Newton's Law of Universal Gravitation
Enter two masses and the center-to-center distance between them to calculate gravitational force.
F = G × (m₁ × m₂) / r²where
G = 6.67430 × 10⁻¹¹ N·m²/kg²
What is gravitational force?
Gravitational force is the attractive force between any two objects that have mass. It is one of the four fundamental interactions in physics and explains everything from falling apples to planetary orbits and galaxy structure. The bigger the masses, the stronger the attraction. The greater the distance between them, the weaker the force.
How to use this gravitational force calculator
- Enter Mass 1 and choose its unit.
- Enter Mass 2 and choose its unit.
- Enter the distance between their centers and select a distance unit.
- Click Calculate Force.
The calculator converts all values into SI units (kg and meters), then applies Newton's law directly.
Understanding the formula
1) The gravitational constant (G)
G = 6.67430 × 10⁻¹¹ N·m²/kg². This is a very small number, which is why gravity between everyday objects is usually weak unless at least one object is very massive (like Earth).
2) Mass dependence
The force is proportional to the product of the two masses:
F ∝ m₁ × m₂
If either mass doubles, the force doubles. If both double, force becomes four times larger.
3) Distance dependence (inverse-square law)
The force decreases with the square of distance:
F ∝ 1 / r²
If distance doubles, force drops to one-fourth. If distance triples, force drops to one-ninth.
Example scenarios
Earth and a 70 kg person
Use mass 1 = 1 Earth mass, mass 2 = 70 kg, distance = 1 Earth radius. The result is close to the person's weight force near Earth's surface (about 686 N).
Two spacecraft in orbit
If both spacecraft are relatively small and far apart, the force can be tiny. Even tiny forces matter in orbital mechanics when acting over long times.
Common mistakes to avoid
- Using edge-to-edge distance instead of center-to-center distance.
- Forgetting unit conversions (especially km vs m).
- Entering zero or negative distance, which is physically invalid.
- Assuming this equation includes relativity effects (it does not).
When this calculator is accurate
This calculator uses classical Newtonian gravity, which is highly accurate for most everyday and many astronomical problems. For extreme gravity conditions (near black holes) or ultra-precise relativistic predictions, general relativity is required.
Quick FAQ
Is gravitational force always attractive?
Yes, for normal matter in Newtonian gravity, the force is always attractive.
Can I use scientific notation?
Yes. Values like 5.972e24 are accepted.
What unit is the output?
The output force is in newtons (N), the standard SI unit of force.
Final thought
Gravity links tiny local interactions to massive cosmic behavior. With a simple equation and careful units, you can model forces between objects ranging from lab-scale masses to planets and stars.