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Units defined only by physical constants
In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants:
Planck_units
Units of measurement based on universal physical constants
units. The Planck system of units is now understood to use the reduced Planck constant, ℏ, in place of the Planck constant, h. The geometrized units system
Natural_units
Physical constant in quantum mechanics
the Planck constant is used, together with other constants, to define the kilogram, the SI unit of mass. The SI units are defined such that the Planck constant
Planck_constant
German physicist (1858–1947)
used to derive a set of units, now called Planck units, expressed in terms of physical constants. The Planck relation, E= h {\displaystyle h} ν, states
Max_Planck
Early system of natural units
Planck units are more commonly used than Stoney units in modern physics, especially for quantum gravity (including string theory). Rarely, Planck units
Stoney_units
As of April 2024, the following Max Planck Institutes and Research Units exist (in alphabetical order): Max Planck Institute for the Study of Living Conditions
List_of_Max_Planck_Institutes
Collection of units of measurement and rules relating them to each other
A system of units of measurement, also known as a system of units or system of measurement, is a collection of units of measurement and rules relating
System of units of measurement
System_of_units_of_measurement
Definition of the units kg, A, K and mol
defined by setting exact numerical values, when expressed in SI units, for the Planck constant (h), the elementary electric charge (e), the Boltzmann
2019_revision_of_the_SI
Natural number
constants are set to 1 in natural unit systems in order to simplify the form of equations; for example, in Planck units the speed of light equals 1. Dimensionless
1
Spectral density of light emitted by a black body
In physics, Planck's law (also Planck radiation law) describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium
Planck's_law
Universal and unchanging physical quantity
expressed in the natural units Planck length per Planck time. While its numerical value can be defined at will by the choice of units, the speed of light itself
Physical_constant
Space observatory
Planck was a space observatory operated by the European Space Agency (ESA) from 2009 to 2013. The project aimed to map the anisotropies of the cosmic microwave
Planck_(spacecraft)
Attempts to unify relativity, gravitation, and quantum mechanics
are given special consideration because they can be used to define all Planck units and thus all physical quantities. The three constants are therefore used
CGh_physics
SI unit of frequency
electronics are driven. The units are sometimes also used as a representation of the energy of a photon, via the Planck relation E = hν, where E is the
Hertz
constant Planck postulate Planck's law of black body radiation Planck-taper window Planck–Bessel window Planck–Einstein relation Planck units Planck energy
List of things named after Max Planck
List_of_things_named_after_Max_Planck
Magnitude or dimension of a thing
physics, the Planck length, denoted ℓP, is a unit of length, equal to 1.616199(97)×10−35 metres. It is a unit in the system of Planck units, developed by
Size
Hypothetical conflict with the laws of physics as currently known
used in the definition of units. For example, in Stoney units, the elementary charge is set to e = 1 while the reduced Planck constant is subject to measurement
Time-variation of fundamental constants
Time-variation_of_fundamental_constants
Metric unit of mass
kilogramme) is the base unit of mass in the International System of Units (SI), equal to one thousand grams. It has the unit symbol kg. The word "kilogram"
Kilogram
Unit of length
is not a part of the International System of Units (SI). Up to 2019, it was listed as a compatible unit by both the International Bureau of Weights and
Angstrom
One of the seven units of measurement that define the metric system
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
SI_base_unit
Principle in theoretical physics
1/4; the entropy of a black hole is one quarter its horizon area in Planck units. The entropy is proportional to the logarithm of the number of microstates
Holographic_principle
Value representing energy density of space
constant". The dimension of Λ is generally understood as length−2. Using the Planck units, and the value evaluated in 2025 for the Hubble constant H0 = 76.5±2
