MotionLab

Gravitational Force Calculator

The force that holds moons in orbit and drops an apple — same formula, wildly different scales.

Mass 1 (kg)

Mass 2 (kg)

Distance (m)

Gravitational force (N)

687.137

F = G·m₁m₂ / r² (Newton's law of universal gravitation)

What you entered

Mass 1 (kg): 5.97e+24Mass 2 (kg): 70Distance (m): 6371000

1
F = G × m₁m₂ ÷ r²
6.674e-11 × 5.97e+24 × 70 ÷ 6371000²= 6.8714e+2 N

Result

Gravitational force (N): 687.137

The gravitational attraction between the two masses is 687.137 N.

What a 70 kg person weighs on each world, from Newton's law

Every row uses F = G x m1 x m2 / r squared with mass 2 fixed at 70 kg and r set to the body's mean radius, so the force is what that person would weigh standing on the surface. Enter the mass and distance from a row to reproduce its force.

Body	Mass m1 (kg)	Distance r (m)	Force on a 70 kg person (N)
Sun	1.989e30	6.957e8	19,198.841
Jupiter	1.898e27	6.9911e7	1,814.218
Neptune	1.024e26	2.4622e7	789.11
Saturn	5.683e26	5.8232e7	782.958
Earth	5.97e24	6.371e6	687.137
Uranus	8.681e25	2.5362e7	630.503
Venus	4.867e24	6.0518e6	620.835
Mars	6.417e23	3.3895e6	260.943
Mercury	3.301e23	2.4397e6	259.094
Moon	7.35e22	1.737e6	113.808

G is 6.674e-11 and the Earth row uses the calculator's own default inputs. The Sun and the four gas giants have no solid surface, so their figures are what you would feel at the quoted radius rather than anywhere you could stand. Because force falls off with the square of r, Neptune outweighs Saturn here despite being far less massive: it is much smaller, so the surface sits closer to the centre of mass.

Why everyday objects don't noticeably attract each other

The gravitational constant G is extremely small (6.674×10⁻¹¹), so gravitational force between everyday-sized objects is vanishingly tiny — it only becomes significant when at least one mass is astronomically large, like a planet.

Distance matters more than you'd think

Force falls off with the square of distance — doubling the distance between two masses cuts the gravitational force to a quarter, not half, which is why gravity weakens quickly as you move away from a planet.

Frequently asked questions

Two 50 kg people stand 1 m apart. What gravitational force do they exert on each other?

F = G×m₁×m₂/r² = 6.674×10⁻¹¹ × 50 × 50 / 1 = 1.67×10⁻⁷ N. That's about 17 micrograms of force — utterly negligible. You'd need planet-scale masses to feel gravity.

How does gravity on the Moon compare to Earth?

Surface gravity depends on mass and radius. The Moon has g ≈ 1.62 m/s² (about 1/6 of Earth's 9.81). Mars: 3.71 m/s². Jupiter: 24.8 m/s². A 70 kg person weighs 687 N on Earth but only 113 N on the Moon.

What is the difference between this and the gravitational force calculator?

This calculator uses Newton's universal gravitation (F = Gm₁m₂/r²) for any two masses at any distance. The gravitational force calculator may handle the same formula with a different interface. Both give the same result — use whichever input layout suits your problem.

Why doesn't gravity have a 'negative' or 'repulsive' mode?

Gravity is always attractive — there is no negative mass (as far as we know) and no gravitational repulsion. This makes gravity unique among fundamental forces. Electromagnetism, by contrast, has both attraction and repulsion. See the Coulomb's law calculator for the electric analog.

How strong is Earth's pull on the Moon?

F = G × M_Earth × M_Moon / r² = 6.674×10⁻¹¹ × 5.97×10²⁴ × 7.35×10²² / (3.84×10⁸)² ≈ 1.98×10²⁰ N. That's 20 billion billion newtons — enough to keep the Moon in orbit at 1 km/s orbital velocity.