Tidal Force Calculator
A tidal force is not the total gravity a body feels but the difference in that gravity across its width. The near side of a moon or ocean is pulled slightly harder than the far side, and that difference stretches the body along the line toward the larger mass. Because tidal force is the gradient of an inverse-square law, it falls off as the inverse cube of distance, dropping eightfold when the distance doubles. This calculator applies the standard differential approximation F = 2 G M m r / d cubed to return the stretching force in newtons for any pair of masses and separation.
Tidal force formula
Tidal force = 2 * G * M * m * r / d^3
Mean gravity = G * M * m / d^2
G = gravitational constant (default 6.674e-11)
The tidal force is the leading term in the difference between the gravity at the near edge and the center of the small body, valid when r is much smaller than d. Mean gravity is shown for comparison so you can see how much smaller the tidal stretch is than the bulk attraction.
Tidal force facts
- Tidal force scales as one over distance cubed, so it weakens eightfold when distance doubles.
- Ocean tides on Earth are raised mainly by the Moon, with the Sun contributing about 46 percent as much.
- Inside the Roche limit, tidal force exceeds a fluid body's self-gravity and tears it apart.
- The default large mass shown is the Moon and the default separation is the mean Earth-Moon distance.
- The gravitational constant G is a user-editable input set to the 2022 CODATA value.
Tidal force: frequently asked questions
What is a tidal force?
A tidal force is the difference in gravitational pull a large body exerts across the diameter of a smaller body. The near side is pulled harder than the far side, stretching the smaller body along the line to the larger one. This differential, not the total gravity, is what raises ocean tides and can tear apart a body that strays too close.
What is the tidal force formula?
For a small body of mass m and radius (or half-separation) r at distance d from a mass M, the tidal force is F = 2 * G * M * m * r / d^3, where G is the gravitational constant 6.674e-11 N m^2 / kg^2. The force scales with the inverse cube of distance, so it falls off far faster than ordinary gravity.
Why does tidal force fall off as the cube of distance?
Gravity itself falls as 1 over distance squared. The tidal force is the gradient (the rate of change) of that gravity across the body, and the derivative of an inverse-square law is an inverse-cube law. Doubling the distance therefore weakens the tidal force by a factor of eight, not four.
What units does this calculator use?
All inputs are SI: mass M and m in kilograms, distance d and radius r in meters, and the gravitational constant in N m^2 / kg^2. The output tidal force is in newtons. The constant G is shown as a user-editable input set to the 2022 CODATA value 6.674e-11 so you can refine it if a later value is published.
What is the Roche limit's relationship to tidal force?
The Roche limit is the distance at which the tidal force stretching a body exceeds the self-gravity holding it together, causing it to break apart. This calculator returns the tidal force at a chosen distance; comparing it to a body's internal cohesion or self-gravity indicates whether the body is inside its Roche limit.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.