Gravitational Force Calculator

What is the Gravitational Force Calculator?

This calculator uses Newton's law of universal gravitation to find the attractive force between any two objects with mass. It's most commonly used in physics courses when studying planetary motion, orbital mechanics, or just trying to understand why gravity affects things the way it does. CalciHub's version handles the formula for you, useful when the numbers get unwieldy, since astronomical masses and distances often involve very large exponents.

How Does It Work?

Every two objects with mass attract each other. The strength of that attraction depends on both masses and the distance between them, specifically the square of the distance. So double the distance and the force drops to a quarter of what it was.

F = G × (m₁ × m₂) / r²

• F = Gravitational force, in newtons (N)

• G = Gravitational constant = 6.674 × 10⁻¹¹ N·m²/kg²

• m₁ = Mass of first object, in kilograms

• m₂ = Mass of second object, in kilograms

• r = Distance between centers of mass, in meters

How to Use CalciHub's Gravitational Force Calculator

1. Enter the mass of the first object in kilograms.

2. Enter the mass of the second object in kilograms.

3. Enter the distance between the two objects (center to center) in meters.

4. Click Calculate.

Tip: For planetary calculations, express masses in scientific notation. Earth's mass is 5.972 × 10²⁴ kg, and the Moon is 7.342 × 10²² kg, those numbers don't fit on a regular calculator easily.

A Quick Example

What is the gravitational force between Earth and the Moon?

• m₁ = 5.972 × 10²⁴ kg (Earth)

• m₂ = 7.342 × 10²² kg (Moon)

• r = 3.844 × 10⁸ m (average distance)

• G = 6.674 × 10⁻¹¹

F = (6.674 × 10⁻¹¹ × 5.972 × 10²⁴ × 7.342 × 10²²) / (3.844 × 10⁸)² ≈ 1.98 × 10²⁰ N

That's about 198 quintillion newtons the force keeping the Moon in its orbit around Earth.

Frequently Asked Questions