Boltzmann constant
= 1.380 649 × 10−23 J K−1
- Value
- 1.380 649 × 10−23 J K−1
- Standard uncertainty
- exact
- Relative uncertainty
- exact
- Status
- Exact since the 2019 SI redefinition
- Symbol
- Source
- CODATA 2022 via NIST · NIST entry
Use in a calculation
# Boltzmann constant, CODATA 2022 (NIST)
k_B = 1.380649e-23 # J K^-1, exact
# SciPy: scipy.constants.physical_constants['Boltzmann constant']What it is
The bridge between temperature and energy. In a gas at temperature T, each molecule carries on average 3kT/2 of kinetic energy from its motion. Since 2019 the value is exact and defines the kelvin, so temperature is now measured as an energy scale rather than against the triple point of water.
This is one of the seven defining constants of the SI. Its value was measured until the CODATA 2017 special adjustment fixed it, and it has been exact since the new definitions took effect on 20 May 2019.
Equations
- mean kinetic energy of a gas molecule
- Boltzmann's entropy formula
- ideal gas law
- molar gas constant
In other units
How the value changed, 1998–2022
Each point is one CODATA adjustment, plotted as its difference from the 2022 value; the bars show one standard uncertainty (an arrowhead means the bar runs off the chart). Diamonds mark adjustments in which the value was exact.
Relative uncertainty
| CODATA | Value (uncertainty) | Relative uncertainty | Change from previous |
|---|---|---|---|
| 2022 | 1.380 649 × 10−23 | exact | exact |
| 2018 | 1.380 649 × 10−23 | exact | +0.6 σ of 2014 |
| 2014 | 1.380 648 52(79) × 10−23 | 5.7 × 10−7 | −0.2 σ of 2010 |
| 2010 | 1.380 6488(13) × 10−23 | 9.4 × 10−7 | −0.7 σ of 2006 |
| 2006 | 1.380 6504(24) × 10−23 | 1.7 × 10−6 | +0.0 σ of 2002 |
| 2002 | 1.380 6504(24) × 10−23 | 1.7 × 10−6 | +0.0 σ of 1998 |
| 1998 | 1.380 6503(24) × 10−23 | 1.7 × 10−6 |
“Change from previous” is the shift in the value divided by the standard uncertainty of the previous adjustment. Earlier values are converted into the current unit where NIST changed it (for example J s to J Hz⁻¹).