k is the gas constant per molecule instead of per mole: k = R/Nₐ. At room temperature, kT ≈ 0.025 eV.
Value of k in different units
| Value | Use it when |
|---|---|
| 1.381 × 10⁻²³ J K⁻¹ | SI. Exact since 2019: 1.380649 × 10⁻²³. |
| 8.617 × 10⁻⁵ eV K⁻¹ | When energy is in eV. |
| 1.381 × 10⁻¹⁶ erg K⁻¹ | CGS. |
Formulas that use k
- Average KE = (3/2)kT
- PV = NkT
- k = R/Nₐ
Its dimensional formula is worked out on the dimensional formula of boltzmann constant k page.
Other constants
- Gas constant (R): 8.314 J mol⁻¹ K⁻¹
- Planck's constant (h): 6.626 × 10⁻³⁴ J s
- Avogadro's number (Nₐ): 6.022 × 10²³ mol⁻¹
- Speed of light (c): 3 × 10⁸ m/s
- Charge of an electron (e): 1.602 × 10⁻¹⁹ C
- Mass of an electron (mₑ): 9.109 × 10⁻³¹ kg
- Mass of a proton (mₚ): 1.673 × 10⁻²⁷ kg
- Mass of a neutron (mₙ): 1.675 × 10⁻²⁷ kg
- Universal gravitational constant (G): 6.674 × 10⁻¹¹ N m² kg⁻²
- Acceleration due to gravity (g): 9.8 m/s²
- Boltzmann constant (k): 1.381 × 10⁻²³ J/K
- Faraday constant (F): 96 485 C/mol
- Permittivity of free space (ε₀): 8.854 × 10⁻¹² C² N⁻¹ m⁻²
- Permeability of free space (μ₀): 4π × 10⁻⁷ T m/A
- Rydberg constant (R): 1.097 × 10⁷ m⁻¹
- Stefan–Boltzmann constant (σ): 5.67 × 10⁻⁸ W m⁻² K⁻⁴
- Wien's constant (b): 2.898 × 10⁻³ m K
- Bohr radius (a₀): 0.529 Å
- Molar volume of a gas at STP (Vₘ): 22.4 L/mol
The full list, searchable, is on the physical constants page.
Questions students ask
What is the value of Boltzmann constant?
k = 1.381 × 10⁻²³ J/K. In other units: 1.381 × 10⁻²³ J K⁻¹; 8.617 × 10⁻⁵ eV K⁻¹; 1.381 × 10⁻¹⁶ erg K⁻¹.
What is k in physics and chemistry?
k is the gas constant per molecule instead of per mole: k = R/Nₐ. At room temperature, kT ≈ 0.025 eV.
Which value of k should I use?
1.381 × 10⁻²³ J K⁻¹: SI. Exact since 2019: 1.380649 × 10⁻²³. 8.617 × 10⁻⁵ eV K⁻¹: When energy is in eV. 1.381 × 10⁻¹⁶ erg K⁻¹: CGS.
What is the dimensional formula of Boltzmann constant?
See the dimensional formula of Boltzmann constant, worked out step by step on its own page.