ForHosting KIT · Science

Photon sphere radius calculator

A black hole of 1.98847e+30 kg, the mass of the Sun, has its photon sphere 4430.009073100317 m from the centre, one and a half times its event horizon radius of 2953.3393820668784 m. Free in your browser.

  • Free
  • Runs in your browser
  • No sign-up
  • Your data stays on your device
Run — free How it works & API
Use it from WebAPIEmailTelegramApp soon

Run — free

Worked example

If you enter
Mass kg
1,988,470,000,000,000,000,000,000,000,000
You get
Schwarzschild radius m
2,953.3393820669
Photon sphere radius m
4,430.0090731003

The photon sphere radius calculator finds the location of the circular light orbit around an ideal, non-rotating black hole. Enter the black hole mass in kilograms and the calculator first obtains the Schwarzschild radius, then multiplies it by 1.5. The result is returned in metres together with the intermediate radius and formula. This deterministic calculation is useful for astronomy study, relativity checks, simulation setup, and comparing black holes of different masses without repeatedly handling physical constants by hand.

What the photon sphere radius represents

A photon sphere is the spherical region where gravity is strong enough for light to follow a circular path around a black hole. For a Schwarzschild black hole, which is the standard idealization of a black hole with mass but no rotation and no electric charge, this orbit lies outside the event horizon. The event horizon is located at the Schwarzschild radius, while the photon sphere is located at one and a half times that radius.

The orbit is unstable: a tiny disturbance sends a photon either outward or inward, so the value should not be interpreted as a durable ring made of trapped light. It is instead a precise geometric radius in the Schwarzschild spacetime. The calculator reports both radii in metres so that the relationship is visible and easy to check.

This distinction matters when studying gravitational lensing, black hole shadows, relativistic ray paths, or educational diagrams, because the event horizon, photon sphere, and observed shadow are related concepts but are not identical boundaries.

How the calculation uses black hole mass

Provide mass in kilograms as a positive finite number. Because the expression is directly proportional to mass, doubling the mass doubles both returned radii, and halving the mass halves them. No numerical integration, observational lookup, or approximation based on a named black hole is involved.

The supplied mass alone determines the result under the non-rotating model. Zero and negative masses are rejected because they do not define the intended black hole solution, while missing, nonnumeric, and non-finite values are rejected to prevent misleading output. Scientific notation is convenient for stellar masses, but its value must still represent kilograms rather than solar-mass units.

Interpreting and applying the result

The output is most appropriate for textbook Schwarzschild geometry, quick consistency checks, unit-tested scientific software, and rough comparisons among non-rotating black holes. It should not be substituted unchanged for a rotating Kerr black hole: rotation makes photon orbits depend on direction and spin, so there is no single radius described by this simple formula. The value also is not automatically the apparent radius of a black hole shadow on a telescope image, since observed appearance includes light propagation, viewing geometry, and distance.

Preserve enough significant digits for your downstream task and apply any display rounding only after receiving the metre values.

What you can do with it

Check relativity coursework

Compute the photon sphere and event-horizon radii from a given mass, then compare their exact 1.5 ratio.

Prepare a ray-tracing model

Generate the Schwarzschild photon sphere radius needed as a reference scale in a non-rotating black hole scene.

Compare black hole masses

Evaluate how the characteristic light-orbit radius scales across stellar-mass and supermassive black holes.

FAQ

What mass unit should I enter?

Enter the black hole mass in kilograms. Values expressed in solar masses must be converted to kilograms before submission.

What unit does the calculator return?

Both the Schwarzschild radius and photon sphere radius are returned in metres.

Does this work for a rotating black hole?

No. It assumes a non-rotating, uncharged Schwarzschild black hole. Kerr black holes have spin-dependent photon orbits.

Is the photon sphere the same as the event horizon?

No. The event horizon sits at the Schwarzschild radius, and the photon sphere lies outside it at one and a half times that distance. The calculator shows both radii so you can compare them.

Can light keep circling on that orbit forever?

No. The circular light orbit is unstable: the slightest disturbance sends a photon outward or inward. It is a precise geometric radius, not a lasting ring of trapped light.

Related tools

Black hole event horizon area calculatorScienceSchwarzschild radius calculatorScienceBlack hole evaporation time calculatorSciencePlanet mass from density and radius calculatorScienceStellar surface escape velocity calculatorScienceGeostationary orbit calculatorScienceSphere of influence calculatorScienceEscape velocity at altitude calculatorScience

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

POSThttps://api.kit.forhosting.com/astro/photon-sphere-radius

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/photon-sphere-radius \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"mass_kg":1.98847e+30}'

Example request

{
  "mass_kg": 1.98847e+30
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "astro.photon_sphere_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

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Errors

HTTPCodeMeaning
401unauthorizedMissing or invalid API key.
402insufficient_balanceYour balance doesn't cover the task price.
404unknown_typeThat task type doesn't exist.
429rate_limitedToo many requests. Use the webhook instead of polling.

Technical notes

How the calculation uses black hole mass

The calculation uses the gravitational constant G = 6.67430 × 10^-11 m^3 kg^-1 s^-2 and the speed of light c = 299,792,458 m/s. It first evaluates the Schwarzschild radius r_s = 2GM/c^2. It then evaluates r_ph = 1.5r_s, which is equivalently r_ph = 3GM/c^2.

Interpreting and applying the result

Use the photon_sphere_radius_m field as the radial Schwarzschild coordinate measured from the idealized center of the black hole. The schwarzschild_radius_m field provides the event-horizon radius used in the multiplication, making it straightforward to audit the 1.5 ratio or pass both quantities into another calculation. For automated use, each request costs $0.002; the browser version uses the same deterministic solver.

Technical questions

Why is the photon sphere 1.5 times the Schwarzschild radius?

For the Schwarzschild geometry, the unstable circular null orbit occurs at r = 3GM/c^2, while the event horizon is at r_s = 2GM/c^2.

What happens if the mass is zero or negative?

The request returns an invalid_input error because the required black hole mass must be strictly positive.

Read the full KIT documentation →