Gravitational Force Calculator

What Is a Gravitational Force Calculator?

A Gravitational Force Calculator uses Newton's law of universal gravitation to determine the attractive force between two objects when their masses and the distance between their centres of mass are known. The calculator applies the equation F = Gm₁m₂/r² and returns the resulting force in newtons or a selected force unit.

This calculator can be useful for physics students, teachers, engineers, researchers, technicians and anyone studying or working with gravitational interactions. It can also help when checking physics exercises, demonstrating how mass and distance affect gravity, or performing basic gravitational force calculations.

Why Use a Gravitational Force Calculator?

Calculating gravitational force manually requires careful handling of the gravitational constant, mass units and the squared distance term. This calculator performs the calculation directly while converting supported input units into the SI units required by the formula.

How to Use the Gravitational Force Calculator

Enter the two masses and the distance separating their centres of mass, select the appropriate units and calculate the resulting gravitational force.

1. Enter Mass 1 — Enter the mass of the first object and select its unit.
2. Enter Mass 2 — Enter the mass of the second object and select its unit.
3. Enter the Distance — Enter the distance between the centres of mass of the two objects and select its unit.
4. Calculate the Force — Select the desired force unit, click Calculate and review the gravitational force and calculation details.

Gravitational Force Formula

Newton's law of universal gravitation gives the gravitational force between two masses as F = Gm₁m₂/r². In this equation, F represents gravitational force in newtons, G is the gravitational constant, m₁ and m₂ are the two masses in kilograms, and r is the distance between their centres of mass in metres.

The gravitational constant used by the calculator is approximately 6.67430 × 10⁻¹¹ N·m²/kg². Because the distance is squared in the denominator, even a relatively small change in separation can produce a significant change in the calculated gravitational force.

How to Calculate Gravitational Force

To calculate gravitational force, multiply the first mass by the second mass and by the gravitational constant, then divide the result by the square of the distance between their centres of mass. For example, if two objects have masses of 1,000 kg and 2,000 kg and are separated by 10 m, the calculation is F = (6.67430 × 10⁻¹¹ × 1,000 × 2,000) ÷ 10², producing approximately 1.33486 × 10⁻⁶ N.

How Mass and Distance Affect Gravity

Gravitational force increases in direct proportion to either mass. Doubling one mass doubles the gravitational force, while doubling both masses increases the force by a factor of four. Distance has an inverse-square effect: doubling the distance reduces the gravitational force to one quarter of its original value, while tripling the distance reduces it to one ninth.

Gravitational Force Calculator Accuracy and Limitations

The calculator uses the standard gravitational constant G = 6.67430 × 10⁻¹¹ N·m²/kg² and converts supported mass and distance units into kilograms and metres before applying Newton's law of universal gravitation. The numerical result is subject to the precision of the values entered.

This calculation treats the objects as point masses, or as bodies for which their masses can reasonably be considered concentrated at their centres of mass. It does not account for complex gravitational fields, irregular mass distributions, relativistic effects or other-body interactions. For many ordinary physics calculations involving sufficiently separated objects, Newtonian gravitation provides a useful approximation.

Frequently Asked Questions