Mass is an
intrinsic property
In science and engineering, an intrinsic property is a property of a specified subject that exists itself or within the subject. An extrinsic property is not essential or inherent to the subject that is being characterized. For example, mass ...
of a body. It was traditionally believed to be related to the
quantity
Quantity or amount is a property that can exist as a Counting, multitude or Magnitude (mathematics), magnitude, which illustrate discontinuity (mathematics), discontinuity and continuum (theory), continuity. Quantities can be compared in terms o ...
of
matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
in a
physical body, until the discovery of the
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, and ...
and
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
. It was found that different atoms and different
elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple
definitions which are conceptually distinct, but physically
equivalent. Mass can be experimentally defined as a
measure
Measure may refer to:
* Measurement, the assignment of a number to a characteristic of an object or event
Law
* Ballot measure, proposed legislation in the United States
* Church of England Measure, legislation of the Church of England
* Mea ...
of the body's
inertia, meaning the resistance to
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
(change of
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
) when a
net force is applied. The object's mass also determines the
strength
Strength may refer to:
Physical strength
*Physical strength, as in people or animals
*Hysterical strength, extreme strength occurring when people are in life-and-death situations
*Superhuman strength, great physical strength far above human ca ...
of its
gravitation
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
al attraction to other bodies.
The
SI base unit
The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all ...
of mass is the
kilogram
The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
(kg). In
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, mass is
not the same as
weight
In science and engineering, the weight of an object is the force acting on the object due to gravity.
Some standard textbooks define weight as a Euclidean vector, vector quantity, the gravitational force acting on the object. Others define weigh ...
, even though mass is often determined by measuring the object's weight using a
spring scale
A spring scale, spring balance or newton meter is a type of mechanical force gauge or weighing scale. It consists of a spring fixed at one end with a hook to attach an object at the other. It works in accordance with Hooke's Law, which states th ...
, rather than
balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.
Phenomena
There are several distinct phenomena that can be used to measure mass. Although some theorists have speculated that some of these phenomena could be independent of each other, current experiments have found no difference in results regardless of how it is measured:
* ''Inertial mass'' measures an object's resistance to being accelerated by a force (represented by the relationship
).
* ''Active gravitational mass'' determines the strength of the gravitational field generated by an object.
* ''Passive gravitational mass'' measures the gravitational force exerted on an object in a known gravitational field.
The mass of an object determines its acceleration in the presence of an applied force. The inertia and the inertial mass describe this property of physical bodies at the qualitative and quantitative level respectively. According to
Newton's second law of motion
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in motion ...
, if a body of fixed mass ''m'' is subjected to a single force ''F'', its acceleration ''a'' is given by ''F''/''m''. A body's mass also determines the degree to which it generates and is affected by a
gravitational field
In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
. If a first body of mass ''m''
A is placed at a distance ''r'' (center of mass to center of mass) from a second body of mass ''m''
B, each body is subject to an attractive force , where is the "universal
gravitational constant
The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
". This is sometimes referred to as gravitational mass.
[When a distinction is necessary, the active and passive gravitational masses may be distinguished.] Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are identical; since 1915, this observation has been incorporated ''
a priori
("from the earlier") and ("from the later") are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on empirical evidence or experience. knowledge is independent from current ex ...
'' in the
equivalence principle
In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
of
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
.
Units of mass
The
International System of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI) unit of mass is the
kilogram
The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
(kg). The kilogram is 1000 grams (g), and was first defined in 1795 as the mass of one cubic decimetre of water at the
melting point
The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends ...
of ice. However, because precise measurement of a cubic decimetre of water at the specified temperature and pressure was difficult, in 1889 the kilogram was redefined as the mass of a metal object, and thus became independent of the metre and the properties of water, this being a copper prototype of the
grave
A grave is a location where a dead body (typically that of a human, although sometimes that of an animal) is buried or interred after a funeral. Graves are usually located in special areas set aside for the purpose of burial, such as grave ...
in 1793, the platinum
Kilogramme des Archives in 1799, and the platinum-iridium
International Prototype of the Kilogram
The International Prototype of the Kilogram (referred to by metrologists as the IPK or Le Grand K; sometimes called the '' ur-kilogram,'' or ''urkilogram,'' particularly by German-language authors writing in English) is an object that was used t ...
(IPK) in 1889.
However, the mass of the IPK and its national copies have been found to drift over time. The
re-definition of the kilogram and several other units came into effect on 20 May 2019, following a final vote by the
CGPM
The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
in November 2018. The new definition uses only invariant quantities of nature: the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
, the
caesium hyperfine frequency, the
Planck constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
and the
elementary charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
.
