Gravitational Force Calculator (Newton's law)
Calculate the attraction between two masses with F = Gm₁m₂/r², plus surface gravity, escape velocity, and orbits.
Both masses feel the same force — it is their accelerations that differ, because the same push moves a small mass far more than a large one.
Surface gravity across the solar system
Every column below is worked out from the body's mass and equatorial radius with the same formula the calculator uses — nothing here is a quoted number. The last column is what a 70 kg person would weigh standing there.
| Body | Mass | Radius | Surface gravity | Relative to Earth | Escape velocity | Weight of 70 kg |
|---|---|---|---|---|---|---|
| Earth | 5.972e+24 kg | 6 378.1 km | 9.798 m/s² | 1 g | 11.18 km/s | 685.9 N |
| Moon | 7.342e+22 kg | 1 737.4 km | 1.623 m/s² | 0.166 g | 2.375 km/s | 113.6 N |
| Sun | 1.988e+30 kg | 695 700 km | 274.2 m/s² | 28 g | 617.7 km/s | 19 190 N |
| Mercury | 3.301e+23 kg | 2 439.7 km | 3.702 m/s² | 0.378 g | 4.25 km/s | 259.1 N |
| Venus | 4.868e+24 kg | 6 051.8 km | 8.87 m/s² | 0.905 g | 10.36 km/s | 620.9 N |
| Mars | 6.417e+23 kg | 3 396.2 km | 3.713 m/s² | 0.379 g | 5.022 km/s | 259.9 N |
| Jupiter | 1.898e+27 kg | 71 492 km | 24.79 m/s² | 2.53 g | 59.53 km/s | 1 735 N |
| Saturn | 5.683e+26 kg | 60 268 km | 10.44 m/s² | 1.07 g | 35.48 km/s | 731 N |
| Uranus | 8.681e+25 kg | 25 559 km | 8.869 m/s² | 0.905 g | 21.29 km/s | 620.8 N |
| Neptune | 1.024e+26 kg | 24 764 km | 11.15 m/s² | 1.14 g | 23.5 km/s | 780.2 N |
| Pluto | 1.303e+22 kg | 1 188.3 km | 0.6159 m/s² | 0.0629 g | 1.21 km/s | 43.11 N |
Newton's law of universal gravitation
Every mass attracts every other mass. The strength of that attraction rises with both masses and falls with the square of the distance between their centres — and the same short formula covers an apple, a satellite, and a galaxy.
F = G · m₁ · m₂ / r²
G is the gravitational constant, 6.6743e-11 N·m²/kg². It is a very small number, which is why gravity is only noticeable when at least one of the masses is planet-sized. Two people standing a metre apart attract each other with a force of well under a millionth of a newton.
Worked example
A 70 kg person on Earth's surface: m₁ = 5.97 × 10²⁴ kg, m₂ = 70 kg, and r is Earth's radius, 6 378 km — not zero, because the distance is measured to the centre. That gives about 687 N, which is simply their weight. Dividing by the 70 kg gives 9.8 m/s², the familiar g.
Surface gravity is the same law rearranged
Because the force on any mass m is proportional to m, the acceleration it produces does not depend on m at all: g = GM/r². That single expression generates the whole table above. It also explains an apparent oddity in it — Uranus is fifteen times Earth's mass yet has almost identical surface gravity, because it is also four times the radius, and the r² in the denominator cancels the extra mass almost exactly.
Escape velocity and orbits
Escape velocity is the speed at which kinetic energy exactly matches the energy needed to climb out of the gravitational well: v = √(2GM/r). Orbiting needs less — a circular orbit requires √(GM/r), a factor of √2 slower. Feeding Earth's mass and a radius of 42 164 km into that gives a period of almost exactly 24 hours, which is how geostationary orbit is defined.
The small print
This treats both bodies as points, or as perfect spheres of uniform density, which is exact outside a sphere and a good approximation for planets. Real planets are oblate and lumpy, so local gravity varies by a fraction of a percent. The table also ignores rotation: your measured weight at the equator is slightly less than the figure shown, because some of the gravitational force is spent keeping you moving in a circle.
For the everyday version of this near Earth's surface, use theforce calculator with a = 9.81, or thefree fall calculator for a dropped object.