How to Convert Newtons to G-Force

By David Robinson
Everything on Earth experiences the effect of gravity.

We are all used to the effects of normal gravity; we've lived with it since we were born. Scientists refer to our gravity as a force of 1 g, or 1 G-force. The Newton is, according to Professor Russ Rowlett of the University of North Carolina, the force that accelerates a mass of one kilogram at the rate of one meter per second per second. To convert Newtons to G-force you must know both the mass of the object and its acceleration.

Calculate the force due to normal gravity when at rest by using the equation force = mass * acceleration, where force is in Newtons, mass in kg and acceleration due to gravity is in m/s/s. The acceleration due to gravity is 9.8 m/s/s.

For example, the normal force of gravity on a resting person weighing 80 kg is 784 Newtons because 80 * 9.8 = 784. This is the force of "one gravity" on that person, or 1 G-force.

Divide the total number of Newtons by the number of Newtons equivalent to 1 g. The result is the value in Newtons converted to G-force.

For example, if the 80-kg person experiences a force of 2,744 Newtons, he is subjected to 3.5 g because 2,744 / 784 = 3.5.

Check for errors by reversing your calculations. Multiply the number of G-forces by the force experienced by the object at rest. If the result is not the number of Newtons you converted, then there was an error. Repeat the calculations until they are correct.


For approximate calculations, change the acceleration of gravity to 10 m/s/s. This makes the math much easier so you can do it in your head.


Precise calculations require the exact force of gravity at your location. This varies according to latitude and is calculated using the International gravity formula: g(p) = 9.7803267714(1+0.00193185138639sin^2(p) )/ √(1-0.0069437999013sin^2(p)), where "p" is your latitude.

About the Author

David Robinson has written professionally since 2000. He is a Fellow of the Royal Geographical Society and the Royal Meteorological Society. He has written for the "Telegraph" and "Guardian" newspapers in the U.K., government publications, websites, magazines and school textbooks. He holds an honors Bachelor of Arts in geography and education and a teaching certificate from Durham University, England.