Tidal Force Calculator
Calculate the gravitational force between two celestial bodies separated by a given distance. Useful for understanding tidal interactions, orbital dynamics, and the gravitational pull between moons, planets, and stars.
Last updated: September 2026
Formula below · 2 sources (nasa.gov, Wikipedia) · Updated Sep 2026
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About this calculator
A tidal force is the difference between the gravitational pull of one body (the primary, which raises the tide) on the near side of a second body and its pull on that body's centre. For a secondary of mass m and radius R at distance d from a primary of mass M, the stretching force is approximately F_tidal = 2·G·M·m·R / d³, where G = 6.674 × 10⁻¹¹ N·m²/kg². Dividing by m gives the tidal acceleration 2GMR/d³ that every kilogram at the near surface feels. Distances are entered in kilometres and the radius defaults to Earth's 6,371 km. Note the 1/d³ dependence: halving the distance makes the tide eight times stronger, which is why tides — unlike gravity itself, which falls as 1/d² — are dominated by nearby bodies; the Moon raises about twice the tide the much more massive Sun does.
How to use
Take the Moon (primary, M = 7.35 × 10²² kg) raising tides on Earth (secondary, m = 5.972 × 10²⁴ kg, R = 6,371 km) at a distance of 384,400 km. F = 2 × 6.674 × 10⁻¹¹ × 7.35 × 10²² × 5.972 × 10²⁴ × 6.371 × 10⁶ / (3.844 × 10⁸)³ ≈ 6.6 × 10¹⁸ N. Per kilogram that is 2GMR/d³ ≈ 1.1 × 10⁻⁶ m/s² — about one ten-millionth of Earth's surface gravity, yet enough to raise the ocean tides. For comparison, the plain gravitational attraction between Earth and Moon is 1.98 × 10²⁰ N, about 30 times larger.
Frequently asked questions
How does distance affect the gravitational tidal force between two bodies?
Gravitational force follows an inverse-square law, F = GMm/r², but the tidal force is the difference in that pull across the body and falls off as the inverse cube, 2GMmR/r³. Doubling the distance cuts the tide by a factor of eight; tripling it, by 27. For example, the Moon's tidal influence on Earth's oceans would be drastically weaker if the Moon were twice as far away. In close binary star systems or planets near massive gas giants, tidal forces can be extreme enough to deform the shape of the smaller body or generate significant internal heating through tidal flexing.
What is the difference between gravitational force and tidal force?
Gravitational force is the total attractive force between two bodies as given by F = GMm/r². Tidal force, strictly speaking, is the differential gravitational force — the difference in gravitational pull felt across the diameter of the secondary body. The near side of the Moon is pulled more strongly than the far side, creating a stretching effect. Tidal force scales as 2GMmΔr/r³, where Δr is the body's radius. This calculator returns that tidal force, using the secondary's radius as Δr. Both quantities are essential in understanding oceanic tides, tidal locking, and the Roche limit.
Why are tidal forces important in planetary and stellar science?
Tidal forces shape planetary systems in profound ways. They are responsible for tidal locking — the reason one side of the Moon always faces Earth. They drive volcanic activity on Jupiter's moon Io by flexing its interior. They govern the Roche limit, inside which a satellite is torn apart rather than held together by its own gravity. In stellar binaries, extreme tidal forces can transfer mass between stars. Even Earth's ocean tides, driven by the Moon and Sun's gravity, have gradually slowed Earth's rotation over billions of years. Understanding tidal forces is therefore central to planetary geology, orbital evolution, and habitability studies.