A mole is chemistry's counting unit: it turns a mass on a balance into a number of atoms or molecules, and its definition changed in 2019. We set that change against ordinary rounding. Taking water's molar mass from 18.015 to 18 g/mol changes an answer by 8 parts in 10,000. That is hundreds of thousands of times the gap, about one part in a billion on CODATA's 2022 value, between 1 and the factor converting relative mass to grams per mole. Since 20 May 2019 one mole has contained exactly 6.022 140 76 × 10²³ specified entities, and the molar mass of carbon-12 has been a measured value rather than a defined 12 g/mol. IUPAC calls the uncertainty this leaves "of no practical relevance for chemistry".
Mass no longer decides how many entities make a mole
The 1971 definition started from a mass. A mole held as many entities as there are atoms in 0.012 kilogram of carbon-12, so the count had to be found by experiment, and the SI Brochure (9th edition of 2019, version 4.01 of June 2026) records that this definition depended on the artefact definition of the kilogram.
Resolution 1 of the General Conference on Weights and Measures, passed in 2018, abrogated that wording "effective from 20 May 2019". IUPAC, chemistry's international union, had recommended a definition by number. The count now comes first. An entity may be an atom, a molecule, an ion, an electron, or another particle or specified group. The bare figure is the Avogadro number; with its unit, mol⁻¹, it is the Avogadro constant.
Carbon-12 still sets the relative atomic mass scale
Only one thing about carbon-12 stopped being exact: its molar mass, written M(¹²C). The relative atomic mass of carbon-12 is still, by definition, the number 12. That atom's mass in kilograms was already a measured value before 2019.
School notation hides the distinction. Relative molecular mass, Mr, is a pure number. Molar mass, M, carries the unit g/mol. The two used to match numerically because the factor between them was exactly 1.
The molar mass constant now carries a measured uncertainty
That factor is the molar mass constant, Mu, equal to M(¹²C) divided by 12. The Brochure says M(¹²C) "must be determined experimentally", and IUPAC draws the consequence: Mu "is no longer 1 g mol⁻¹ exactly".
The change of definition did not itself shift the number. At adoption M(¹²C) equalled 0.012 kg/mol with a relative standard uncertainty of 4.5 × 10⁻¹⁰, a standard uncertainty being a statement of how far a measured value could plausibly be off. CODATA's task group on fundamental constants publishes each value with its uncertainty. In its 2022 table Mu reads 1.000 000 001 05 ± 0.000 000 000 31 g/mol. In parts per billion (ppb), the measured value sits 1.05 above 1 and could be off by 0.31.
CODATA's 2022 table already reads above the old exact value
The central value and the uncertainty are distinct, as the two adjustments published since the redefinition show. The last column is our arithmetic.
| CODATA | Gap from 1 g/mol, ppb | Uncertainty, ppb | Gap ÷ uncertainty |
|---|---|---|---|
| 2018 | −0.35 | 0.30 | −1.2 |
| 2022 | +1.05 | 0.31 | +3.4 |
The sign changed. The 2018 value was consistent with 1 g/mol; the 2022 value sits 3.4 standard uncertainties above it.
IUPAC wrote in 2017, before any adjustment under the new definition, that Mu remains 1 g/mol within its uncertainty. On CODATA 2022 that no longer holds strictly, while the practical conclusion does: the uncertainty is still under IUPAC's one part in a billion. The CODATA 2022 paper says Mu is proportional to α⁻², where α is the fine-structure constant, and the change in tabulated α accounts for almost all of the move, by our arithmetic. CODATA adjusts every four years, so the next table may move the figure again.
Graphite at twelve grams was not quite a mole under the old definition
A 1980 note from the International Committee for Weights and Measures read the 1971 definition as applying to unbound atoms at rest and in their ground state. IUPAC's final text concludes that 0.012 kg of pure carbon-12 as graphite is "not exactly 1 mol" under that definition if solid and at room temperature, an error it calls negligible and similar in size to the relative uncertainty of Mu.
Our order-of-magnitude check agrees. Graphite's atomisation enthalpy of 716.68 ± 0.45 kJ/mol, a 298 K figure converted through E = mc², comes to about 0.66 ppb of 12 g. Bound atoms weigh less, so 12 g of graphite holds slightly more atoms than 12 g of unbound ones, whereas the +1.05 ppb in Mu points to fewer. We give no net figure.
Even school-level rounding dwarfs the gap hundreds of thousands of times over
The ladder uses water, with abridged atomic weights giving M = 18.015 g/mol. Sizes are our arithmetic, scaled to the CODATA 2022 central value.
| Source of difference | Step it touches | Relative size | Order, against the Mu gap |
|---|---|---|---|
| Rounding M to 18 | Mass to moles | 8.3 × 10⁻⁴ | 10⁵ |
| 0.01 g reading on 18 g | Measured mass | 5.6 × 10⁻⁴ | 10⁵ |
| Using 6.02 for the constant | Moles to particles | 3.55 × 10⁻⁴ | 10⁵ |
| Using 6.022 for the constant | Moles to particles | 2.34 × 10⁻⁵ | 10⁴ |
| Full IUPAC span for H₂O | Mass to moles | 7.1 × 10⁻⁵ | 10⁴ |
| 0.1 mg reading on 18 g | Measured mass | 5.6 × 10⁻⁶ | 10³ |
| Mu gap, CODATA 2022 | Mass to moles | 1.05 × 10⁻⁹ | 1 |
The rows do not add up. A balance reading is resolution, never uncertainty, and the water span is a bound from the CIAAW intervals at both extremes, which fourteen elements with no single weight covers. The Avogadro rows are unaffected by Mu, because counting from moles uses only the fixed constant.
Applied to 18.015 g of water, the Mu gap is about 19 ng of mass. Our mole conversion calculator works from the molar mass you type: mass 18.015 g with molar mass 18.015 g/mol returns 1.0000 mol and 6.0221 × 10²³ particles. Until 1 November 2026 it read its own output shape, 6.02×10²³, as 6.02 particles, and on its Indonesian page turned 0,5 into 5 mol. The fix dated that day reads both correctly and refuses ambiguous input.
Cambridge still prints the constant to different precision by level
The only exam syllabuses we read are Cambridge's, and they do not print one figure. Its IGCSE Chemistry 0620 syllabus for 2026–2028 says, in Supplement content, "one mole contains 6.02 × 10²³ particles". Its A Level Chemistry 9701 syllabus for 2025–2027 prints L = 6.022 × 10²³ mol⁻¹, with the unit attached. Both round the fixed value, by the amounts in the ladder. Molar volume brings conditions of its own, set out in why 22.4 litres needs a pressure. Neither syllabus gives the nine digits the SI fixed in 2019, and a paper's working figure is the one that paper states.
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