Every mass attracts every other mass. The force is tiny for everyday objects but governs the motion of moons, planets, stars and galaxies. Newton’s law also explains why weight is smaller on the Moon and why tides happen.
How to use the Gravitational Force Calculator
- Mass 1 (M)
- Mass 2 (m)
- Distance between centres R
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter both masses and the distance between their centres. The field strength g is the force per kilogram produced by the first mass at that distance.
Inputs explained
| Field | What to enter |
|---|---|
| Mass 1 (M) | Units: kg, M⊕ (Earths), M☉ (Suns), t |
| Mass 2 (m) | Units: kg, g, mg, t, lb, oz |
| Distance between centres R | Units: km, m, mi, nmi, ft |
What each result means
- Gravitational force F = 6.6743e-11×[Mass 1 (M)]×[Mass 2 (m)]÷[Distance between centres R]^2
- Field strength of mass 1 at R = 6.6743e-11×[Mass 1 (M)]÷[Distance between centres R]^2
Example values
How the main result changes when Mass 1 changes and everything else stays at the example values above:
| Mass 1 (M) (kg) | Gravitational force F (N) |
|---|---|
| 2.99e24 | 343.7106 |
| 4.48e24 | 515.5659 |
| 5.97e24 | 687.4212 |
| 7.47e24 | 859.2765 |
| 8.96e24 | 1,031.1317 |
| 1.19e25 | 1,374.8423 |
Formula
F = G·M·m / R², G = 6.6743 × 10⁻¹¹ N·m²/kg², g = G·M / R²
Worked example
Inputs — Mass 1 (M): 5.9722e+24 kg; Mass 2 (m): 70 kg; Distance between centres R: 6,371 km.
Results — Gravitational force F = 687.421161 N; Field strength of mass 1 at R = 9.820302 m/s².
Key terms
- Gravitational constant G
- 6.6743 × 10⁻¹¹ N·m²/kg².
Frequently asked questions
Why don't I feel the pull of a person next to me?
The force between two 70 kg people 1 m apart is about 0.3 µN.
What happens if the distance doubles?
The force falls to a quarter (inverse-square law).
Is gravity always attractive?
Yes, for ordinary mass.
Who measured G?
Henry Cavendish, using a torsion balance in 1798.