How To Convert Newtons To G-Force

You often hear the word G-force used in the context of astronauts being launched into space. An astronaut experiencing a force of ten Gs, for example, is experiencing a force equal to 10 times the force of gravity. To convert from force in Gs to force in Newtons, you need two crucial pieces of information. The first is the acceleration due to gravity in the MKS (meter, kilogram, second) system, since Newtons are the units of force in that system. This number is 9.8 meters/second². The second is the mass of the person (or object) experiencing the acceleration, in kilograms. This obviates an important point: Different objects (or people) experience different G-forces.

A discussion about G-force in one in which the difference between weight and mass becomes particularly important. The mass of a body is its inertial resistance to a change of its state of motion. It's measured in kilograms in the SI system. Weight, on the other hand, is the force exerted upon that body by Earth's gravitational field. Newton's Second Law tells you that force (F) equals mass (m) times acceleration(a)

\(F=ma\)

The acceleration due to gravity on Earth is usually denoted by a lowercase g. This makes one G, which is the force exerted by gravity on any body in Earth's gravitational field, equal to the mass of the body (m) times the acceleration due to gravity.

\(1G=mg\)

This also happens to be the weight of the body. In the MKS system, weight is measured in Newtons, where 1 Newton = 1 kg-m/s². Once you have measured the mass of a body in kilograms and calculated its weight in Newtons using the value 9.8 m/s² for g, you can easily convert to Gs and back again. Two Gs equal twice the weight of the object, a quarter G equals one-fourth its weight and so on.

Force is a vector quantity, which means it has a directional component. Earth's gravity always acts to pull objects toward the center of the planet, and the Earth's surface exerts an equal force in the opposite direction to prevent everything on the surface from falling into the center. Physicists call this the normal force, and it creates the sensation of weight. Every body on earth's surface experiences a normal force of 1 G.

An astronaut accelerating into space experiences an additional normal force generated by the floor of the rocket ship, which adds to the sensation of weight. When calculating upward G-force, you have to add 1 G to the thrust generated by the craft you're in because, when the craft is at rest, you still experience a normal force of 1 G.

A pilot in a jet that is accelerating, not just falling, toward the ground would feel a force in the direction opposite to that exerted by the surface of the earth. This force would cancel the normal force generated by the floor of the craft only if the acceleration is greater than g. You have to subtract 1 G from the total G-force generating by a craft accelerating toward the ground.