What Is Gravitational Force and How Is It Calculated?
Gravitational force is the attractive force between any two objects that have mass. It is directly proportional to the product of the two masses and inversely proportional to the square of the distance between their centers, as described by Isaac Newton's law of universal gravitation, published in 1687.
Newton's law of universal gravitation is: F = G × m₁ × m₂ ÷ r², where F is the force in newtons (N), G is the gravitational constant (6.6743 × 10⁻¹¹ N·m²/kg², the CODATA 2018 value), m₁ and m₂ are the masses in kilograms, and r is the distance between the centers of the two masses in metres. Henry Cavendish first measured G in 1798 with a torsion balance.
According to NASA, the Moon sits an average of 384,400 km from Earth, and the gravitational pull between the two bodies is about 1.98 × 10²⁰ N. Because force falls with the square of distance, doubling the distance cuts the force to one quarter.
How to Use This Gravitational Force Calculator
Enter the two masses and the distance between them; results update instantly:
- Mass of object 1 (m₁): Usually the larger body, such as a planet or star. It is also the body used for orbital speed and escape velocity.
- Mass of object 2 (m₂): The smaller body, such as a moon, satellite or person.
- Distance (r): Measured between the centers of the two masses, not between their surfaces. For an object on Earth's surface, use Earth's mean radius of 6,371 km.
Scientific notation is accepted, so you can type 5.972e24 for the mass of Earth. Switch between metric (kg, m, newtons) and US units (lb, miles, pounds-force); all results are stored in the URL so you can share a calculation. Orbital speed and escape velocity assume m₁ is much more massive than m₂.
Gravitational Force Examples and Typical Values
The table lists gravitational force and escape velocity for familiar systems. NASA gives Earth's escape velocity at the surface as about 11.19 km/s (25,000 mph), and the International Space Station orbits at roughly 7.66 km/s.
| System | Distance (center to center) | Gravitational force |
|---|---|---|
| Earth & 70 kg person | 6.371 × 10⁶ m | 687 N (≈154 lbf) |
| Earth & Moon | 3.844 × 10⁸ m | 1.98 × 10²⁰ N |
| Sun & Earth | 1.496 × 10¹¹ m | 3.54 × 10²² N |
| Two 1 kg masses, 1 m apart | 1 m | 6.67 × 10⁻¹¹ N |
The law is universal and the SI unit is the newton worldwide, but US sources often quote weight in pounds-force and distances in miles. Use the unit tabs to convert automatically.
Frequently Asked Questions About Gravitational Force
What is the formula for gravitational force?
Gravitational force equals the gravitational constant times the product of two masses divided by the square of the distance between their centers: F = G × m₁ × m₂ ÷ r². G is 6.6743 × 10⁻¹¹ N·m²/kg², and the force is measured in newtons.
What is the difference between gravitational force and weight?
Weight is the gravitational force a planet exerts on an object at its surface, calculated as W = m × g, where g is about 9.81 m/s² on Earth. Gravitational force is the more general quantity between any two masses at any distance.
How do you calculate escape velocity?
Escape velocity is v = √(2GM ÷ r), where M is the mass of the larger body and r is the distance from its center. For Earth's surface this gives about 11,186 m/s, regardless of the mass of the escaping object.
Why does gravitational force decrease with distance?
Gravity follows an inverse-square law: force is proportional to 1/r². Doubling the distance between two masses reduces the force to one quarter, and tripling it reduces the force to one ninth, because the influence spreads over a sphere whose area grows with r².
How accurate is this gravitational force calculator?
The calculator uses the exact Newtonian formula with the CODATA 2018 value of G and is accurate for spherical bodies or point masses. It does not model general relativity, non-spherical mass distributions or third-body effects, which matter for precision orbital mechanics.