Tidal Disruption Radius Calculator

Calculate how close a star can orbit a black hole before tidal forces shred it apart — and find the black hole mass above which the star is swallowed whole instead, producing no observable flare.

Tidal disruption radius calculator

Black hole scenarios (Sun-like star)

Star type

The simple, non-relativistic tidal disruption radius: $r_t = R_\star \left(\frac{M_{\rm BH}}{M_\star}\right)^{1/3}$ .

Because $r_t$ grows only as the cube root of black hole mass while the Schwarzschild radius $r_s = 2GM_{\rm BH}/c^2$ grows linearly with it, a massive enough black hole has $r_s > r_t$ — the star is swallowed whole, crossing the event horizon before tidal forces ever get the chance to shred it. No debris stream forms outside the horizon, so no observable flare results.

Black hole mass (

M_{\rm BH}

)

Star mass (

M_\star

)

Star radius (

R_\star

)

r_t

≈ 1.132 × 10⁸ km ·

r_s

≈ 1.269 × 10⁷ km

r_t / r_s

≈ 8.916 · swallowed-whole threshold for this star ≈ 1.144 × 10⁸ M☉

Real, observable tidal disruption — the star is shredded outside the event horizon, producing a debris stream and flare.

Dashed circle is the tidal disruption radius; the solid dark disk is the black hole's Schwarzschild radius (event horizon). The star is drawn stretched into debris right at the tidal radius, outside the horizon.

$r_t \propto M_{\rm BH}^{1/3}$ and $r_s \propto M_{\rm BH}$ are both straight lines in log-log space, with different slopes — the point where they cross is exactly the mass above which this star would be swallowed whole rather than tidally disrupted.

A star that wanders too close to a black hole doesn’t just fall in quietly. Long before it reaches the black hole, the difference in gravitational pull across the star’s near and far sides — the tidal force — can grow strong enough to overcome the star’s own self-gravity, stretching it into a long stream of debris in a matter of minutes. Some of that debris falls onto the black hole and lights up as a brilliant flare; the rest is flung away. This violent event is called a tidal disruption event, or TDE, and the distance at which it happens is the tidal disruption radius.

The formula

The simple, non-relativistic estimate used here:

r_t = R_\star \left(\frac{M_{\rm BH}}{M_\star}\right)^{1/3}

$R_\star$ and $M_\star$ are the star’s radius and mass; $M_{\rm BH}$ is the black hole’s mass. This is the same functional form as a Roche-limit-style estimate (see this site’s Roche Limit calculator), applied to a star and a point-mass disruptor. More careful treatments add structure-dependent factors of a few, but this simple form captures the right scaling and order of magnitude, and it’s the standard back-of-envelope figure quoted in TDE literature and popular explainers.

The single most interesting thing about this formula

Here’s the twist that makes tidal disruption events astrophysically strange: $r_t$ only grows as the cube root of black hole mass, while the black hole’s own event horizon — its Schwarzschild radius,

r_s = \frac{2GM_{\rm BH}}{c^2}

— grows linearly with mass. A linear function eventually overtakes a cube-root function no matter how far behind it starts. So for small and moderate black hole masses, $r_t$ comfortably exceeds $r_s$ : the star gets torn apart in plain view, well outside the horizon, and the resulting flare is observable from Earth.

But push the black hole mass high enough, and $r_s$ catches up to and overtakes $r_t$ . Past that crossover, the star would be tidally shredded only inside the event horizon — which is physically meaningless, because nothing that happens inside the horizon is observable, and the star has already fallen through it, whole, before tides ever got the chance to act. The result: the black hole simply swallows the star intact. No debris stream forms outside the horizon, no disk lights up, no flare. This is a genuine, well-known limit on TDE detectability discussed in the astrophysical literature, commonly quoted at roughly $M_{\rm BH} \gtrsim 10^8\ M_\odot$ for a Sun-like star — this calculator derives that crossover mass directly from the algebra (solving $r_t(M) = r_s(M)$ exactly) for whatever star you enter, rather than hard-coding the commonly cited figure.

Real observed tidal disruption events

Real TDEs have been caught by wide-field sky surveys and X-ray telescopes for decades now. ASASSN-14li (2014) was one of the best-studied optical/UV/X-ray TDEs, discovered by the All-Sky Automated Survey for SuperNovae around a supermassive black hole roughly a few million solar masses — squarely in the regime this calculator would call a real, observable disruption. Swift J1644+57 (2011) was a much more exotic case: a relativistic jet launched by a TDE, bright enough in gamma rays to initially be mistaken for a gamma-ray burst, and one of the events that helped establish TDEs with jets as a distinct phenomenon. Both are real, named, well-studied events — cited here as illustrative context for what this simplified formula is describing, not as exact numerical matches to its output.

Reading the two visuals

The disruption diagram draws the black hole’s Schwarzschild radius as a solid dark event-horizon disk and the tidal disruption radius as a dashed boundary around it. When the tidal radius sits outside the horizon, the star is drawn stretched into a debris stream right at that boundary — a real, observable disruption. When the tidal radius would fall inside the horizon, the star is instead drawn intact, disappearing straight into the black disk — swallowed whole.
The mass-vs-radius chart plots both $r_t$ and $r_s$ against black hole mass on log-log axes, for your current star. Because each is a pure power law with a different exponent, both are straight lines — and they cross exactly once, at the swallowed-whole threshold mass, labeled directly on the chart.

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Changelog

2026-09-07Published.