Gravitational Force Calculator (Newton)
Gravitational force calculator using Newton's law of universal gravitation: force, distance or either mass.
F = G m1 m2r²
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
Every two masses attract each other with F = G·m₁·m₂/r², where r is the distance between their centres.
Your weight is this force between you and the Earth.
Formula
F = G m1 m2r²
| Symbol | Quantity | Units |
|---|---|---|
| m1 | Mass 1 | kg, g, mg, µg, t, lb, oz, st, US ton, ct, Da |
| m2 | Mass 2 | kg, g, mg, µg, t, lb, oz, st, US ton, ct, Da |
| r | Distance between centres | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| F | Gravitational force | N, kN, mN, dyn, lbf, kgf |
Constants used: G = 6.6743 × 10⁻¹¹ N·m²/kg²
Worked example
Given: m1 = 5.972 × 1024 kg · m2 = 70 kg · r = 6 371 000 m
F = G m1 m2r²
Result: F = 687.398 N
Frequently asked questions
Force between the Earth and a 70 kg person on the surface?
About 687 N.