Gravitational Force Calculator

If you want to calculate the force between two masses, try our gravitational force calculator.

Gravitational force736.519 Nequal and opposite on each mass, however unequal they are

Field strength from the first mass9.820253 m/s²1.0014 g

Acceleration of the second mass9.820253 m/s²identical to the field strength — mass cancels

Acceleration of the first mass1.23325e-22 m/s²far smaller, because it is heavier

G used6.6743e-11 m³/(kg·s²)known to only about 5 significant figures — the least precise fundamental constant

Escape velocity from this distance11,186.1371 m/s11.186 km/s

Circular orbital speed here7,909.7934 m/sescape velocity is exactly √2 times this

Orbital period at this radius5,060.84 s84.35 minutes

Gravitational potential energy-4.6924 GJnegative by convention, taking zero at infinite separation

At 2× the distance184.1297 N25% of the force — inverse square, not inverse

At 10× the distance7.3652 N1% of the force — inverse square, not inverse

The formula

F = Gm₁m₂ ÷ r²; g = GM ÷ r²

Equal and opposite, however lopsided

The force the Earth exerts on you and the force you exert on the Earth are exactly equal. What differs is the acceleration each produces: the same force divided by the Earth's vastly greater mass gives an acceleration too small to measure. This is Newton's third law, and it is why the field strength above equals the acceleration of the smaller mass — its own mass cancels out of the calculation entirely.

The inverse square is the substance of the law and it falls off fast: at ten times the distance the force is one percent, not one tenth. That steepness is why orbits are stable and why tidal forces, which depend on the difference in field across an object, fall off even faster still.

Escape velocity is exactly √2 times the circular orbital speed at the same radius — a tidy result that follows from comparing the energy needed to reach infinity with the energy of a circular orbit. Note that G is the least precisely measured of the fundamental constants, so gravitational calculations cannot be quoted to more than about five significant figures however careful the arithmetic.