In science and engineering, the weight of an object is usually taken to be the force on the object due to gravitation. Weight is a Euclidean vector whose 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: . 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, and about onesixth as much on the Moon. In this sense of weight, a body can be weightless only if it is distant (in principle infinitely far away) from any other mass. Although weight and mass are scientifically distinct quantities, the terms are often confused with each other in everyday use (i.e. comparing and converting force weight in pounds to mass in kilograms and vice versa).The National Standard of Canada, CAN/CSAZ234.189 Canadian Metric Practice Guide, January 1989:There is also a rival tradition within Newtonian physics and engineering which sees weight as that which is measured when one uses scales. There the weight is a measure of the magnitude of the reaction force exerted on a body. Typically, in measuring an object's weight, the object is placed on scales at rest with respect to the earth, but the definition can be extended to other states of motion. Thus, in a state of free fall, the weight would be zero. In this second sense of weight, terrestrial objects can be weightless. Ignoring air resistance, the famous apple falling from the tree, on its way to meet the ground near Isaac Newton, is weightless.
Further complications in elucidating the various concepts of weight have to do with the theory of relativity according to which gravity is modelled as a consequence of the curvature of spacetime. In the teaching community, a considerable debate has existed for over half a century on how to define weight for their students. The current situation is that a multiple set of concepts coexist and find use in their various contexts.
According to Aristotle, weight was the direct cause of the falling motion of an object, the speed of the falling object was supposed to be directly proportionate to the weight of the object. As medieval scholars discovered that in practice the speed of a falling object increased with time, this prompted a change to the concept of weight to maintain this cause effect relationship. Weight was split into a "still weight" or pondus, which remained constant, and the actual gravity or gravitas, which changed as the object fell. The concept of gravitas was eventually replaced by Jean Buridan's impetus, a precursor to momentum.
The rise of the Copernican view of the world led to the resurgence of the Platonic idea that like objects attract but in the context of heavenly bodies. In the 17th century, Galileo made significant advances in the concept of weight. He proposed a way to measure the difference between the weight of a moving object and an object at rest. Ultimately, he concluded weight was proportionate to the amount of matter of an object, and not the speed of motion as supposed by the Aristotelean view of physics.
Newton considered time and space to be absolute. This allowed him to consider concepts as true position and true velocity. Newton also recognized that weight as measured by the action of weighing was affected by environmental factors such as buoyancy. He considered this a false weight induced by imperfect measurement conditions, for which he introduced the term apparent weight as compared to the true weight defined by gravity.
Although Newtonian physics made a clear distinction between weight and mass, the term weight continued to be commonly used when people meant mass. This led the 3rd General Conference on Weights and Measures (CGPM) of 1901 to officially declare "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", thus distinguishing it from mass for official usage.
In 1901, the 3rd General Conference on Weights and Measures (CGPM) established this as their official definition of weight:
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 gravitational acceleration varies from place to place. Sometimes, it is simply taken to have a standard gravity of , 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 kgwt)Chester, W. Mechanics. George Allen & Unwin. London. 1979. ISBN 0045100594. Section 3.2 at page 83.
The operational definition, as usually given, does not explicitly exclude the effects of buoyancy, which reduces the measured weight of an object when it is immersed in a fluid such as air or water. As a result, a floating balloon or an object floating in water might be said to have zero weight.
The definition is dependent on the chosen frame of reference. When the chosen frame is comoving with the object in question then this definition precisely agrees with the operational definition. If the specified frame is the surface of the Earth, the weight according to the ISO and gravitational definitions differ only by the centrifugal effects due to the rotation of the Earth.
The distinction between mass and weight is unimportant for many practical purposes because the strength of gravity does not vary too much on the surface of the Earth. In a uniform gravitational field, the gravitational force exerted on an object (its weight) is directly proportional to its mass. For example, object A weighs 10 times as much as object B, so therefore the mass of object A is 10 times greater than that of object B. This means that an object's mass can be measured indirectly by its weight, and so, for everyday purposes, weighing (using a weighing scale) is an entirely acceptable way of measuring mass. Similarly, a balance measures mass indirectly by comparing the weight of the measured item to that of an object(s) of known mass. Since the measured item and the comparison mass are in virtually the same location, so experiencing the same gravity, the effect of varying gravity does not affect the comparison or the resulting measurement.