Cosmological_constant
Condition in which spacetime itself breaks down
{\displaystyle J} exceeds G M 2 / c {\displaystyle GM^{2}/c} (or in Planck units, J > M 2 {\displaystyle J>M^{2}} ); i.e. the spin exceeds what is normally
Gravitational_singularity
Torricelli troland (Td), luminance (human eye) – Leonard Troland Planck units – Max Planck Stoney units – George Stoney Mercalli intensity scale, earthquake effects –
List of scientific units named after people
List_of_scientific_units_named_after_people
Comparison of a wide range of timescales
time units of minutes, hours, days, and Julian years. Geologic time scale International System of Units Orders of magnitude (frequency) Planck units Scale
Orders_of_magnitude_(time)
Laser interferometer at Fermilab
exceeding the sensitivity required to detect the smallest units in the universe, called Planck units. Fermilab stated: "Everyone is familiar these days with
Fermilab_Holometer
Topics referred to by the same term
to: Planck (crater), on the Moon Planck (spacecraft), a space observatory Planck units, in particle physics and physical cosmology Amalia Planck (1834–1908)
Planck_(disambiguation)
Law of physics
frequency dependence of this approximation) or, by introducing natural Planck units, I ( ν , x ) = 2 ν 3 e − x , {\displaystyle I(\nu ,x)=2\nu ^{3}e^{-x}
Wien_approximation
Measurement unit for time
other units used are multiples or divisions of these three. Unit of frequency Orders of magnitude (time) List of obsolete units of measurement "Units of
Unit_of_time
French microbiologist, biochemist and Nobel laureate (born 1968)
Max Planck Institute for Infection Biology in Berlin since 2015. Three years later, she founded an independent research institute, the Max Planck Unit for
Emmanuelle_Charpentier
Physical constant for the strength of gravity induced by a mass
constant in some systems of natural units, particularly geometrized unit systems such as Planck units and Stoney units, the value of the gravitational constant
Gravitational_constant
Association of German research institutes
The Max Planck Society for the Advancement of Science (German: Max-Planck-Gesellschaft zur Förderung der Wissenschaften e. V.; MPG) is a formally independent
Max_Planck_Society
Unit system used in the physics of relativity
A geometrized unit system or geometrodynamic unit system is a system of natural units in which the base physical units are chosen so that the speed of
Geometrized_unit_system
German research institute
The Max Planck Institute of Geoanthropology (German: Max-Planck-Institut für Geoanthropologie) is a research institute of the Max Planck Society dedicated
Max Planck Institute of Geoanthropology
Max_Planck_Institute_of_Geoanthropology
Topics referred to by the same term
planet discovered in the first half of October of each year Planck time (tP), a Planck unit in cosmology Tp ligands, a class of scorpionate ligands Trispyrazolylborate
TP
Maximum or minimum values of quantities
usually represented within a particular energy or length scale, such as Planck units. When used in this context, the traditional terms "infrared" and "ultraviolet"
Cutoff_(physics)
Modern form of the metric system
comprises a coherent system of units of measurement starting with seven base units, which are the second (symbol: s, the unit of time), metre (m, length)
International_System_of_Units
Partial differential equation
In statistical mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the
Fokker–Planck_equation
Physical theory of the cosmos
measured energy density of dark energy, and the one naively predicted from Planck units. During the 1970s and the 1980s, various observations showed that there
Big_Bang
Numerical coefficient in loop quantum gravity
gravity. The Immirzi parameter measures the size of the quantum of area in Planck units. As a result, its value is currently fixed by matching the semiclassical
Immirzi_parameter
Low energy theories not compatible with string theory
remain subextremal, we must have | q | < m {\displaystyle |q|<m} in Planck units where the extremality condition takes the form | Q | = M {\displaystyle
Swampland_(physics)
Mechanism in physical cosmology
carry an entropy equal to one fourth of the area of the event horizon in Planck units. Later, in 1981, Bekenstein argued for the Bekenstein bound as a limit
Fischler–Susskind holographic bound
