How to Calculate Force of Gravity

By Matthew D'Antuono

Gravity is the weakest of the three fundamental forces of the universe, but the Earth is large enough that the force of gravity can hold us on the surface. Every object exerts a force of gravity on every other object in the universe, but the force of gravity is only noticeable for very large objects. This article will show you how to calculate the force of gravity between two objects.

Find the mass in kilograms of the object for which you would like to find the force of gravity. Pounds is already a measure of force in the English system of measurement. The force of gravity is different for objects of different mass.

Force equation

Multiply the mass of the object in kilograms by 9.8, which is the acceleration due to gravity. An object dropped near the surface of the earth will accelerate at a rate of 9.8 meters per second squared. This is the gravitational force between the Earth and the object in question. Both objects exert an equal force on each other.

Check the units on your answer to make sure they have kilograms times meters per second squared. These units make up the Newton, the unit of force in the International Standard System of measurements.

Find the mass of each object in kilograms and the distance between the two objects in meters. For example, a young man may have a mass of 70 kilograms and a young woman may have a mass of 60 kilograms. If they are sitting on opposite sides of a subway car, they may be two meters apart.

Multiply the masses of the two objects. Using our example of the young man and the young woman, 60 times 70 is 4,200.

Divide the product from the previous step by the square of the distance. In our example, you would divide 4,200 by 4, which would give you 1,050.

Universal Gravitation Equation

Multiply the quotient from Step 3 by 0.0000000000667. Our example would give us 0.000000070035. This product is the force of gravity in Newtons between the two objects. So, the young man and the young woman on the subway have a natural attraction of 0.000000070035 Newtons.

Tip

Write out each step. You minimize your chances of making a mistake if you write everything out.

About the Author

Matthew D'Antuono is a freelance writer whose work has appeared on websites, such as eHow.com. When he's not writing, he teaches high school physics. D'Antuono earned both a Bachelor of Science in physics and a Bachelor of Arts in philosophy from James Madison University and William Paterson University respectively; he is currently pursuing a master's degree in special education.