Gravitational Force Calculator
Newton's law of universal gravitation gives the attraction between any two masses. It governs falling apples and planetary orbits alike.
Formula
F = G × m₁ × m₂ ÷ r²
- G = 6.674 × 10⁻¹¹ N·m²/kg²
- r = distance between the centres of mass
- The inverse square: double the distance, quarter the force
Two 1,000 kg masses 1 m apart attract with 6.674 × 10⁻⁵ N
The Law
F = G × (m₁ × m₂) ÷ r²
Where G is the gravitational constant, 6.674 × 10−11 N·m²/kg², and r is the distance between the centres of the two masses.
Two 100 kg people one metre apart attract with a force of about 6.67 × 10−7 N — roughly the weight of a grain of sand.
Why Gravity Feels Strong Anyway
Gravity is by far the weakest of the fundamental forces. A small fridge magnet lifts a paperclip against the pull of the entire Earth.
It dominates at astronomical scale for two reasons: it is always attractive, never cancelling out the way positive and negative charges do, and it has unlimited range. Accumulate enough mass and the sum becomes overwhelming.
The Inverse Square Law
Force falls with the square of distance, so doubling the separation quarters the attraction and tripling it cuts the force to a ninth.
Note that r is measured centre to centre, not surface to surface. This is why gravity at the top of a tall building is only marginally weaker than at ground level: you have added a few hundred metres to Earth's 6,371 km radius. The ISS at 400 km altitude still experiences about 90% of surface gravity — astronauts float because they are in continuous free fall, not because gravity has stopped.
Quick Reference
| Body | Surface gravity | Relative to Earth |
|---|---|---|
| Moon | 1.62 m/s² | 0.17× |
| Mars | 3.72 m/s² | 0.38× |
| Earth | 9.81 m/s² | 1.00× |
| Neptune | 11.15 m/s² | 1.14× |
| Jupiter | 24.79 m/s² | 2.53× |
| Sun | 274 m/s² | 27.9× |
Frequently Asked Questions
- What is the gravitational constant?
- G is 6.674 × 10⁻¹¹ N·m²/kg². It is one of the least precisely measured constants in physics, because gravity is so weak.
- Why is gravity considered weak?
- A small magnet can lift a paperclip against the entire Earth's pull. Gravity dominates at large scales only because it always attracts and never cancels out.
- Why do astronauts float if gravity is still strong up there?
- The ISS experiences about 90 per cent of surface gravity. Astronauts float because they are in continuous free fall around the Earth, not because gravity is absent.
- Do I measure distance from the surface or the centre?
- From the centre of each mass. For Earth that means adding altitude to the 6,371 km radius, which is why height above ground barely changes the result.