Maths & Data Reference Undergraduate

Physical Constants

A table of 14 physical constants with symbol, unit and provenance, marking which values are exact by definition and which are measured.

Physical constants, with the values the calculators on this site compute with.
Symbol	Constant	Value	Unit	Status	Notes
c	Speed of light in vacuum	299,792,458	m/s	Exact by definition	Exact since 1983, when the metre was redefined as the distance light travels in 1/299,792,458 of a second. Measuring c more precisely now refines the metre, not the speed.
h	Planck constant	6.62607015 × 10⁻³⁴	J·s	Exact by definition	Fixed in 2019, which is what defines the kilogram. The Kibble balance realises a mass from this number rather than from a metal cylinder kept near Paris.
ℏ	Reduced Planck constant	1.054571817… × 10⁻³⁴	J·s	Exact, derived	h divided by 2 pi. Exact as a definition but irrational as a decimal, so any printed form is truncated.
e	Elementary charge	1.602176634 × 10⁻¹⁹	C	Exact by definition	Fixed in 2019, which defines the ampere. Also the conversion from electronvolts to joules, since one electronvolt is the energy one elementary charge gains across one volt.
k	Boltzmann constant	1.380649 × 10⁻²³	J/K	Exact by definition	Fixed in 2019, which defines the kelvin. It converts a temperature into an energy per particle, which is why it appears wherever thermal energy meets a single molecule.
N_A	Avogadro constant	6.02214076 × 10²³	mol⁻¹	Exact by definition	Fixed in 2019, which defines the mole. The mole is now a count rather than a mass of carbon-12, so this number carries no uncertainty.
R	Molar gas constant	8.31446261815324	J/(mol·K)	Exact, derived	Exactly N_A times k, so it inherited their exactness in 2019. Watch the unit: this is the value for pascals and cubic metres, and 0.082057 L·atm/(mol·K) is the same constant.
F	Faraday constant	96,485.33212…	C/mol	Exact, derived	Exactly N_A times e, the charge on a mole of electrons. Converts between moles of electrons and coulombs in any electrochemical calculation.
σ	Stefan-Boltzmann constant	5.670374419… × 10⁻⁸	W/(m²·K⁴)	Exact, derived	Built from k, h and c, so exact. The fourth power is why a modest temperature rise makes a large difference to radiated power.
b	Wien’s displacement constant	2.897771955… × 10⁻³	m·K	Exact, derived	Peak wavelength times absolute temperature. Divide by a temperature to get the wavelength a black body radiates most strongly at.
g₀	Standard gravity	9.80665	m/s²	Exact by definition	A convention, not a measurement, and not the value anywhere in particular. Local gravity runs from about 9.78 m/s² near the equator to 9.83 m/s² at the poles.
atm	Standard atmosphere	101,325	Pa	Exact by definition	Exactly 101,325 Pa by definition. Distinct from the IUPAC standard pressure of 1 bar, which is 100,000 Pa, and the two give different molar volumes.
T₀	Ice point	273.15	K	Exact by definition	Zero degrees Celsius in kelvin, exactly. The offset every gas law needs, and one that cancels out of any temperature difference, so q = mcΔT never needs it.
G	Gravitational constant	6.67430(15) × 10⁻¹¹	m³/(kg·s²)	Measured	The least precisely known constant on this page, and the only measured one in the table. CODATA gives 6.67430(15), so the uncertainty is in the fifth digit: about 1 part in 45,000, which is enormous next to everything above.

Left out of the table because their digits moved between the 2018 and 2022 CODATA adjustments: the vacuum permittivity ε₀, Coulomb’s constant kₑ and the vacuum permeability μ₀. Each has its own page with its value and uncertainty: CODATA 2022’s for ε₀ and μ₀, and for kₑ, which CODATA does not list, the figure that follows from CODATA’s ε₀.

Citing this tool

Last updated 3 October 2026. Add the date you accessed it as well, which a citation of a page that can change asks for.

