Why are supermassive black holes gentler than stellar ones?

Tidal force scales as M/r³. The event horizon scales as M, so tides at the horizon scale as 1/M². A 10-solar-mass black hole rips you apart ~500 km above the horizon, but at Sagittarius A* (4 million M☉) you cross the horizon completely intact.

Spaghettification

Falling in, stretched thin.

Gravity pulls your feet harder than your head. Past a point, that difference rips a body into a filament. Where it happens depends entirely on the black hole's mass.

Distance from BH

— km

Tidal stretch · head→toe

— g

Event horizon (rₛ)

— km

Your body

Intact

Black hole mass

log₁₀ solar masses10 M☉

Distance from singularity

log₁₀ kilometres1,000 km

Real black holes

How to use

Drag the mass slider from a stellar-collapse black hole up to a supermassive one, and set your distance from the center. The figure on the left stretches as the head-to-toe tidal difference grows. The body snaps around 10 g across its length.

Try the presets, then watch the event-horizon readout: for the smallest holes you spaghettify well outside it — for the largest you sail across whole.

Why supermassive black holes are gentler

Tidal force scales as M / r³. At the event horizon the Schwarzschild radius r_s = 2GM/c² scales as M. So the tidal force at the horizon scales as M / M³ = 1/M² — bigger holes are weaker at their own edge.

A 10-solar-mass black hole rips you apart ~500 km above the horizon. Sagittarius A* (4 million M☉)? You cross the horizon completely intact and only spaghettify after, deep inside.

The math

Tidal stretch on a 2 m human at distance r from mass M: Δg = 2GM·h / r³ with h ≈ 2 m. The human body snaps around 10 g across its length.

Snap radius: r ≈ (2GMh / g_snap)^(1/3). For Sgr A* (4×10⁶ M☉) that's ~400,000 km — well inside the event horizon (~12 million km). For a stellar black hole it sits hundreds of km outside the horizon.

Citations

Misner, Thorne & Wheeler (1973) — Gravitation. Tidal-force treatment near Schwarzschild horizons.
Schwarzschild (1916) — Original metric, Sitzungsberichte der Preussischen Akademie.
Hawking & Ellis (1973) — The Large Scale Structure of Space-Time.
EHT Collaboration (2019) — M87* horizon-scale image, ApJL 875, L1.
GRAVITY Collaboration (2020) — Sgr A* mass = 4.30×10⁶ M☉, A&A 636, L5.

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