Gravitational Force Calculator

What Is Gravitational Force?

Gravitational force is the attractive force between any two objects that have mass. Every object in the universe attracts every other object. The more massive the objects and the closer they are, the stronger the gravitational pull.

Gravity is the weakest of the four fundamental forces of nature, but it acts over infinite distance and always attracts — it never repels. It is the force responsible for your weight, the orbits of planets, and the structure of galaxies.

How to Calculate Gravitational Force

Newton's Law of Universal Gravitation

Where:

• F = gravitational force (N)
• G = gravitational constant = 6.674 × 10⁻¹¹ N⋅m²/kg²
• m₁, m₂ = masses of the two objects (kg)
• r = distance between the centers of the objects (m)

The force is proportional to the product of the masses and inversely proportional to the square of the distance — this is the inverse-square law.

Worked Example: Your Weight

The gravitational force between a 70 kg person and the Earth (mass = 5.972 × 10²⁴ kg, radius = 6.371 × 10⁶ m):

F = (6.674 × 10⁻¹¹ × 5.972 × 10²⁴ × 70) / (6.371 × 10⁶)²
F = 686.4 N (154.3 lbs)

This is exactly the same as calculating weight with W = mg = 70 × 9.81 = 686.7 N. The acceleration due to gravity (g = 9.81 m/s²) is itself derived from the universal gravitation equation.

Gravity on Other Planets

Surface gravity depends on both the planet's mass and radius. The Moon's gravity is about 1.62 m/s² (1/6 of Earth's), so a 70 kg person weighs only 113.4 N there. Mars has a surface gravity of 3.72 m/s². Jupiter's is 24.79 m/s² — nearly 2.5 times Earth's.