Mass is a physical property that represents the amount of matter an object contains. It does not change when an object changes shape or size, but it can be affected by the strength of gravity.

One kilogram (kg) is the unit of mass used in the International System of Units. The primary standard of mass in the United States is a platinum-iridium cylinder kept at NIST.

## Metric System

The metric system is used around the world to measure length, time and mass. Developed in late 18th century France, the system was designed to replace the disparate systems of measurement that existed at the time with a single, natural and universal set of units. Several basic or fundamental units exist in the metric system, including the metre for length, kilogram for mass and cubic decimetre (dm3) for volume. These base units are related to each other by a series of unvarying constants defined from natural or technical properties, notably the size of the Earth’s circumference and the density of water.

Multiples and submultiples of metric base values are related by powers of 10. This, together with the use of prefixes to define sizes that extend below the base value, make converting measurements between metric units as straightforward as a multiplication or division of decimals. This system of measurement is also referred to as the International System of Units or SI.

## Units of Mass

Although the terms weight and mass are often used interchangeably, they are actually different measurements. Mass is a measure of the amount of matter in an object, while weight measures the force of gravity pulling on that object.

A common mistake that students make is to think that mass can change, but it does not, except in some extreme cases when a large amount of energy is given or taken from an object. Mass is a property of all objects and cannot be changed.

The unit of mass in the Metric System is the kilogram (kg), and its decimal multiples and sub-multiples. The kg is one of the seven SI base units, and it is also a part of the International System of Units. The standard kilogram is a platinum-iridium cylinder kept at the United States National Institute of Standards and Technology, and it serves as the primary prototype for all mass standards worldwide. Other units of mass include the gram (g), tonne (t) and decimal multiples and sub-multiples of the kilogram.

## Density

Density expresses the mass of a material per unit volume. It is commonly expressed as a ratio: mass (g) / volume (cm3). Different substances have different densities. Steel is much heavier for its size than feathers, for example.

The characteristic property of density is useful for identifying pure substances because it does not depend on the amount of substance present. It is often used with reference charts of known materials and in quality control to check that a sample has not been adulterated or diluted.

For solids the density can be measured by a balance or in a graduated cylinder. For liquids a digital density meter is often used. A pycnometer or hydrometer can be used for viscous samples. The density of a solution can be determined by buoyancy, following Archimedes’ principle that when a body immerses in a fluid it shows an apparent loss of weight equal to the weight of the fluid it displaces.

## Passive Gravitational Mass

Mass has a double role in physics: it measures inertia and determines the force of gravitation on a body. Depending on which role it plays, it is sometimes referred to as passive or active gravitational mass. The reaction of a body to a gravitational field depends on its passive gravity mass and its center of mass. The stronger this response is, the more the object weighs.

The weak equivalence principle states that two objects with equal passive graviational mass and different inertial masses will fall at the same rate, regardless of their material composition. This is because the gravitational field caused by these two bodies affects them equally.

The strong equivalence principle is similar to the weak one, but it requires that the freely falling test masses have equal inertial masses and a common centre of mass (C). It also specifies a limit on the change in an object’s mass when it absorbs thermal energy.