Gravitational Force Calculator
Newton's Universal Law
In 1687, Isaac Newton realized that the force that causes an apple to fall from a tree is the exact same force that keeps the Moon in orbit around the Earth.
He proposed the Law of Universal Gravitation: Every object in the universe attracts every other object with a force directed along the line of centers for the two objects.
This means that right now, there is a gravitational pull between you and your computer screen. However, because your masses are so small compared to the Earth, you don't feel it.
The Formula
- F: The Gravitational Force (Newtons).
- G: The Gravitational Constant ($6.674 \times 10^{-11}$). A tiny number that scales the force down.
- m₁ & m₂: The masses of the two objects (kg).
- r: The distance between their centers (meters).
The Inverse Square Law
Gravity gets weaker very quickly as you move away. Because the distance ($r$) is squared ($r^2$) in the denominator, doubling the distance reduces the force to one-fourth.
- 2x Distance = 1/4 Gravity
- 3x Distance = 1/9 Gravity
- 10x Distance = 1/100 Gravity
This explains why astronauts float in the ISS. They aren't in "Zero Gravity" (Earth still pulls on them by about 90%), but they are in a constant state of free fall that feels like zero gravity.
Is Gravity a Weak Force?
Yes. In fact, Gravity is the weakest of the four fundamental forces of nature (Electromagnetism, Weak Nuclear, Strong Nuclear, Gravity).
A tiny kitchen magnet can lift a paperclip off the table.
Think about that: The magnetic force of a tiny magnet is stronger than the gravitational pull of the entire planet Earth pulling down on that paperclip.
Calculating Your Weight
Weight is simply the name we give to the Gravitational Force between you and a planet.
If you plug your mass ($m_1$), Earth's mass ($m_2$), and Earth's radius ($r$) into this calculator, the result ($F$) will be your weight in Newtons.
Dividing that Force by your Mass ($F/m$) gives you Earth's acceleration due to gravity: 9.81 m/s².