Fischler–Susskind_holographic_bound
Research institute in Berlin, Germany
The Max Planck Institute for Infection Biology (MPIIB) is a non-university research institute of the Max Planck Society located in the heart of Berlin
Max Planck Institute for Infection Biology
Max_Planck_Institute_for_Infection_Biology
Observation in physical cosmology
terms of Planck units, obtained by multiplying H0 by 1.75×10−63 (from definitions of parsec and tP), for example for H0 = 70, a Planck unit version of
Hubble's_law
Continuous progression from past to future
Planck time (c. 5.4 × 10−44 seconds) is the unit of time in the system of natural units known as Planck units. Current established physical theories are
Time
Variant of the centimetre–gram–second unit system
and Heaviside–Lorentz units. Some other unit systems are called "natural units", a category that includes atomic units, Planck units, and others. The International
Gaussian_units
Type of system of units of measurement
of its derived units. A coherent derived unit is a derived unit that, for a given system of quantities and a chosen set of base units, is a product of
Coherence (units of measurement)
Coherence_(units_of_measurement)
Research Institute
Max Planck Institute for Legal History and Legal Theory (German: Max-Planck-Institut für Rechtsgeschichte und Rechtstheorie; formerly Max Planck Institute
Max Planck Institute for Legal History and Legal Theory
Max_Planck_Institute_for_Legal_History_and_Legal_Theory
Physical quantity of hot and cold
scientific purposes. The kelvin is one of the seven base units in the International System of Units (SI). Absolute zero, i.e., zero kelvin, 0 K = −273.15 °C
Temperature
Theory of rapid universe expansion
{\displaystyle \ V\ } is the potential, and the equations are written in reduced Planck units. Technically, this is because the inflaton potential is expressed as
Cosmic_inflation
Hypothetical phenomenon
{\displaystyle J} exceeds G M 2 / c {\displaystyle GM^{2}/c} (or in Planck units, J > M 2 {\displaystyle J>M^{2}} ), i.e. the spin exceeds what is normally
Naked_singularity
Physical law for entropy and heat
Boltzmann constant, h is the Planck constant, ν is frequency, and the quantities Kv and Lv are the energy and entropy fluxes per unit frequency, area, and solid
Second_law_of_thermodynamics
Unit of action or angular momentum
the Planck constant. Angular momentum is the product of an object's moment of inertia, with the unit kg⋅m2 and its angular velocity with the unit rad⋅s−1
Joule-second
Equation used to calculate the electromigration of ions in a fluid
The Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It extends Fick's
Nernst–Planck_equation
Hypothetical elementary particle that mediates gravity
Analogies between Maxwell's and Einstein's field equations Planck units – Units defined only by physical constants Polarizable vacuum – Theory of
Graviton
Standard unit of mass for atomic-scale entities
to grams and other metric units of mass. The 2019 revision of the SI redefined the kilogram by fixing the value of the Planck constant (h), improving the
Dalton_(unit)
Approximation of a black body's spectral radiance
of classical physics is commonly known as the ultraviolet catastrophe. Planck's law, which gives the correct radiation at all frequencies, has the Rayleigh–Jeans
Rayleigh–Jeans_law
Reference value of length
are the metric units, used in every country globally. In the United States the U.S. customary units are also in use. British Imperial units are still used
Unit_of_length
Physical constant relating particle kinetic energy with temperature
occurs in the definitions of the kelvin (K) and the molar gas constant, in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used
Boltzmann_constant
Non-mainstream theory in physics
physical quantity being normalized against its corresponding Planck unit. When Planck units are used and such equations of physical law are expressed in
Variable_speed_of_light
Energy carried by a photon
Fundamentals of Atmospheric Science". "2022 CODATA Value: Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18
Photon_energy
Hypothesis about life in the universe
assumptions such as that dark energy density is a constant. In terms of Planck units, and as a natural dimensionless value, Λ is on the order of 10−122. This
Fine-tuned_universe
Physical constant with no units
