What this force of gravity calculator does
This calculator computes the gravitational force between two objects using Newton’s law of universal gravitation. If you know the two masses and the distance between their centers, you can estimate how strongly they attract each other.
The result is shown in newtons (N), with extra context in kilonewtons and meganewtons for larger values. This tool is useful for physics homework, astronomy intuition, and quick engineering estimates.
The formula behind the calculator
The equation is:
F = G × (m₁ × m₂) / r²
- F = gravitational force in newtons (N)
- G = 6.67430 × 10⁻¹¹ N·m²/kg² (gravitational constant)
- m₁, m₂ = masses in kilograms
- r = center-to-center distance in meters
Because distance is squared, force drops quickly as objects move apart. Double the distance, and the force becomes one-fourth.
How to use the calculator correctly
1) Enter both masses
You can use kilograms, grams, or pounds. The calculator converts everything to SI units internally.
2) Enter the center-to-center distance
Choose meters, kilometers, miles, or feet. For planets or moons, make sure you’re using center distance, not surface gap.
3) Click “Calculate Force”
You’ll get the force plus acceleration context for each mass:
- a₁ = F / m₁
- a₂ = F / m₂
Example calculations
Earth and Moon
If you use Earth mass, Moon mass, and average center distance, the result is around 2 × 10²⁰ N, which is the huge force that keeps the Moon in orbit.
Two everyday objects
Try 1 kg and 1 kg at 1 meter apart. The force is tiny (about 6.67 × 10⁻¹¹ N), which is why gravity between small objects is hard to notice compared with friction or electromagnetic effects.
Common mistakes to avoid
- Using surface distance instead of center-to-center distance
- Forgetting that values must be positive and non-zero
- Mixing unit systems without conversion
- Assuming this equation includes air resistance or other forces (it does not)
Frequently asked questions
Is this the same as weight?
Related, but not always identical in setup. Weight near a planet’s surface is usually simplified to W = m × g.
This calculator is the general two-body gravity equation.
Can I use scientific notation?
Yes. Inputs like 5.972e24 work for large astronomical masses.
What units does the result use?
The primary output is newtons (N), the SI unit of force.
Final note
Gravity is weak at human scale but dominates at planetary and cosmic scale. This calculator gives you a fast way to explore that contrast and build intuition with real numbers.