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    Relativity

    Black Hole Schwarzschild Radius Calculator

    Event-horizon radius of a non-rotating black hole of any mass.

    r_s = 2GM / c²

    Inputs

    Results

    Schwarzschild radius
    12,699,000 km
    Event horizon diameter
    25,398,000 km
    Photon sphere radius (1.5 r_s)
    19,048,500 km
    Mean density inside r_s
    996,730 kg/m³
    Worked solution
    1. r_s = 2 × 6.6743 × 10^-11 × 8.5502 × 10^36 / (299,792,458)² = 1.2699 × 10^10 m

    How the result changes

    Radius (km) plotted against Mass (Solar masses), from one quarter to four times your input, with your input marked.20,000,00040,000,0005,000,00010,000,00015,000,000Mass (Solar masses)Radius (km)your input
    Radius vs mass

    How it works

    Karl Schwarzschild found this solution of Einstein's equations in 1916. Compress the Sun into a sphere about 2.95 km in radius and not even light could escape. The Event Horizon Telescope imaged the shadows of M87* (2019) and Sagittarius A* (2022).

    Variables

    • r_s — Schwarzschild radius
    • M — mass

    Assumptions and limits

    • Non-rotating, uncharged black hole (Schwarzschild solution)
    • Rotating (Kerr) black holes have a smaller horizon, down to r_s/2 for maximal spin

    For education only. These models are simplified and are not suitable for spacecraft navigation or safety-critical engineering. See our scientific accuracy policy.