ConstantID

Molar Planck constant

Physico-chemicalExact

NAh = 3.990 312 712… × 10−10 J Hz−1 mol−1

Value
3.990 312 712… × 10−10 J Hz−1 mol−1
Standard uncertainty
exact
Relative uncertainty
exact
Status
Exact since the 2019 SI redefinition
Symbol
NAh
Source
CODATA 2022 via NIST · NIST entry

NIST prints this exact value cut to 10 digits. ConstantID recomputes it from the defining constants: 3.990 312 712 893 4314 × 10−10…

Use in a calculation

# molar Planck constant, CODATA 2022 (NIST)
molar_planck_constant = 3.9903127128934314e-10  # J Hz^-1 mol^-1, exact

# SciPy: scipy.constants.physical_constants['molar Planck constant']

What it is

The Planck constant times the Avogadro constant. Before 2019 it was known far more precisely than either factor, which made it a bridge between atomic and laboratory-scale masses; now it is exact.

It is built only from constants that have exact values since 20 May 2019, so it is exact too; CODATA 2018 was the first adjustment to list it that way.

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.

molar Planck constant: CODATA values 1998–2022 relative to the 2022 value, in parts per billion, with one-standard-uncertainty bars−15−10−50+5+10+15parts per billion1998200220062010201420182022

Relative uncertainty

molar Planck constant: relative standard uncertainty in each CODATA adjustment, logarithmic scale10⁻¹⁰10⁻⁹10⁻⁸199820022006201020142018exact2022exact
CODATAValue (uncertainty)Relative uncertaintyChange from previous
20223.990 312 712… × 10−10exact exact
20183.990 312 712… × 10−10exact +0.6 σ of 2014
20143.990 312 7110(18) × 10−104.5 × 10−10 −2.4 σ of 2010
20103.990 312 7176(28) × 10−107.0 × 10−10 +6.2 σ of 2006
20063.990 312 6821(57) × 10−101.4 × 10−9 −1.3 σ of 2002
20023.990 312 716(27) × 10−106.8 × 10−9 +0.9 σ of 1998
19983.990 312 689(30) × 10−107.5 × 10−9

“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).