What is Newton's law of universal gravitation?

Newton's law states that every mass attracts every other mass with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers: F = G × m1 × m2 / r². G is the gravitational constant, approximately 6.674 × 10⁻¹¹ N·m²/kg².

What is the gravitational constant G?

G is the universal gravitational constant with the value 6.674 × 10⁻¹¹ N·m²/kg². It was first measured experimentally by Henry Cavendish in 1798 using a torsion balance.

What units does this calculator use?

All inputs and outputs use SI units: masses in kilograms (kg), distance in meters (m), and force in Newtons (N). Convert your values to SI before entering them.

Why does doubling the distance reduce the force by a factor of 4?

Because gravity follows an inverse-square law: F ∝ 1/r². If r doubles, r² quadruples, so F becomes 1/4 of its original value. This is a key property of any field that spreads over a spherical surface.

Can I calculate mass or distance instead of force?

Yes. Rearranging the formula gives m2 = F × r² / (G × m1) for the second mass, and r = √(G × m1 × m2 / F) for the distance. Use the "Solve for" selector to pick the unknown.

Does this work for everyday objects, not just planets?

Yes. The law applies to all masses. The force between everyday objects (like two people standing next to each other) is real but extremely small — roughly 10⁻⁷ N — because G is so tiny.

How do you find gravitational force with mass and distance?

Multiply the two masses, multiply by the gravitational constant G (6.674 × 10⁻¹¹ N·m²/kg²), then divide by the distance squared: F = G × m1 × m2 / r². For example, two 1,000 kg masses 2 m apart attract with F = 6.674e-11 × 1000 × 1000 / 4 ≈ 1.67 × 10⁻⁵ N.

Gravitational Force Calculator

Calculate the gravitational force between two masses using Newton's law of universal gravitation (F = G × m1 × m2 / r²).

Inputs

Select what to solve for, then fill in the remaining values.

Solve for

Mass 1 (m1)

Mass 2 (m2)

Distance between centers (r)

G = 6.674 × 10⁻¹¹ N·m²/kg² (universal gravitational constant)

Result

Enter values and click Calculate.

Formula Reference

Find Force

F = G·m1·m2 / r²

Find Mass 2

m2 = F·r² / (G·m1)

Find Distance

r = √(G·m1·m2 / F)

Summary

The Gravitational Force Calculator computes the attractive force between any two objects with mass, using Newton's law of universal gravitation. Enter both masses and the distance between their centers to instantly find the gravitational force in Newtons. The tool also supports solving for either mass or the separation distance when the force is known.

How it works

Select what you want to solve for: Force, Mass 2, or Distance.
Enter the required values — masses in kilograms and distance in meters.
Click Calculate to apply the formula F = G × m1 × m2 / r².
The result is displayed with a full step-by-step breakdown.
Use the Reset button to clear all fields and start over.

Use cases

Physics homework and exam problems on gravitation and orbital mechanics.
Estimating the gravitational pull between planets, moons, and stars.
Engineering calculations involving large-scale mass interactions.
Classroom demonstrations of Newton's inverse-square law.
Comparing gravitational forces at different separation distances.
Verifying textbook examples of the universal gravitational constant G.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu