A measure of a body's inertia, i.e. its resistance to acceleration. According to Newton's laws of motion, if two unequal masses, m1 and m2, are allowed to collide, in the absence of any other forces both will experience the same force of collision. If the two bodies acquire accelerations a1 and a2 as a result of the collision, then m1a1 = m2a2. This equation enables two masses to be compared. If one of the masses is regarded as a standard of mass, the mass of all other masses can be measured in terms of this standard. The body used for this purpose is a 1-kg cylinder of platinum–iridium alloy, called the international standard of mass. Mass defined in this way is called the inertial mass of the body.
Mass can also be defined in terms of the gravitational force it produces. Thus, according to Newton's law of gravitation, mg = Fd2/MG, where M is the mass of a standard body situated a distance d from the body of mass mg; F is the gravitational force between them and G is the gravitational constant. The mass defined in this way is the gravitational mass. In the 19th century Lóránd Eötvös (1848–1919) showed experimentally that gravitational and inertial mass are indistinguishable, i.e. mi = mg. Experiments performed in the 20th century have confirmed this conclusion to even greater accuracy.
Although mass is formally defined in terms of its inertia, it is usually measured by gravitation. The weight (W) of a body is the force by which a body is gravitationally attracted to the earth corrected for the effect of rotation and equals the product of the mass of the body and the acceleration of free fall (g), i.e. W = mg. In the general language, weight and mass are often used synonymously; however, for scientific purposes they are different. Mass is measured in kilograms; weight, being a force, is measured in newtons. Weight, moreover, depends on where it is measured, because the value of g varies at different localities on the earth's surface. Mass, on the other hand, is constant wherever it is measured, subject to the special theory of relativity. According to this theory, announced by Albert Einstein in 1905, the mass of a body is a measure of its total energy content. Thus, if the energy of a body increases, for example by an increase in kinetic energy or temperature, then its mass will increase. According to this law an increase in energy ΔE is accompanied by an increase in mass Δm, according to the mass–energy equation Δm = ΔE/c2, where c is the speed of light. Thus, if 1 kg of water is raised in temperature by 100 K, its internal energy will increase by 4 × 10−12 kg. This is, of course, a negligible increase and the mass–energy equation is only significant for extremely high energies. For example, the mass of an electron is increased sevenfold if it moves relative to the observer at 99% of the speed of light.