Second

The second, symbol s, is the base unit of time in the International System of Units (SI). Its definition fixes the frequency of a particular transition in the caesium-133 atom at exactly 9,192,631,770 hertz. This atomic reference provides a reproducible standard independent of irregularities in Earth’s rotation and underlies modern scientific and civil timekeeping. (bipm.org)

Definition

The defining quantity is the unperturbed ground-state hyperfine transition frequency of caesium-133, written $\Delta\nu_{\mathrm{Cs}}$. Its numerical value is fixed by the exact relation

where the hertz equals one inverse second. Equivalently, one second is the duration of 9,192,631,770 periods of the electromagnetic radiation corresponding to that transition. The reference is an atomic transition frequency, not a mechanical rotation or vibration of the whole atom. (bipm.org)

“Unperturbed” distinguishes the ideal defining frequency from frequencies observed under experimental conditions. A laboratory must account for effects that shift its measured resonance rather than treating any caesium clock reading as an exact realization. The distinction between an exact definition and a realization with finite measurement uncertainty is fundamental to metrology. Modern caesium fountain standards realize the definition with fractional uncertainties approaching $10^{-16}$. (nist.gov)

Historical development

Before the atomic definition, the second was associated with astronomical timekeeping. It was traditionally defined as $1/86\,400$ of the mean solar day. Observations showed that irregularities in the rotation of Earth made this an inadequate reference for increasingly precise measurements. A replacement, the ephemeris second, used a specified fraction of the tropical year associated with 1900. The international metrological authorities approved it in 1956, and the General Conference on Weights and Measures (CGPM) adopted it in 1960. (nvlpubs.nist.gov)

Experiments connected the new atomic reference to this astronomical standard. Comparisons between the United Kingdom’s National Physical Laboratory and the United States Naval Observatory, conducted from 1955 to 1958, yielded a caesium frequency of 9,192,631,770 cycles per ephemeris second, with an estimated uncertainty of ±20 cycles per second. That measurement supplied the number subsequently made exact in the atomic definition, preserving continuity with the earlier unit. (nvlpubs.nist.gov)

The CGPM adopted the caesium-based definition in 1967. In 2018 it approved revised wording that expressed the definition through a fixed numerical value of the caesium frequency. This retained the same atomic reference rather than changing the duration of the unit. (bipm.org)

Practical realization

An atomic clock uses atomic resonance to establish a frequency reference. In a caesium fountain, laser beams slow and cool atoms, then launch them upward through a microwave cavity. Under gravity, the atoms fall through the cavity again. Their interaction with the microwaves changes the populations of the two clock states; optical detection reveals how strongly the atoms responded. Repeated measurements allow the microwave frequency to be adjusted toward the atomic resonance. (nist.gov)

The fountain geometry permits longer observation times than conventional clocks using fast-moving atomic beams. Longer interrogation, together with control of atomic motion and frequency biases, improves the precision of the reference. These devices do not simply display civil time: they also calibrate other clocks and measure the rate of time scales against the SI second. (nist.gov)

Notation and related units

The symbol s is written in upright type, does not take a plural ending, and is separated from a numerical value by a space: 15 s. Decimal prefixes form smaller units, including the millisecond ($10^{-3}$ s), microsecond ($10^{-6}$ s), and nanosecond ($10^{-9}$ s). A minute equals 60 s, an hour 3,600 s, and a day as a unit of duration 86,400 s. (bipm.org)

The second also enters derived units: frequency is measured in inverse seconds, speed in metres per second, and acceleration in metres per second squared. Its role extends to other base-unit definitions. The metre depends on the fixed speed of light together with the second; the kilogram depends on the fixed Planck constant and the definitions of the metre and second. (bipm.org)

Atomic and civil time scales

A unit of duration is distinct from a time scale assigning dates and clock readings. The International Bureau of Weights and Measures computes International Atomic Time (TAI), a continuous scale based on realizations of the SI second and data contributed by timing laboratories worldwide. (bipm.org)

Coordinated Universal Time (UTC) is derived from TAI using leap seconds to maintain approximate agreement with time determined by Earth’s rotation. UTC and TAI have the same rate but differ by an integer number of seconds. A leap second adjusts the numbering of civil time; it does not redefine or lengthen the SI second. (bipm.org)

Prospective optical definition

Optical clocks have surpassed the best caesium fountain realizations, with some achieving substantially smaller systematic uncertainties. Proposed definitions would fix either one optical atomic transition frequency or a weighted geometric average of several transition frequencies. Readiness criteria include reliable international comparisons, contributions to time scales, and continuity with the caesium-based unit. (bipm.org)

As of October 2026, the second remains caesium-defined. The BIPM’s September 2026 account describes a draft resolution requesting further work toward a proposal for the 2030 CGPM, together with a recommendation for implementation timing. This is a prospective change, not an adopted optical definition. (bipm.org)