The Boltzmann constant, written as $k_B$, links temperature to energy at the particle scale.

In SI units, it is:

$$k_B = 1.380649 \times 10^{-23}\ \mathrm{J\,K^{-1}}$$

A useful interpretation is that thermal energy per particle is on the order of:

$$E \sim k_B T$$

where $T$ is the absolute temperature in kelvin.

For example, at room temperature ($T \approx 300\,\mathrm{K}$):

$$k_B T \approx 4.14 \times 10^{-21}\ \mathrm{J}$$

In statistical mechanics, the same constant appears in the Boltzmann factor:

$$P(E) \propto e^{-E/(k_B T)}$$

This tells us that higher-energy states are exponentially less likely, with the scale set by $k_B T$.

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