# Weight

In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude (a scalar quantity), often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus: W = mg. When considered a vector, weight is often denoted by a bold letter W. The unit of measurement for weight is that of force, which in the International System of Units (SI) is the newton. For example, an object with a mass of one kilogram has a weight of about 9.8 newtons on the surface of the Earth, about one-sixth as much on the Moon, and zero when in deep space far away from all bodies imparting gravitational influence.

In the 20th century, the Newtonian concepts of gravitation were challenged by relativity. Einstein's principle of equivalence put all observers, accelerating in space far from gravitating bodies, or held in place against gravitation near such a body, on the same footing. This led to an ambiguity as to what exactly is meant by the "force of gravity" and (in consequence) by weight. The ambiguities introduced by relativity led, starting in the 1960s, to considerable debate in the teaching community as how to define weight for their students. The choice was a Newtonian definition of weight as the contact reaction-force against the force of gravity, for an object at rest on the ground, or an operational definition defined by the act of weighing. In the operational definition, weight becomes zero in conditions of weightlessness such as Earth orbit or free fall in vacuum. In such situations, the Newtonian view is that there remains a force due to gravity which is not measured (thus causing an apparent weight of zero), while the Einsteinian view is that there never does exist a measurable force due to gravity, even in everyday experience. Instead, weight and all sensation of weight are always produced by contact forces (push or pull) from the ground, or a scale. In free-fall, no force is measured simply because the force due to gravity is (still) never felt, and the floor (or the scale) now fails to exert the mechanical force that is what is always observed as "weight."

In everyday usage the term "weight" is commonly used to mean mass, which scientifically is an entirely different concept. On the surface of the Earth, the acceleration due to gravity (the "strength of gravity") is approximately constant; this means that the ratio of the weight force of a motionless object on the surface of the Earth to its mass is almost independent of its location, so that an object's weight force can stand as a proxy for its mass, and vice versa.

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