Black Hole Shadow Calculator
Calculate the Angular Size of a Black Hole Shadow
Based on the Schwarzschild metric and the Event Horizon Telescope observations
Result:
Photon Sphere Diameter: km
Apparent Angular Diameter (on sky): μas (microarcseconds)
Shadow Diameter (as observed): μas ≈ milliarcseconds
The famous 2019 EHT image of M87* showed a shadow of ~42 μas — very close to the prediction!
About the Black Hole Shadow Calculator
The Black Hole Shadow Calculator is a scientifically accurate online tool that computes the apparent angular size of a black hole’s event horizon shadow as seen from Earth. This calculator strictly follows the predictions of Einstein’s General Theory of Relativity using the Schwarzschild metric — the same physics that produced the historic first image of a black hole (M87*) by the Event Horizon Telescope (EHT) in 2019 and Sgr A* in 2022.
What is a Black Hole Shadow?
A Black Hole Shadow is the dark, nearly circular region seen against the bright background of glowing hot plasma orbiting the black hole. General relativity predicts that light rays passing near the event horizon are strongly bent, creating a “photon sphere” at 1.5 times the Schwarzschild radius (rₛ). The apparent size of the shadow is approximately ≈ 5.2 × rₛ when viewed from a large distance due to gravitational lensing.
Scientific Formula Used (Peer-Reviewed)
The Schwarzschild radius for a non-rotating black hole is:
rₛ = 2GM / c² ≈ 2.95 × M/M☉ km
The gravitational lensing magnification makes the observed shadow diameter ≈ 5.2 × rₛ (for spin = 0; slightly larger for high spin).
The angular diameter δ in microarcseconds (μas) is:
δ ≈ 10.4 × (M / M☉) / (D / Mpc) μas
This exact formula was confirmed by the EHT collaboration papers (2019, 2022) and matches observations within a few percent.
Why is the Black Hole Shadow Calculator Important?
This tool bridges cutting-edge astrophysics with public education. It allows students, researchers, and space enthusiasts to:
- Compare real supermassive black holes (M87*, Sgr A*, etc.) with theoretical predictions
- Understand the extreme curvature of spacetime near the event horizon
- Appreciate why the EHT needed a planet-sized telescope to resolve ~40 μas features
- Test how shadow size changes with mass and distance
When Should You Use This Calculator?
Use this Black Hole Shadow Calculator whenever you want to:
- Verify EHT results for M87* (6.5×10⁹ M☉ at 16.8 Mpc) or Sgr A* (4.3×10⁶ M☉ at 0.008 Mpc)
- Explore hypothetical nearby black holes
- Teach general relativity and gravitational lensing
- Plan future interferometric observations (ngEHT, BlackHoleCam, etc.)
Example Calculations
M87*: 6.5 billion solar masses at 16.8 Mpc → shadow ≈ 42 μas (matches 2019 EHT image)
Sagittarius A*: 4.3 million solar masses at ~8 kpc (0.008 Mpc) → shadow ≈ 53 μas (matches 2022 EHT image)
Limitations & Accuracy
This calculator assumes a non-spinning (Schwarzschild) black hole viewed face-on. Real black holes have spin (Kerr metric), which makes the shadow slightly asymmetric and up to ~10% larger for near-maximal spin. However, the simple formula used here is accurate to better than 10% for all observed supermassive black holes and is the standard reference in EHT publications.
Credits & Further Reading
Calculations based on:
- The Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875, L1-L6 (2019)
- Falcke, Melia & Agol, Astrophys. J. 528, L13 (2000) – original shadow prediction
- Luminet, J.-P., Black Hole Imaging (1979) – first simulations
Made with ❤️ for science lovers by Agri Care Hub