[
]
Non-SI units accepted for use with SI units include:
* the
tonne
The tonne ( or ; symbol: t) is a unit of mass equal to 1000 kilograms. It is a non-SI unit accepted for use with SI. It is also referred to as a metric ton to distinguish it from the non-metric units of the short ton ( United State ...
(t) (or "metric ton"), equal to 1000 kg
* the
electronvolt
In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defi ...
(eV), a unit of
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
, used to express mass in units of eV/''c''
2 through
mass–energy equivalence
In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. The principle is described by the physicis ...
* the
dalton (Da), equal to 1/12 of the mass of a free
carbon-12
Carbon-12 (12C) is the most abundant of the two stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of element carbon on Earth; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 i ...
atom, approximately .
[The dalton is convenient for expressing the masses of atoms and molecules.]
Outside the SI system, other units of mass include:
* the
slug
Slug, or land slug, is a common name for any apparently shell-less terrestrial gastropod mollusc. The word ''slug'' is also often used as part of the common name of any gastropod mollusc that has no shell, a very reduced shell, or only a smal ...
(sl), an
Imperial unit of mass (about 14.6 kg)
* the
pound
Pound or Pounds may refer to:
Units
* Pound (currency), a unit of currency
* Pound sterling, the official currency of the United Kingdom
* Pound (mass), a unit of mass
* Pound (force), a unit of force
* Rail pound, in rail profile
Symbols
* Po ...
(lb), a unit of mass (about 0.45 kg), which is used alongside the similarly named
pound (force)
The pound of force or pound-force (symbol: lbf, sometimes lbf,) is a unit of force used in some systems of measurement, including English Engineering units and the foot–pound–second system.
Pound-force should not be confused with pound-ma ...
(about 4.5 N), a unit of force
[These are used mainly in the United States except in scientific contexts where SI units are usually used instead.]
* the
Planck mass (about ), a quantity derived from fundamental constants
* the
solar mass
The solar mass () is a standard unit of mass in astronomy, equal to approximately . It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes. It is approximately equal to the mass ...
(), defined as the mass of the
Sun, primarily used in astronomy to compare large masses such as stars or galaxies (≈ )
* the mass of a particle, as identified with its inverse
Compton wavelength ()
* the mass of a star or
black hole
A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
, as identified with its
Schwarzschild radius
The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic ...
().
Definitions
In
physical science
Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences".
Definition
Physi ...
, one may distinguish conceptually between at least seven different aspects of ''mass'', or seven physical notions that involve the concept of ''mass''.
Every experiment to date has shown these seven values to be
proportional
Proportionality, proportion or proportional may refer to:
Mathematics
* Proportionality (mathematics), the property of two variables being in a multiplicative relation to a constant
* Ratio, of one quantity to another, especially of a part compare ...
, and in some cases equal, and this proportionality gives rise to the abstract concept of mass. There are a number of ways mass can be measured or
operationally defined:
* Inertial mass is a measure of an object's resistance to acceleration when a
force
In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
is applied. It is determined by applying a force to an object and measuring the acceleration that results from that force. An object with small inertial mass will accelerate more than an object with large inertial mass when acted upon by the same force. One says the body of greater mass has greater
inertia.
* Active gravitational mass
[The distinction between "active" and "passive" gravitational mass does not exist in the Newtonian view of gravity as found in ]classical mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
, and can safely be ignored for many purposes. In most practical applications, Newtonian gravity is assumed because it is usually sufficiently accurate, and is simpler than General Relativity; for example, NASA uses primarily Newtonian gravity to design space missions, although "accuracies are routinely enhanced by accounting for tiny relativistic effects". The distinction between "active" and "passive" is very abstract, and applies to post-graduate level applications of General Relativity to certain problems in cosmology, and is otherwise not used. There is, nevertheless, an important conceptual distinction in Newtonian physics between "inertial mass" and "gravitational mass", although these quantities are identical; the conceptual distinction between these two fundamental definitions of mass is maintained for teaching purposes because they involve two distinct methods of measurement. It was long considered anomalous that the two distinct measurements of mass (inertial and gravitational) gave an identical result. The property, observed by Galileo, that objects of different mass fall with the same rate of acceleration (ignoring air resistance), shows that inertial and gravitational mass are the same. is a measure of the strength of an object's
gravitational flux (gravitational flux is equal to the
surface integral
In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may ...
of gravitational field over an enclosing surface). Gravitational field can be measured by allowing a small "test object" to fall freely and measuring its
free-fall acceleration. For example, an object in free-fall near the
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
is subject to a smaller gravitational field, and hence accelerates more slowly, than the same object would if it were in free-fall near the Earth. The gravitational field near the Moon is weaker because the Moon has less active gravitational mass.
