Tidal Force Calculator

Kaava

How this is calculated

Tides arise because gravity weakens with distance, so the near side of a body is pulled harder than its far side. The source mass M is the object generating the field (for example a planet or the Sun), the center distance d is measured between the two centers of mass, and the body radius r is the half-size of the affected body over which the pull varies. The optional affected-body mass m converts the per-kilogram acceleration into a total force.

The tidal acceleration is the gradient of gravitational acceleration times the radius: starting from g = GM/d² and differentiating with respect to d gives dg/dd = -2GM/d³, so over a span r the difference is Δg = 2·G·M·r / d³. Multiplying by the body mass gives the tidal force F = 2·G·M·m·r / d³. Note the strong inverse-cube dependence on distance, which is why tidal effects fall off far faster than ordinary gravity.

All inputs use SI units: kilograms for mass, meters for distance and radius, giving acceleration in m/s² and force in newtons. The distance must be nonzero, and it must exceed the body radius for the linear approximation to hold. The result is a first-order estimate; very close encounters (near the Roche limit) require the full nonlinear field. Force output requires the optional mass m to be supplied.