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Gravitational definition

The most common definition of weight found in introductory physics textbooks defines weight as the force exerted on a body by gravity. This is often expressed in the formula W = mg, where W is the weight, m the mass of the object, and g gravitational acceleration.

In 1901, the 3rd General Conference on Weights and Measures (CGPM) established this as their official definition of weight:

The word weight denotes a quantity of the same nature as a force: the weight of a body is the product of its mass and the acceleration due to gravity.

This resolution defines weight as a vector, since force is a vector quantity. However, some textbooks also take weight to be a scalar by defining:

The weight W of a body is equal to the magnitude F of the gravitational force on the body.

The gravitational acceleration varies from place to place. Sometimes, it is simply taken to have a standard value of 9.80665 m/s, which gives the standard weight.

The force whose magnitude is equal to mg newtons is also known as the m kilogram weight (which term is abbreviated to kg-wt)