Chapter 3: The Seven SI Base Units

Every physical quantity used in science is ultimately expressed in terms of seven base units, one for each of the seven base quantities discussed in Chapter 1. This chapter lists each base unit's name, symbol, the quantity it measures, and — most importantly for competitive exams — its precise modern definition as fixed by the 2019 redefinition of the SI, which ties every base unit to an unchanging constant of nature rather than to a physical object or a specific laboratory procedure.

3.1 Overview Table of SI Base Units

3.2 Detailed Definitions (Post-2019 Redefinition)

Metre (m) — unit of length

The metre is defined by taking the fixed numerical value of the speed of light in vacuum, c, to be 299,792,458 when expressed in the unit metre per second, where the second is defined in terms of the caesium frequency. In simple terms, the metre is the distance travelled by light in vacuum in exactly 1/299,792,458 of a second. This definition, adopted in 1983 (and retained through the 2019 redefinition), replaced the earlier krypton-86 wavelength standard (1960) and, before that, the original platinum-iridium metre bar kept in Paris.

Kilogram (kg) — unit of mass

The kilogram is defined by taking the fixed numerical value of the Planck constant, h, to be 6.62607015 × 10⁻³⁴ when expressed in the unit joule-second (kg·m²·s⁻¹), with the metre and second already defined. This 2019 definition replaced the famous International Prototype of the Kilogram (IPK), a cylinder of platinum-iridium alloy kept at the BIPM near Paris since 1889, which had been the sole physical artefact defining any SI base unit — a fact frequently asked in exams. The kilogram remains the only SI base unit whose name historically carries a prefix ("kilo").

Second (s) — unit of time

The second is defined by taking the fixed numerical value of the caesium frequency, ΔνCs — the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom — to be 9,192,631,770 when expressed in the unit hertz (s⁻¹). In simple language, one second is the time taken for 9,192,631,770 oscillations of the radiation emitted during a specific transition between two energy levels of a caesium-133 atom, as measured by atomic clocks. This atomic definition, adopted in 1967, replaced older astronomical definitions based on the rotation of the Earth or its orbit around the Sun.

Ampere (A) — unit of electric current

The ampere is defined by taking the fixed numerical value of the elementary charge, e, to be 1.602176634 × 10⁻¹⁹ when expressed in the unit coulomb (A·s). Before 2019, the ampere was defined by the force between two long parallel current-carrying conductors placed one metre apart in vacuum. The new definition is exactly equivalent in practice but is now tied to a fundamental constant rather than to an idealised experimental set-up.

Kelvin (K) — unit of thermodynamic temperature

The kelvin is defined by taking the fixed numerical value of the Boltzmann constant, k, to be 1.380649 × 10⁻²³ when expressed in the unit joule per kelvin (kg·m²·s⁻²·K⁻¹). Before 2019, the kelvin was defined using the triple point of water (273.16 K), a specific, reproducible physical condition where ice, liquid water, and water vapour coexist in equilibrium. The kelvin scale has no negative values; 0 K, called absolute zero, is the theoretical lowest possible temperature. Note that kelvin is written without a degree symbol ("°"), unlike Celsius and Fahrenheit — this is a commonly tested distinction.

Mole (mol) — unit of amount of substance

The mole is defined by taking the fixed numerical value of the Avogadro constant, NA, to be 6.02214076 × 10²³ when expressed in the unit per mole (mol⁻¹). One mole of any substance therefore contains exactly 6.02214076 × 10²³ elementary entities (atoms, molecules, ions, electrons, or other specified particles) — this fixed number is called the Avogadro number/constant. Before 2019, the mole was linked to the number of atoms in exactly 12 grams of carbon-12.

Candela (cd) — unit of luminous intensity

The candela is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² hertz, Kcd, to be 683 when expressed in the unit lumen per watt (lm/W, equivalent to cd·sr·kg⁻¹·m⁻²·s³). This frequency corresponds to green light, near the peak sensitivity of the human eye. The candela measures luminous intensity — the perceived power of light emitted by a source in a particular direction, as sensed by the human eye — and was the only SI base unit definition left essentially unchanged in substance by the 2019 redefinition.

3.3 Two Supplementary (Dimensionless) SI Units

Besides the seven base units, SI recognises two supplementary units used to measure angles. These are dimensionless (they have no associated physical dimension) but are extremely important and are frequently tested.