About the Gravitational Force Calculator
What is the Gravitational Force Calculator?
Every mass attracts every other mass. This gravitational force calculator applies Newton's law of universal gravitation, where the force falls with the square of the distance.
The defaults show the pull between the Earth and the Moon, about 2 × 10²⁰ newtons.
How to use the Gravitational Force Calculator
- Mass 1 (kg) (sample: 59,72,00,00,00,00,00,00,32,71,55,712)
- Mass 2 (kg) (sample: 73,41,99,99,99,99,99,99,68,54,272)
- Distance between Centres (m) (sample: 38,44,00,000)
- Press Calculate Gravitational Force (results also refresh as you type). The result card shows the Gravitational Force, along with Acceleration of mass 2 towards mass 1, Acceleration of mass 1 towards mass 2 and Gravitational constant used.
Formula used
F = G × m₁ × m₂ ÷ r²
- G = 6.6743 × 10⁻¹¹ N·m²/kg²
- r = distance between the centres of mass
Values can be entered in scientific notation, for example 5.972e24.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Mass 1 (kg) | 59,72,00,00,00,00,00,00,32,71,55,712 |
| Mass 2 (kg) | 73,41,99,99,99,99,99,99,68,54,272 |
| Distance between Centres (m) | 38,44,00,000 |
| Result | Value |
|---|---|
| Gravitational Force | 1.98 × 10²⁰ N |
| Acceleration of mass 2 towards mass 1 | 0.002697 m/s² |
| Acceleration of mass 1 towards mass 2 | 3.316 × 10⁻⁵ m/s² |
| Gravitational constant used | 6.6743 × 10⁻¹¹ N·m²/kg² |
Tips for using the Gravitational Force Calculator
- Gravity between everyday objects is tiny – two 1,000 kg masses 1 m apart attract with 0.000067 N.
- Doubling the distance cuts the force to a quarter.