Sevres.science / The SI

The seven defining constants

The seven numbers

• Hyperfine transition frequency of caesium-133 → secondΔν_Cs = 9 192 631 770 Hz
• Speed of light in vacuum → metrec = 299 792 458 m/s
• Planck constant → kilogramh = 6.626 070 15 × 10⁻³⁴ J s
• Elementary charge → amperee = 1.602 176 634 × 10⁻¹⁹ C
• Boltzmann constant → kelvink = 1.380 649 × 10⁻²³ J/K
• Avogadro constant → moleN_A = 6.022 140 76 × 10²³ mol⁻¹
• Luminous efficacy of 540 THz radiation → candelaK_cd = 683 lm/W

Three were already fixed

The caesium frequency has defined the second since 1967–1968. The speed of light has defined the metre since 1983. The luminous efficacy K_cd has defined the candela since 1979. The 2019 revision kept all three as they were.

Why constants rather than objects

For 130 years the kilogram was a single object kept in a vault in Sèvres. Everything that weighed anything in the SI depended on that one cylinder. Its mass was exactly one kilogram by definition, so if it changed, nobody could tell: the whole world’s kilogram would change with it.

A constant of nature has no such weakness. The speed of light or the Planck constant is the same in every laboratory and at every time, so anyone with the right experiment can realise the unit without travelling to Sèvres. The definitions also stop depending on the technology of a given century, so better experiments simply give better realisations.

Four were fixed in 2018

In November 2018 the 26th General Conference on Weights and Measures fixed the values of the Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant. The numbers were taken from a special adjustment of the best measurements available, prepared by CODATA in 2017.

The values were chosen to match the old units as closely as measurement allowed, so that the switch would not be noticed in daily life. The previous definitions of all seven base units were withdrawn at the same time.

What became measured instead

Fixing four constants meant releasing four other numbers that had been exact by definition. The mass of the International Prototype of the Kilogram, the temperature of the triple point of water (273.16 K), the molar mass of carbon-12 (0.012 kg/mol) and the magnetic constant μ₀ are now determined by experiment.

On the day of the switch each still had its old value, now with a small uncertainty: between about two parts in ten billion (the magnetic constant) and four parts in ten million (the triple point of water). Future measurements may shift them very slightly.

Did anything change for you?

No. The BIPM’s advice to users is that ordinary measurements are not affected, and that measurements made under the old definitions remain valid within their stated uncertainties. Scales, thermometers and rulers did not need recalibrating. The work fell on national metrology institutes and the most precise laboratories.

Measured first, fixed later

Before the four constants could be fixed, they had to be measured with an uncertainty small enough not to disturb the units. The Planck constant was measured with Kibble balances and, through the Avogadro constant, with spheres of silicon-28. Those same experiments are now used the other way round: with the constant fixed, they realise the kilogram.

What may change next

The caesium frequency that defines the second may itself be replaced. Optical clocks now outperform the caesium fountains by about two orders of magnitude, and work is under way on a new definition, based either on one optical transition or on a combination of several. In 2026 the General Conference asked for a proposal to be presented at its next meeting, in 2030, noting that no consensus on the approach had yet been reached. For everyday timekeeping nothing will change.