Tidal Force Calculator

About this calculator

This calculator estimates the differential tidal acceleration, a ≈ 2·G·M·r/d³, the stretching force a massive body M exerts across an extended object of radius r at distance d. It arises because gravity is stronger on the near side of an object than the far side; the formula captures that difference to first order, and the d³ term shows why tidal effects fall off much faster with distance than ordinary gravity (which falls as 1/d²).

Astrophysicists use this relationship to explain ocean tides raised by the Moon and Sun, to predict tidal locking (why the Moon always shows the same face to Earth), and to find the Roche limit — the distance inside which a body is torn apart by its host's tidal pull, relevant to planetary rings and comets passing close to planets. It's also the physics behind the (fictional but real-formula) idea of "spaghettification" near a black hole, where r is large enough and d small enough for the stretching to become extreme.