Gravitational Force Calculator
Calculate the pull between any two masses with Newton’s law of universal gravitation, or solve for a mass or distance. Pre-filled with the Earth and the Moon.
F = G m₁ m₂ ÷ r²
Solve for
F
Gravitational force
N
4 sig figs: 1.982e+20
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Same value in
1.982 × 10²³ mN · 1.982 × 10²⁵ dyn · 4.456 × 10¹⁹ lbf
- Rearrange: F = G m₁ m₂ ÷ r²
- Substitute: m₁ = 5.972e24 kg, m₂ = 7.348e22 kg, r = 384400 km (converted to SI units first).
- Result: F = 1.98211 × 10²⁰ N, rounded to 4 significant figures because the least precise input has 4.
G = 6.674 × 10⁻¹¹ N·m²/kg² (CODATA 2018).
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Useful masses and distances
| Body | Mass (kg) | Mean radius (km) |
|---|---|---|
| Sun | 1.989 × 10³⁰ | 696 000 |
| Earth | 5.972 × 10²⁴ | 6 371 |
| Moon | 7.348 × 10²² | 1 737 |
| Mars | 6.417 × 10²³ | 3 390 |
| Jupiter | 1.898 × 10²⁷ | 69 911 |
Earth–Moon distance averages 384 400 km; Earth–Sun 1.496 × 10⁸ km. Source: NASA Planetary Fact Sheet.
Frequently asked questions
What is Newton's law of universal gravitation?
Every two masses attract with F = G m₁ m₂ ÷ r², where r is the distance between their centres and G = 6.674 × 10⁻¹¹ N·m²/kg². Double the distance and the force drops to a quarter.
Why don’t I feel attracted to other people?
G is tiny. Two 70 kg people 1 m apart attract with about 3 × 10⁻⁷ N, roughly the weight of a grain of sand. Gravity only becomes large when at least one mass is planet-sized.
How does this relate to g = 9.81 m/s²?
Set F = mg for an object on Earth’s surface: g = GM ÷ R² = 6.674 × 10⁻¹¹ × 5.972 × 10²⁴ ÷ (6.371 × 10⁶)² = 9.82 m/s².
What distance should I use for r?
Centre to centre. For a satellite, add its altitude to Earth’s radius (6371 km). The ISS at 420 km altitude is at r = 6791 km.