpretation, and practical limits
The calculator evaluates v = sqrt(2GM/R), where v is escape velocity in metres per second, G is the gravitational constant 6.6743 × 10^-11 cubic metres per kilogram per second squared, M is stellar mass in kilograms, and R is photospheric radius in metres. The square-root relationship matters when interpreting comparisons: doubling mass at fixed radius multiplies escape velocity by the square root of two, rather than doubling it. Likewise, doubling radius at fixed mass divides the speed by the square root of two.
Use the returned value as a Newtonian surface benchmark. Very compact objects can require relativistic treatment, so this calculator should not replace general-relativity methods for neutron stars, black-hole horizons, or situations where the computed speed becomes a substantial fraction of light speed. A star's published radius can also depend on wavelength, model, or observational method because a photosphere is not a hard solid boundary.
Record the mass and radius source when reproducibility matters. For numerical checks, confirm that both inputs are SI quantities, calculate 2GM/R, and then take its non-negative square root.
What you can do with it
Compare stellar gravitational wells
Calculate the photospheric escape speeds of stars with different masses and radii using one consistent SI formula.
Check astronomy coursework
Verify a hand calculation of v = sqrt(2GM/R) and retain the exact mass, radius, and constant used.
FAQ
What formula does the calculator use?
It uses the standard Newtonian formula v = sqrt(2GM/R), evaluated at the photospheric radius.
Which units should I enter?
Enter stellar mass in kilograms and photospheric radius in metres. The result is returned in metres per second.
Does this model stellar rotation or plasma drag?
No. It is an ideal Newtonian calculation that assumes spherical symmetry and ignores rotation, drag, and further propulsion.
Can I use this for neutron stars or black holes?
Use caution. Compact objects may require general relativity, especially when the Newtonian result is a substantial fraction of light speed.
What happens to escape speed if I double the star's mass?
At the same radius it grows by the square root of two, not by a factor of two, because mass sits under the square root. Doubling the radius at fixed mass divides the speed by the square root of two instead.
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/stellar-escape-velocity \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"mass_kg":1.98847e+30,"radius_m":695700000}'const res = await fetch("https://api.kit.forhosting.com/astro/stellar-escape-velocity", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"mass_kg": 1.98847e+30,
"radius_m": 695700000
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/astro/stellar-escape-velocity",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"mass_kg": 1.98847e+30,
"radius_m": 695700000
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/astro/stellar-escape-velocity", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"mass_kg":1.98847e+30,"radius_m":695700000}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"mass_kg":1.98847e+30,"radius_m":695700000}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/astro/stellar-escape-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
{
"mass_kg": 1.98847e+30,
"radius_m": 695700000
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "astro.stellar_escape_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.
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
How to enter mass and photospheric radius
Convert solar masses and solar radii to SI units before calling the capability; do not send labels such as solar masses, kilometres, or scientific-unit abbreviations inside the numeric value. Radius must be greater than zero because division by a zero radius is undefined and a negative physical radius has no meaning. Mass may be zero for mathematical completeness, producing zero metres per second, but negative mass is rejected. Keeping the input contract in SI units makes repeated calculations easy to compare and prevents silent unit assumptions from changing the answer. Provide mass_kg as the star's mass in kilograms and radius_m as its photospheric radius in metres. The shorter aliases mass and radius are accepted for clients that already use those field names. Ordinary JSON numbers and strict numeric strings, including scientific notation, are accepted. On success, the response returns escape_velocity_m_s along with the normalized mass, radius, gravitational constant, and formula label. The API price for a successful request is $0.002; the same deterministic calculation can run in the browser.
Formula, interpretation, and practical limits
Because the implementation has no network access, clock use, or random values, identical valid inputs produce identical JSON numeric results in the API and browser execution paths.
Integration use cases
Create simulation fixtures
Generate deterministic metre-per-second reference values for stellar dynamics software and automated regression tests.
Technical questions
What happens when radius is zero or negative?
The request returns an invalid_input error because escape velocity cannot be evaluated at a non-positive radius.