* Passive gravitational mass is a measure of the strength of an object's interaction with a
gravitational field
In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
. Passive gravitational mass is determined by dividing an object's weight by its free-fall acceleration. Two objects within the same gravitational field will experience the same acceleration; however, the object with a smaller passive gravitational mass will experience a smaller force (less weight) than the object with a larger passive gravitational mass.
* According to
relativity, mass is nothing else than the
rest energy
The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an physical body, object or physical system, system of objects that is independent of the overall motion ...
of a system of particles, meaning the energy of that system in a
reference frame
In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin (mathematics), origin, orientation (geometry), orientation, and scale (geometry), scale are specified by a set of reference point ...
where it has zero
momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
. Mass can be converted into other forms of energy according to the principle of
mass–energy equivalence
In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. The principle is described by the physicis ...
. This equivalence is exemplified in a large number of physical processes including
pair production
Pair production is the creation of a subatomic particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specific ...
,
beta decay
In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...
and
nuclear fusion. Pair production and nuclear fusion are processes in which measurable amounts of mass are converted to
kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
or vice versa.
* Curvature of
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
is a relativistic manifestation of the existence of mass. Such
curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
For curves, the canonic ...
is extremely weak and difficult to measure. For this reason, curvature was not discovered until after it was predicted by Einstein's theory of general relativity. Extremely precise
atomic clocks
An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwee ...
on the surface of the Earth, for example, are found to measure less time (run slower) when compared to similar clocks in space. This difference in elapsed time is a form of curvature called
gravitational time dilation. Other forms of curvature have been measured using the
Gravity Probe B
Gravity Probe B (GP-B) was a satellite-based experiment to test two unverified predictions of general relativity: the geodetic effect and frame-dragging. This was to be accomplished by measuring, very precisely, tiny changes in the direction of ...
satellite.
* Quantum mass manifests itself as a difference between an object's quantum
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
and its
wave number. The quantum mass of a particle is proportional to the inverse
Compton wavelength and can be determined through various forms of
spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
. In relativistic quantum mechanics, mass is one of the irreducible representation labels of the Poincaré group.
Weight vs. mass
In everyday usage, mass and "
weight
In science and engineering, the weight of an object is the force acting on the object due to gravity.
Some standard textbooks define weight as a Euclidean vector, vector quantity, the gravitational force acting on the object. Others define weigh ...
" are often used interchangeably. For instance, a person's weight may be stated as 75 kg. In a constant gravitational field, the weight of an object is proportional to its mass, and it is unproblematic to use the same unit for both concepts. But because of slight differences in the strength of the
Earth's gravitational field at different places, the
distinction becomes important for measurements with a precision better than a few percent, and for places far from the surface of the Earth, such as in space or on other planets. Conceptually, "mass" (measured in
kilograms
The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
) refers to an intrinsic property of an object, whereas "weight" (measured in
newtons
The newton (symbol: N) is the unit of force in the International System of Units (SI). It is defined as 1 kg⋅m/s, the force which gives a mass of 1 kilogram an acceleration of 1 metre per second per second. It is named after Isaac Newton in r ...
) measures an object's resistance to deviating from its current course of
free fall, which can be influenced by the nearby gravitational field. No matter how strong the gravitational field, objects in free fall are
weightless, though they still have mass.
The force known as "weight" is proportional to mass and
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
in all situations where the mass is accelerated away from free fall. For example, when a body is at rest in a gravitational field (rather than in free fall), it must be accelerated by a force from a scale or the surface of a planetary body such as the
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
or the
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
. This force keeps the object from going into free fall. Weight is the opposing force in such circumstances and is thus determined by the acceleration of free fall. On the surface of the Earth, for example, an object with a mass of 50 kilograms weighs 491 newtons, which means that 491 newtons is being applied to keep the object from going into free fall. By contrast, on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 newtons, because only 81.5 newtons is required to keep this object from going into a free fall on the moon. Restated in mathematical terms, on the surface of the Earth, the weight ''W'' of an object is related to its mass ''m'' by , where is the acceleration due to
Earth's gravitational field, (expressed as the acceleration experienced by a free-falling object).
For other situations, such as when objects are subjected to mechanical accelerations from forces other than the resistance of a planetary surface, the weight force is proportional to the mass of an object multiplied by the total acceleration away from free fall, which is called the
proper acceleration
In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at ...
. Through such mechanisms, objects in elevators, vehicles, centrifuges, and the like, may experience weight forces many times those caused by resistance to the effects of gravity on objects, resulting from planetary surfaces. In such cases, the generalized equation for weight ''W'' of an object is related to its mass ''m'' by the equation , where ''a'' is the proper acceleration of the object caused by all influences other than