Boltzmann constant, k

The constant that converts a temperature into an energy per particle. A gas molecule carries an average of ½kT of kinetic energy for each direction it can move in, which is why k appears wherever heat meets a single atom.

k = 1.380649 × 10⁻²³ J/K

Exact by definition, so it has no uncertainty at all.

In other units

Values marked … are exact, but their decimals run on, so they stop at ten significant figures instead of being rounded.

Boltzmann constant in SI units and in other units
Quantity	Value
k	1.380649 × 10⁻²³ J/K
k	8.617333262… × 10⁻⁵ eV/K
kT at 25 °C	4.1164049935 × 10⁻²¹ J
kT at 25 °C	0.02569257912… eV

k in eV/K

1.380649 × 10⁻²³ J/K ÷ (1.602176634 × 10⁻¹⁹ J/eV)
= 8.617333262… × 10⁻⁵ eV/K

kT at 25 °C in J

1.380649 × 10⁻²³ J/K × 298.15 K
= 4.1164049935 × 10⁻²¹ J

kT at 25 °C in eV

4.1164049935 × 10⁻²¹ J ÷ (1.602176634 × 10⁻¹⁹ J/eV)
= 0.02569257912… eV

The thermal energy scale at room temperature.

Where the value comes from

Before 2019 the kelvin was defined by the triple point of water, 273.16 K, and k was measured. The most precise method was acoustic gas thermometry, which infers kT from the speed of sound in a noble gas such as argon or helium.

The revision fixed k at exactly 1.380649 × 10⁻²³ J/K, which turned the definition round: a kelvin is now the change in temperature that changes kT by 1.380649 × 10⁻²³ J. The triple point of water became a measured temperature, still 273.16 K to within a fraction of a millikelvin.

k is also the gas constant per molecule rather than per mole, so it can be recovered by dividing R by the Avogadro constant.

k from R and the Avogadro constant

k = R ÷ N_A
= 8.31446261815324 ÷ (6.02214076 × 10²³)
= 1.380649 × 10⁻²³ J/K

Which form to use

Use k when counting particles and R when counting moles. They describe the same physics at different scales, and R = N_A k converts between them.

In eV/K, k gives thermal energies directly: at 25 °C, kT is 0.02569 eV, a little more than a fortieth of an electronvolt. Set that against hydrogen bonds, around a tenth to a few tenths of an electronvolt, which break and re-form constantly at room temperature, and covalent bonds of several electronvolts, which do not.

In electronics and electrochemistry the same quantity appears as a voltage, kT/e, which is 25.69 mV at 25 °C and equals RT/F.

Common mistakes

Putting a Celsius temperature into kT. The temperature must be absolute: 25 °C is 298.15 K.
Using k with an amount in moles, or R with a count of molecules, which is wrong by a factor of 6.02 × 10²³.
Confusing the Boltzmann constant k with the Stefan-Boltzmann constant σ, which has different units, W/(m²·K⁴), and a different job.

Tools that use it

Kinetic Theory Gas Simulator turns the temperature into molecular speeds with it, and the speeds back into a temperature.
States of Matter Simulator turns argon’s 119.8 K well depth into an energy with it, and the atoms’ kinetic energy back into a temperature.

Related constants

Molar gas constant, R = 8.31446261815324 J/(mol·K)
Avogadro constant, N_A = 6.02214076 × 10²³ mol⁻¹
Stefan-Boltzmann constant, σ = 5.670374419… × 10⁻⁸ W/(m²·K⁴)
Wien’s displacement constant, b = 2.897771955… × 10⁻³ m·K