Reference

ScienceQuest. (2026). Physical Constants [Interactive tool]. Retrieved [date] from https://sciencequest.in/tools/physical-constants/

BibTeX

@misc{sciencequest-physical-constants,
  author       = {{ScienceQuest}},
  title        = {{Physical Constants}},
  howpublished = {\url{https://sciencequest.in/tools/physical-constants/}},
  year         = {2026},
  note         = {Interactive tool, last updated 3 October 2026. Add the date you accessed it as urldate.},
}

What exact by definition actually means

Most of the values in this table carry no uncertainty at all. Not a small uncertainty: none. The speed of light is 299,792,458 m/s because the metre is defined as the distance light travels in 1/299,792,458 of a second, so that figure is a unit conversion rather than a result. A better experiment refines the metre. It cannot move c.

That reads backwards at first, because a constant sounds like something you go out and measure. The resolution is that every measurement compares a quantity against a unit, and the unit has to come from somewhere. Fixing the constant and letting the unit follow is the more stable arrangement, because a defined number cannot drift and a physical object can.

The 2019 revision turned the definitions round

Until 2019 the kilogram was a platinum-iridium cylinder held near Paris, and the Planck constant was whatever experiment said it was in terms of that cylinder. The revision inverted that dependency. h is now fixed at 6.62607015 × 10⁻³⁴ J·s and the kilogram is whatever mass is consistent with it, realised on a Kibble balance rather than by comparison with metal. The same move fixed three further constants and pinned three more units to them:

The elementary charge e defines the ampere.
The Boltzmann constant k defines the kelvin.
The Avogadro constant N_A defines the mole, which became a count rather than a mass of carbon-12.

Exactness is inherited

A constant assembled only from exact constants is itself exact. The molar gas constant is the clearest case: R is exactly N_A × k, so when those two were fixed in 2019 R stopped being a measured quantity and became 8.31446261815324 J/(mol·K), every digit of it. The Faraday constant is exactly N_A × e for the same reason, and the Stefan-Boltzmann constant is built from k, h and c.

Exact does not mean short, and it does not mean unambiguous. Watch the units rather than the digits. The reduced Planck constant is h/2π, exactly defined and irrational, so any printed decimal form of it is truncated. R is listed here for pascals and cubic metres, and the same constant reads 0.082057 L·atm/(mol·K) in the units a gas law question usually arrives in.

The gravitational constant is the one exception

Exactly one row here is a measurement. CODATA gives G as 6.67430(15) × 10⁻¹¹ m³/(kg·s²), so the uncertainty sits in the fifth digit: about 1 part in 45,000. Next to constants with no uncertainty whatsoever that is an enormous gap, and it is there because gravity is desperately weak at bench scale. There is no way to screen an apparatus from the mass of everything else in the room.

The electromagnetic constants are left out of the table on purpose. Several of them moved digits between the 2018 and 2022 CODATA adjustments, and a stale digit in a row of bare values is worse than no row. Each has a page of its own instead, which gives its value with its uncertainty and says where the value comes from: the CODATA 2022 adjustment for the permittivity and the permeability, and for Coulomb’s constant, which CODATA does not list, the CODATA permittivity it is derived from. Standard gravity is worth one caution of its own: at 9.80665 m/s² it is a convention rather than a measurement, and not the local value anywhere in particular. Real surface gravity runs from about 9.78 m/s² near the equator to 9.83 m/s² at the poles.

Common questions

What does it mean for a physical constant to be exact?

It means the value is fixed by definition and has no experimental uncertainty, so no future measurement can change it. The speed of light is exact because the metre is defined from it, and since 2019 the Planck constant, elementary charge, Boltzmann constant and Avogadro constant are exact in the same way. Constants built only from those, such as the molar gas constant, are exact as a consequence. A more precise experiment now sharpens the unit rather than the constant.

Why is the gravitational constant known so much less precisely than the others?

Because it is still measured rather than defined, and gravity is extraordinarily weak at the scale of a laboratory. CODATA quotes 6.67430(15), which puts the uncertainty in the fifth digit, roughly 1 part in 45,000. Separate experiments using different apparatus have disagreed by more than their stated error bars, which is why the accepted uncertainty stays comparatively wide.