constants, measurements require units and the minimum set of dimensioned constants includes the speed of light, the Planck constant, and the gravitational
Dimensionless physical constant
Dimensionless_physical_constant
Units used to measure energy
{\displaystyle \hbar =h/2\pi } is the reduced Planck constant). In this scheme, energy has the same units as momentum, mass, and inverse length, all of
Units_of_energy
Description of gravity using discrete values
researchers Orders of magnitude (length) Penrose interpretation Planck epoch Planck units Swampland (physics) Virtual black hole Weak Gravity Conjecture
Quantum_gravity
Irish physicist (1826–1911)
are named in his honour. Basic concepts of quantum mechanics Planck units Stoney units "George Johnstone Stoney 1826–1911". Daily Express. 6 July 1911
George_Johnstone_Stoney
System of measurement
The atomic units are a system of natural units of measurement that is especially convenient for calculations in atomic physics and related scientific
Atomic_units
Unit of energy
In particle physics, a system of natural units in which the speed of light in vacuum c and the reduced Planck constant ħ are dimensionless and equal to
Electronvolt
Process of assigning numbers to objects or events
International System of Units (SI). This system reduces all physical measurements to a mathematical combination of seven base units. Metrology is the science
Measurement
NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18. Planck Collaboration (2020). "Planck 2018 results. VI. Cosmological
List_of_physical_constants
Physics institute in Erlangen, Germany
scientifically active technology development and service units. It is also the home of several Max Planck Research Groups that are organizationally independent
Max Planck Institute for the Science of Light
Max_Planck_Institute_for_the_Science_of_Light
Research institute in computer science
The Max Planck Institute for Informatics (German: Max-Planck-Institut für Informatik, abbreviated MPI-INF or MPII) is a research institute in computer
Max Planck Institute for Informatics
Max_Planck_Institute_for_Informatics
10−47 6.632×10−47 m2⋅A Unit of magnetic moment in Stoney units 10−45 9.09×10−45 m2⋅A Unit of magnetic moment in Planck units 10−43 ~1×10−43 m2⋅A Expected
Orders of magnitude (magnetic moment)
Orders_of_magnitude_(magnetic_moment)
Irish contributions to science, technology, and engineering
units based on fundamental physical constants. His work anticipated Planck units and contributed to the conceptualisation of fundamental physics. 1883:
Timeline of Irish inventions and discoveries
Timeline_of_Irish_inventions_and_discoveries
Art library in Italy
The Bibliotheca Hertziana – Max Planck Institute for Art History is a German research institute located in Rome, Italy. It was founded by a donation of
Bibliotheca Hertziana – Max Planck Institute for Art History
Bibliotheca_Hertziana_–_Max_Planck_Institute_for_Art_History
Field theory coupling of charge but not higher moments
{\displaystyle {\sqrt {g}}\,d^{4}x} constructed from the metric (in Planck units): S = ∫ d 4 x g ( − 1 2 R + 1 2 ∇ μ φ ∇ μ φ − V ( φ ) ) {\displaystyle
Minimal_coupling
Relationship between the concepts of thermodynamic entropy and information entropy
wave-function, in coordinate, and also momentum space, when expressed in Planck units. The resulting inequalities provide a tighter bound on the uncertainty
Entropy in thermodynamics and information theory
Entropy_in_thermodynamics_and_information_theory
German scientific institution
by the Max Planck Society. The Kaiser Wilhelm Society was an umbrella organisation for many institutes, testing stations, and research units created under
Kaiser_Wilhelm_Society
Type of weak interaction in nuclear and atomic physics
{4\pi \alpha }}~} is the elementary charge expressed as rationalized Planck units, and the expansion uses for its basis vectors the (mostly implicit) Pauli
Weak_charge
Metric unit of mass
numerical value of the Planck constant (h). The only unit symbol for gram that is recognised by the International System of Units (SI) is "g" following
Gram
Minimum amount of a physical entity involved in an interaction
concept of the quantum in physics originates from December 14, 1900, when Max Planck reported his findings to the German Physical Society. He showed that modelling
Quantum
Hypothesis relating age of the universe to physical constants
cosmological parameters (for example density of the universe) and Planck units (for example Planck density). This ratio of densities, and other ratios (using