The Earth's gravity is not uniform but can vary by as much as 0.5% at different locations on Earth (see Earth's gravity). These variations alter the relationship between weight and mass, and must be taken into account in high precision weight measurements that are intended to indirectly measure mass. , which measure local weight, must be calibrated at the location at which the objects will be used to show this standard weight, to be legal for commerce.
This table shows the variation of acceleration due to gravity (and hence the variation of weight) at various locations on the Earth's surface.
Equator  0°  9.7803 
Sydney  33°52′ S  9.7968 
Aberdeen  57°9′ N  9.8168 
North Pole  90° N  9.8322 
The historic use of "weight" for "mass" also persists in some scientific terminology – for example, the chemistry terms "atomic weight", "molecular weight", and "formula weight", can still be found rather than the preferred "atomic mass" etc.
In a different gravitational field, for example, on the surface of the Moon, an object can have a significantly different weight than on Earth. The gravity on the surface of the Moon is only about onesixth as strong as on the surface of the Earth. A onekilogram mass is still a onekilogram mass (as mass is an extrinsic property of the object) but the downward force due to gravity, and therefore its weight, is only onesixth of what the object would have on Earth. So a man of mass 180 pounds weighs only about 30 poundforce when visiting the Moon.
In commercial and everyday use, the term "weight" is usually used to mean mass, and the verb "to weigh" means "to determine the mass of" or "to have a mass of". Used in this sense, the proper SI unit is the kilogram (kg).
The kilogramforce is a nonSI unit of force, defined as the force exerted by a one kilogram mass in standard Earth gravity (equal to 9.80665 newtons exactly). The dyne is the cgs unit of force and is not a part of SI, while weights measured in the cgs unit of mass, the gram, remain a part of SI.
Weight is commonly measured using one of two methods. A spring scale or hydraulic or pneumatic scale measures local weight, the local force of gravity on the object (strictly apparent weight). Since the local force of gravity can vary by up to 0.5% at different locations, spring scales will measure slightly different weights for the same object (the same mass) at different locations. To standardize weights, scales are always calibrated to read the weight an object would have at a nominal standard gravity of 9.80665 m/s^{2} (approx. 32.174 ft/s^{2}). However, this calibration is done at the factory. When the scale is moved to another location on Earth, the force of gravity will be different, causing a slight error. So to be highly accurate, and legal for commerce, must be recalibrated at the location at which they will be used.
A balance on the other hand, compares the weight of an unknown object in one scale pan to the weight of standard masses in the other, using a lever mechanism – a leverbalance. The standard masses are often referred to, nontechnically, as "weights". Since any variations in gravity will act equally on the unknown and the known weights, a leverbalance will indicate the same value at any location on Earth. Therefore, balance "weights" are usually calibrated and marked in mass units, so the leverbalance measures mass by comparing the Earth's attraction on the unknown object and standard masses in the scale pans. In the absence of a gravitational field, away from planetary bodies (e.g. space), a leverbalance would not work, but on the Moon, for example, it would give the same reading as on Earth. Some balances can be marked in weight units, but since the weights are calibrated at the factory for standard gravity, the balance will measure standard weight, i.e. what the object would weigh at standard gravity, not the actual local force of gravity on the object.
If the actual force of gravity on the object is needed, this can be calculated by multiplying the mass measured by the balance by the acceleration due to gravity – either standard gravity (for everyday work) or the precise local gravity (for precision work). Tables of the gravitational acceleration at different locations can be found on the web.
Gross weight is a term that is generally found in commerce or trade applications, and refers to the total weight of a product and its packaging. Conversely, net weight refers to the weight of the product alone, discounting the weight of its container or packaging; and tare weight is the weight of the packaging alone.
Sun  27.90  274.1 
Mercury  0.3770  3.703 
Venus  0.9032  8.872 
Earth  1 (by definition)  9.8226This value excludes the adjustment for centrifugal force due to Earth’s rotation and is therefore greater than the 9.80665 m/s^{2} value of standard gravity. 
Moon  0.1655  1.625 
Mars  0.3895  3.728 
Jupiter  2.640  25.93 
Saturn  1.139  11.19 
Uranus  0.917  9.01 
Neptune  1.148  11.28 
