Gravitational Force Calculator
The Weakest Force, Felt by Everything
Gravity is by far the weakest of the four fundamental forces, yet it's the one that shapes planetary orbits, keeps your feet on the ground, and holds galaxies together — because unlike the other forces, it never cancels out and always adds up over enough mass. Newton's law of universal gravitation, published in 1687, was the first equation to describe this pull mathematically, and it still gives accurate results for anything short of extreme gravitational fields or relativistic speeds.
The Formula
G is the gravitational constant, 6.674×10&supminus;¹¹ N·m²/kg², m1 and m2 are the two masses, and r is the distance between their centers. The tiny value of G is exactly why gravitational force between everyday objects is imperceptible — it takes planet-scale mass to produce forces we actually notice.
Where This Force Is the Whole Story
- Orbital mechanics — satellite orbits, planetary motion, and spacecraft trajectories are all computed from this exact inverse-square relationship.
- Tidal forces — the difference in gravitational pull across an extended body, like the Earth under the Moon's influence, is what generates tides.
- Astrophysics — the mass of stars, black holes, and galaxies is often inferred indirectly by observing gravitational effects on nearby objects.
- Precision measurement — extremely sensitive instruments like torsion balances can detect gravitational attraction between lab-scale masses, which is in fact how G itself was first measured.
Just How Weak Gravity Is at Human Scale
| Scenario | Gravitational Force |
|---|---|
| Two 70 kg people standing 1 m apart | 3.270×10&supminus;&sup7; N |
| Earth and Moon (masses 5.972×10²&sup4; kg and 7.342×10²² kg, 3.844×10&sup8; m apart) | 1.980×10²&sup0; N |
The force between two people is roughly a millionth of a newton — far too small to feel — while planet-scale mass produces a force large enough to hold the Moon in orbit.
How to Use This Calculator
- Enter Mass 1 and Mass 2, in kilograms.
- Enter the Distance Between Centers of the two masses, and choose Meters or Kilometers.
- Select Calculate to get the gravitational force in newtons along with the worked formula.
Related Calculations
To compare this with the far stronger electric force between charges, see the Coulomb's Law Calculator, or convert a known force into the resulting acceleration with the Acceleration Calculator.