Dirac large numbers hypothesis
Dirac_large_numbers_hypothesis
Generalization of special relativity
momentum, and is consequently valid at all energy scales. Planck scale Planck units Planck epoch Fock–Lorentz symmetry Amelino-Camelia, Giovanni (1 November
Doubly_special_relativity
Research institute in Frankfurt, Germany
The Max Planck Institute for Brain Research is located in Frankfurt, Germany. It was founded as Kaiser Wilhelm Institute for Brain Research in Berlin 1914
Max Planck Institute for Brain Research
Max_Planck_Institute_for_Brain_Research
German research institute
The Max Planck Institute for Plasma Physics (German: Max-Planck-Institut für Plasmaphysik, IPP) is a physics institute investigating the physical foundations
Max Planck Institute for Plasma Physics
Max_Planck_Institute_for_Plasma_Physics
Upper bound to the mass of cold, nonrotating neutron stars
order of the mean interparticle separation. In terms of Planck units, with the reduced Planck constant ħ, the speed of light c, and the gravitational
Tolman–Oppenheimer–Volkoff limit
Tolman–Oppenheimer–Volkoff_limit
Variant of the metric system
mass, and the second as the unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different
Centimetre–gram–second system of units
Centimetre–gram–second_system_of_units
Relation between peak wavelengths of black body radiation and temperature
the temperature. The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness or intensity of black-body
Wien's_displacement_law
Electromechanical weight measuring instrument
methods that use the fixed numerical value of the Planck constant are sometimes called the Planck balance. The Kibble balance is an advanced and highly
Kibble_balance
Physics 1992 CERN ESPCI Paris Emmanuelle Charpentier Chemistry 2020 Max Planck Unit for the Science of Pathogens Yves Chauvin Chemistry 2005 French Institute
List of Nobel laureates by university affiliation
List_of_Nobel_laureates_by_university_affiliation
Spatial frequency of a wave
used as unit of energy, since a photon of frequency f {\displaystyle f} has energy h f {\displaystyle hf} , where h {\displaystyle h} is the Planck constant
Wavenumber
Space research institute in Germany
The Max Planck Institute for Solar System Research (abbreviation: MPS; German: Max-Planck-Institut für Sonnensystemforschung) is a research institute
Max Planck Institute for Solar System Research
Max_Planck_Institute_for_Solar_System_Research
Charge carried by one electron
1874 for the first system of natural units, called Stoney units. Later, he proposed the name electron for this unit. At the time, the particle we now call
Elementary_charge
Concept in relativistic physics
(2014). "Ultra-high energy physics and standard basic principles. Do Planck units really make sense?" (PDF). EPJ Web of Conferences. 71: 00062. Bibcode:2014EPJWC
Lorentz_covariance
Mathematical institute
The Max Planck Institute for Mathematics (German: Max-Planck-Institut für Mathematik, MPIM) is a research institute located in Bonn, Germany. It is named
Max Planck Institute for Mathematics
Max_Planck_Institute_for_Mathematics
Estonian astrophysicist (1933–2021)
yearbook material. Sapar, A. (1977). “Evidence for the fundamental role of Planck units in cosmology.” Publ. Tartu Astrofiz. Obs. 45. Sapar, A.; Sapar, L.; Poolamäe
Arved-Ervin_Sapar
Comparison of various scales
original units and one of the desired units (or some intermediary unit), before being rearranged to create a factor that cancels out the original unit. For
Conversion_of_units
Research institute in Munich, Germany
The Max Planck Institute for Physics (MPP) is a research institute located in Garching, near Munich, Germany. It specializes in high energy physics and
Max Planck Institute for Physics
Max_Planck_Institute_for_Physics
Research institute in Mainz, Germany
The Max Planck Institute for Chemistry (Otto Hahn Institute; German: Max Planck Institut für Chemie - Otto Hahn Institut) is a non-university research
Max Planck Institute for Chemistry
Max_Planck_Institute_for_Chemistry
Research institute
The Max Planck Institute for Mathematics in the Sciences (MPI MiS) in Leipzig is a research institute of the Max Planck Society. Founded on March 1, 1996
Max Planck Institute for Mathematics in the Sciences
Max_Planck_Institute_for_Mathematics_in_the_Sciences
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