Boltzmann constant symbol

An italic k, often subscripted B, relating temperature to energy.

Also known as: k, Boltzmann's constant

ScientificMathematicalStandard profile

Meanings

k_B converts a temperature into an energy per particle. Its subscript exists because k alone is badly overloaded — spring constants, rate constants and wavenumbers all claim the same letter.

Common modern usageVerified fact
Relates the average kinetic energy of particles to the thermodynamic temperature of the system they are in.
Contexts: Mathematics, Laboratory
Officially standardisedVerified fact
Has had an exact value since 2019, which is how the kelvin is now defined — by fixing this constant rather than by the triple point of water.
Contexts: Mathematics, Laboratory
Common modern usageVerified fact
Carries a subscript B in careful writing because a bare k is claimed by spring constants, reaction rate constants and wavenumbers in the same literature.
Contexts: Mathematics, Laboratory

Visual description

A lower-case Latin letter k in italic type, usually followed by a small raised-and-lowered capital B set as a subscript.

Symmetry: none
Orientation: upright

Commonly confused with: Kilo prefix symbol
Both are a bare lower-case k, and both appear in physical formulae.
Used alongside: Kelvin symbol
The kelvin is defined by fixing this constant.

Compare: Boltzmann constant (k) vs the kilo prefix (k) →

Confidence

IdentityHigh confidence: High confidence because the identity is defined by a current official standard, but multiple independent sources agree.
Historical originModerate confidence: Moderate confidence because the historical origin is documented in encyclopedic references, but multiple independent sources agree, but early or supporting evidence is limited, but the regional or cultural match to this specific claim is not precise.
Current useHigh confidence: High confidence because the current use is defined by a current official standard, but multiple independent sources agree.
Visual matchHigh confidence: High confidence because the visual match is documented in encyclopedic references, but multiple independent sources agree.

Sources

ISO 80000, Quantities and units — recommended symbols
International Organization for Standardization · retrieved 2026-08-01
Paywalled and NOT READ. Registered so records can note that a recommended notation exists. It is widely departed from in practice, and no record types a meaning `official` on its basis. See docs/paywalled-standards.md.
The SI defining constants
Bureau International des Poids et Mesures · retrieved 2026-08-01
The seven constants whose exact values define the SI since 2019. Cited for the fact that a constant's value is fixed by definition rather than measured — a claim about the unit system, not about the notation.
CODATA Internationally Recommended Values of the Fundamental Physical Constants
NIST / CODATA Task Group on Fundamental Constants · retrieved 2026-08-01
Authoritative for the recommended value and uncertainty of a physical constant, and for whether that value is exact by definition or measured. It fixes values; it does not decide which letter denotes which quantity, and no record cites it for a symbol's meaning.
Boltzmann constant
Wikipedia · retrieved 2026-08-01
Tertiary reference. Used for what a symbol denotes in ordinary scientific practice and for which fields reuse it, never for a claim that any body assigns the letter its meaning.
Physical constant
Wikipedia · retrieved 2026-08-01
Tertiary reference. Used for what a symbol denotes in ordinary scientific practice and for which fields reuse it, never for a claim that any body assigns the letter its meaning.

Last reviewed 2026-07-31

Part of

Physical constants and quantity symbols

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Meanings

k_B converts a temperature into an energy per particle. Its subscript exists because k alone is badly overloaded — spring constants, rate constants and wavenumbers all claim the same letter.

Common modern usageVerified fact

Relates the average kinetic energy of particles to the thermodynamic temperature of the system they are in.

Contexts: Mathematics, Laboratory

Officially standardisedVerified fact

Has had an exact value since 2019, which is how the kelvin is now defined — by fixing this constant rather than by the triple point of water.

Contexts: Mathematics, Laboratory

Common modern usageVerified fact

Carries a subscript B in careful writing because a bare k is claimed by spring constants, reaction rate constants and wavenumbers in the same literature.

Contexts: Mathematics, Laboratory

Confidence

IdentityHigh confidence: High confidence because the identity is defined by a current official standard, but multiple independent sources agree.
Historical originModerate confidence: Moderate confidence because the historical origin is documented in encyclopedic references, but multiple independent sources agree, but early or supporting evidence is limited, but the regional or cultural match to this specific claim is not precise.
Current useHigh confidence: High confidence because the current use is defined by a current official standard, but multiple independent sources agree.
Visual matchHigh confidence: High confidence because the visual match is documented in encyclopedic references, but multiple independent sources agree.

Sources

ISO 80000, Quantities and units — recommended symbols
International Organization for Standardization · retrieved 2026-08-01
Paywalled and NOT READ. Registered so records can note that a recommended notation exists. It is widely departed from in practice, and no record types a meaning `official` on its basis. See docs/paywalled-standards.md.
The SI defining constants
Bureau International des Poids et Mesures · retrieved 2026-08-01
The seven constants whose exact values define the SI since 2019. Cited for the fact that a constant's value is fixed by definition rather than measured — a claim about the unit system, not about the notation.
CODATA Internationally Recommended Values of the Fundamental Physical Constants
NIST / CODATA Task Group on Fundamental Constants · retrieved 2026-08-01
Authoritative for the recommended value and uncertainty of a physical constant, and for whether that value is exact by definition or measured. It fixes values; it does not decide which letter denotes which quantity, and no record cites it for a symbol's meaning.
Boltzmann constant
Wikipedia · retrieved 2026-08-01
Tertiary reference. Used for what a symbol denotes in ordinary scientific practice and for which fields reuse it, never for a claim that any body assigns the letter its meaning.
Physical constant
Wikipedia · retrieved 2026-08-01
Tertiary reference. Used for what a symbol denotes in ordinary scientific practice and for which fields reuse it, never for a claim that any body assigns the letter its meaning.

Last reviewed 2026-07-31

Meanings

Visual description

Related & commonly confused symbols

Meanings

Visual description

Related & commonly confused symbols