MotionLab

Gravitational Force Calculator

Every mass in the universe attracts every other mass — this formula tells you how strongly.

Mass 1 (kg)

Mass 2 (kg)

Distance (m)

Gravitational force (N)

687.367

F = Gm₁m₂ / r²

What you entered

Mass 1 (kg): 5.972e+24Mass 2 (kg): 70Distance (m): 6371000

1
F = G × m₁m₂ ÷ r²
6.674e-11 × 5.972e+24 × 70 ÷ 6371000²= 6.8737e+2 N

Result

Gravitational force (N): 687.367

The gravitational force between masses of 5.972e+24 kg and 70 kg at 6371000 m apart is 687.367 N.

Gravitational attraction between masses

Newton's law of universal gravitation: G times the two masses divided by the distance squared, with G at 6.674e-11.

Mass 1 (kg)	Mass 2 (kg)	Distance (m)	Force (N)	Context
1	1	1	6.6740e-11	Two 1 kg masses, 1 m apart
70	70	1	3.2703e-7	Two people, 1 m apart
1000	1000	10	6.6740e-7	Two tonnes, 10 m apart
5.97e24	70	6.371e6	6.8714e+2	Earth and a 70 kg person
5.97e24	7.35e22	3.844e8	1.9819e+20	Earth and the Moon

The second row is the useful reality check: two people standing a metre apart attract each other with about 0.33 microN, which is why gravity is imperceptible until one of the masses is planetary. Row four reproduces the person's weight of 687 N, matching the force calculator at 70 kg times 9.81 - which is exactly what g is, the gravitational field strength at the Earth's surface. Gravity follows an inverse square law, so doubling the distance quarters the force; it has infinite range and is always attractive.

Why gravity feels strong but is actually weak

Gravity is by far the weakest of the four fundamental forces — it takes the entire mass of the Earth (5.97 × 10²⁴ kg) to hold you down, while a tiny fridge magnet easily overcomes that pull on a paperclip. Gravitational force becomes significant only when at least one mass is astronomical.

The inverse-square law in action

Doubling the distance between two objects cuts the gravitational force to one-quarter — this inverse-square relationship means gravity drops off quickly with distance but never fully reaches zero, which is why the Moon still feels Earth's pull from 384,000 km away.

Frequently asked questions

What gravitational force does Earth exert on a 70 kg person standing on its surface?

F = GMm/r² = 6.674×10⁻¹¹ × 5.97×10²⁴ × 70 / (6.371×10⁶)² = 687 N. This is simply your weight — mg = 70 × 9.81 = 686.7 N. The universal law and the simple 'weight = mg' give the same answer.

How does the gravitational force between Earth and the Sun keep Earth in orbit?

F = GMm/r² = 6.674×10⁻¹¹ × 1.989×10³⁰ × 5.97×10²⁴ / (1.496×10¹¹)² ≈ 3.54×10²² N. This provides exactly the centripetal force needed for Earth's orbital speed of 29.8 km/s.

How is this different from the gravity calculator?

Both use F = Gm₁m₂/r². This calculator may present inputs differently (two masses and distance), but the physics is identical. Use whichever interface matches your problem's given quantities.

At what distance does gravity become negligible?

Gravity never reaches exactly zero — it just becomes immeasurably small. At the Moon's distance (384,000 km), Earth's gravity is about 0.003 m/s² (0.03% of surface gravity). In deep interstellar space, the Sun's pull is present but overwhelmed by nearby stars.