On the left a brass pendulum swings: a full swing takes 2 s, a single pass exactly one second. The letter s shows through it. On the right a caesium atom rises in the tube of an atomic fountain and falls back. Each time it passes through the copper cavity, it flashes in the microwaves. The display reads 9 192 631 770 — that many oscillations fit into one second. A recording light blinks.
Quantity data sheet
SI base unitrev. 2026-10Second s
SI base unit · quantity: time
The second was taken from the Earth and given to the atom
For a long time the second was a fraction of the day: 1/86 400 of one turn of the Earth. Then it turned out that the Earth is a poor clock. It slows down because of the tides, and earthquakes and currents in its core change the length of its day by milliseconds. Clocks that ran more steadily than the Earth began to notice its uneven pace.
Since 1967 the second has been set by the caesium-133 atom. Its outer electron can switch between two levels, and this transition corresponds to radiation with a frequency of exactly 9 192 631 770 Hz. The second is the time it takes for that many oscillations to pass. All caesium atoms are identical, so the second is the same in any laboratory in the world.
The best caesium fountains err by less than one second in 300 million years. Other units depend on the second too: the metre is fixed through the speed of light and the second, and the kilogram through the Planck constant, the metre and the second.
The symbol of the second is a lowercase s, with no full stop: “30 s”. In Russian it is written «с». Capital S is the siemens, the unit of conductance. The quantity time is written with a lowercase t, the period of oscillation with a capital T.
The second of time and the second of arc, ″ — 1/3600 of a degree. The clock day and one turn of the Earth: the Earth rotates unevenly, and its day is longer than 86 400 s by a millisecond or two. That is why a leap second is sometimes added to atomic time.
01 · Definition
oscillations · counting · clock driftAll clocks are built the same way. Inside there is something that repeats one motion at equal intervals: a pendulum, a quartz plate, an electron in an atom. And there is a counter that counts the repeats. The second is simply an agreement on how many repeats of which motion to count.
The higher the frequency of the oscillations and the less it depends on outside conditions, the more accurate the clock. A pendulum swings once a second, and its period changes with temperature because the rod lengthens. Quartz oscillates 32 768 times a second and also feels the heat. The caesium atom oscillates almost ten billion times a second, and almost nothing affects its frequency.
The accuracy of a clock is shown by its drift — how far it will part from the standard in a day. The fraction by which the frequency differs from the right one, multiplied by 86 400 s, is the drift per day.
How far the clocks will drift apart
A pendulum clock, a quartz clock and an atomic clock stand on a shelf. All three were set by the standard and then left in a room at a given temperature. In the pendulum the steel rod lengthens with heat, and it runs slower. Quartz is accurate at 25 °C and lags at any other temperature. Temperature hardly matters to the atomic clock. Move time forward with the “days passed” slider; the “Year” button sets 365 days at once, and above each clock its drift is shown. Blue shows the standard, brass the pendulum, green the atomic clock, red the lag. Below are three views. “Drift” is the accumulated error of each instrument by day on a logarithmic scale. “Oscillations” is the motion of each oscillator, slowed down to visible. “Accuracy” is the fractional error of different clocks, from sundials to optical clocks.
A number that is easy to halve
32 768 is two to the fifteenth power. An electronic circuit of fifteen frequency halvers turns the oscillations of quartz into exactly one pulse per second. A quartz tuning fork for this frequency is a few millimetres long and fits into a wristwatch. A higher frequency is not used: such a tuning fork would consume more power.
02 · Conversion
units · frequency · time scalesFrom seconds to days, years and hertz
Enter a time in any unit. The first tab converts it to seconds, minutes, hours, days and years. The second gives the frequency and the number of caesium oscillations. The third shows how the time scales TAI, UTC and GPS differ.
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The shortest laser flashes last a few tens of attoseconds; the age of the Universe is about 4·10¹⁷ s. Between them lie 35 orders of magnitude. The same second serves as the measure for light and for stars.
04 · Measuring instruments
pendulum · quartz · fountain · optical latticeThe higher the frequency, the more accurate the clock
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05 · Writing rules
s without a full stop · time of day separatelyDuration in seconds, an instant by the clock
A duration is written as a number and a symbol with a space: 45 s, 2.5 ms. An instant is written according to ISO 8601: 2026-10-02T14:30:05Z. The minute and the hour may be used with the SI, but prefixes are not attached to them.
“sec”, “msec” and “hrs” are not SI symbols. A time of day is more convenient with colons, and a duration with units. A date with slashes is read differently in different countries, so year-month-day is used. Capital S is the siemens, not the second; thousands are separated by a space.
06 · Neighbouring units
time and frequency1 Hz = 1/s — oscillations per second.
mThe path of light in 1/299 792 458 s.
d86 400 s — and the uneven turn of the Earth.
07 · Historical section
archive · from Huygens’s pendulum to the atomic fountainHow the second moved from the sky to the atom
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The leap second and its abolition
Atomic time TAI runs steadily, while the Earth rotates unevenly and, on average, more slowly. To keep civil clocks from drifting away from solar noon, a leap second was added to UTC from 1972 — 27 times, the last on 31 December 2016. On such days a minute lasted 61 seconds.
For computers, exchanges and navigation an extra second is a source of failures. In 2022 the General Conference on Weights and Measures decided to stop adding leap seconds no later than 2035 and to let UTC drift further from the rotation of the Earth.
On the right is a clock face at the moment of a leap second: after 23:59:59 the clock shows 23:59:60, and only then does midnight come.
Catalogue of quantities
Time and frequency · 12 unit sheets
Index · all quantities on one pageThe lab at the entrance to the indexA drop of acid changes the colour of the juice, salt colours the flame, water freezes at a tap. Below them are all Simetrium sheets, by discipline and alphabetically.Open the index →
