Gravitational Force Calculator
Calculate the gravitational attraction between two masses using Newton's law of universal gravitation. You can also solve for either mass or the distance between the objects.
Calculate Gravitational Force
Calculation Result
What Is a Gravitational Force Calculator?
A Gravitational Force Calculator determines the attractive force acting between two objects that have mass. It uses Newton's law of universal gravitation, which states that every mass attracts every other mass.
The gravitational force becomes stronger when either object's mass increases. It becomes weaker as the distance between their centers increases. Because distance is squared in the equation, increasing separation can significantly reduce the force.
This calculator converts common mass and distance units into SI units before applying the gravitational equation, making it useful for physics, astronomy, engineering, and educational calculations.
Gravitational Force Formula
The gravitational force equals the gravitational constant multiplied by the product of the two masses, divided by the square of the distance between their centers.
Gravitational Force Calculator Formulas
Use this equation when both masses and their separation are known.
Rearrange Newton's equation to calculate the first mass.
Use known force, distance, and first mass to determine the second mass.
Calculate the separation required to produce a known gravitational force.
What Do the Formula Symbols Mean?
The attractive force between the two masses, measured in newtons (N).
G = 6.67430 × 10−11 N·m²/kg².
The masses of the two interacting objects, converted to kilograms for the equation.
The distance between the centers of mass of the two objects, measured in meters.
How to Use the Gravitational Force Calculator
Select the Unknown Value
Choose whether you want to calculate gravitational force, first mass, second mass, or distance.
Enter the Known Values
Fill in the masses, gravitational force, or separation required for your selected calculation.
Select Your Units
Choose kilograms, grams, pounds, tons, meters, kilometers, feet, or other available measurement units.
Calculate the Result
Click Calculate and the tool automatically converts units, applies Newton's equation, and displays the result.
Gravitational Force Example
Suppose two objects each have a mass of 1,000 kg and their centers are separated by 10 meters.
The gravitational attraction between the two objects is very small because ordinary objects have relatively low masses compared with planets, stars, and other astronomical bodies.
How Mass and Distance Affect Gravitational Force
Increasing Mass
Gravitational force is directly proportional to the product of the two masses. If one mass doubles while everything else remains unchanged, the gravitational force also doubles.
Increasing Distance
Gravity follows an inverse-square relationship with distance. If the distance between two masses doubles, their gravitational force becomes one quarter of its previous value.
If the distance triples, the force becomes one ninth of the original value. This is why separation has such a strong effect on gravitational attraction.
Where Is Gravitational Force Used?
Analyze gravitational interactions involving planets and moons.
Study gravitational forces involved in orbital motion.
Estimate gravitational attraction between celestial objects.
Solve universal gravitation problems and verify manual calculations.
Frequently Asked Questions
Newton's universal gravitation formula is F = Gm₁m₂/r², where G is the gravitational constant, m₁ and m₂ are the two masses, and r is the distance between their centers.
The universal gravitational constant used by this calculator is approximately 6.67430 × 10⁻¹¹ N·m²/kg².
Yes. Gravitational force is directly proportional to the product of the two interacting masses.
Gravitational force decreases with the square of the distance. Doubling the distance reduces the force to one quarter of its original value.
In Newtonian gravity, the gravitational interaction between ordinary positive masses is attractive.
For the standard point-mass equation, distance is the separation between the centers of mass rather than the gap between the surfaces.