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SI 2019 base
Symbol plate SI-B-03 s Latin, lowercasenot "sec"
Unit passport sheet 1 / 1 · revision 2026-08

Second

SI base unit · quantity: time

Symbol s
Defined via Δν(¹³³Cs) = 9 192 631 770 Hz
Atomic definition CGPM, 1967
Reformulated CGPM, 2018 · in force since 2019
Realisation accuracy 10⁻¹⁶ · optical clocks 10⁻¹⁸
Translations ready 24 / 33
Convert a time Historical definitions
01 · Definition

For thousands of years the second was counted out by the rotation of the Earth. In 1967 it was untied from the planet and tied to the caesium atom — the Earth had turned out to be an insufficiently precise clock.

A second is 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. The number looks arbitrary, but it was chosen so that the new second matched the old, astronomical one to the precision of the day. The Earth has slowed since: a day is a couple of milliseconds longer than 86 400 seconds, and the difference is absorbed by inserting a leap second.

Formally
1 s = 9 192 631 770 / Δν(Cs)
Δν(¹³³Cs) = 9 192 631 770 Hz — an exact value by definition, with no uncertainty
¹³³Cs
caesium · the only isotope
9 192 631 770
periods · exactly
9.19 GHz
transition frequency
Chronometer · 60 s dial s
90 s
1 min · 30 s
1 s
Decimal downwards, sexagesimal upwards

Below the second run the SI prefixes: ms, µs, ns, ps. Above it — the Babylonian inheritance: minute, hour, day. Kiloseconds never occur in real life, though formally they are legal.

02 · Conversion

Enter an interval — the passport will convert it

Time is the only quantity where the SI coexists with the sexagesimal system: minutes and hours are not part of the SI, yet they are accepted for use on a par with the second. The year in the table is the Julian one, 365.25 days: it is the year behind the light year.

The minute, the hour and the day are exact multiples of the second by definition: 60, 3600, 86 400. A calendar day, however, may contain 86 401 seconds: a leap second is inserted whenever the divergence from the Earth's rotation reaches 0.9 s.

Conversion table
90 s = 90 s
UnitNameValueWhere it appears
ns nanosecond 9·10¹⁰ CPU cycles, network latency, GPS
µs microsecond 9·10⁷ electronics measurements, response times
ms millisecond 90 000 human reaction, video frames, ping
s second 90 the base notation of time in the SI
min minute 1.5 outside the SI, accepted: timetables, sport
h hour 0.025 outside the SI, accepted: work, tariffs
d day 0.001042 outside the SI, accepted: calendars, deadlines
wk week 1.488·10⁻⁴ daily life and planning, outside the SI
a year (Julian) 2.852·10⁻⁶ 365.25 days — the year of the light year

1 min = 60 s · 1 h = 3600 s · 1 d = 86 400 s — exact multiples by definition

03 · Orders of magnitude
from the yoctosecond to the age of the Universe

Second: a heartbeat

1 s
in human terms: 1 s
10⁻²⁴
10⁻¹⁸
10⁻¹²
10⁻⁶
10⁰
10⁶
10¹²
10¹⁸
04 · Measuring instruments

What counts out the seconds

laboratory · satellite · wristwatch
Caesium fountain

The primary standard: a cloud of cooled atoms is tossed upwards and probed twice with microwaves. Instability 10⁻¹⁶.

Optical lattice clocks

A strontium or ytterbium ion in a laser lattice. Accuracy 10⁻¹⁸ — the candidates for a new definition of the second.

32 768 Hz
Quartz resonator

A quartz tuning fork at 2¹⁵ hertz: halving fifteen times yields exactly one second. Watches, phones, meters.

GNSS receiver

Every satellite carries atomic clocks; the receiver takes the time from the sky for free. Nanoseconds — all of navigation rests on them.

05 · Writing rules

The symbol is lowercase: s, not "sec" and not "sec."

The second is not named after a person, so the symbol is lowercase and takes no full stop. "Sec" and "msec" belong to the typewriter era; in the SI they are s and ms. Minutes and hours are written min and h, and the time of day with a colon: 14:05, not 14 h 05 min.

Correct
30 s
250 ms
1.5 h
Incorrect
30 sec.
250 msec
30S
06 · Neighbouring units

The second sits in the denominator of half the SI: the hertz is an inverse second, the becquerel is one decay per second, the metre per second is speed. Knock the second off, and all three drift.

Hz
frequency
1 / s
s
time
SI base
m/s
speed
metre per second
1 Hz = 1/s   1 m = c · 1 s / 299 792 458

The metre, too, grew out of the second: since 1983 it has been defined via the speed of light and the second — meaning the accuracy of length can never exceed the accuracy of time.

07 · Historical section

What the second was before the atom

archive · withdrawn from use
Antiquity · until 1956
1/86400
Mean solar second

A fraction of the mean solar day. The Earth slows unevenly, so this second slowly drifted.

≈ 1.000 000 02 s
CGPM · 1956–1967
ephem.
Ephemeris second

A fraction of the tropical year 1900.0: time was tied to the Earth's orbit around the Sun rather than to the day.

the basis of today's number 9 192 631 770
Astronomy · in use
sider.
Sidereal second

A fraction of the sidereal day — the Earth's rotation relative to the stars. Shorter than the ordinary one by 0.27 %.

0.997 269 566 s
Babylon · 16th century
tierce
The third division

The sexagesimal series did not end at the second: after the "second small part" came the third, 1/60 of a second.

displaced by the millisecond
Metrological note

The second is the most precise unit in the SI, and the others depend on it

The kilogram is realised to 10⁻⁸, the metre to 10⁻¹¹, and the second to 10⁻¹⁶ in a caesium fountain and to 10⁻¹⁸ in optical clocks. That is why the definitions of the metre, the candela, the ampere and the volt are built on the second: it sets the precision ceiling for the whole system. Such clocks would err by less than a second over the lifetime of the Universe — which is exactly why another redefinition, no longer on caesium, is under discussion.

Catalogue · International System of Units

A passport for every quantity

Seven base units, twenty-two derived ones with names of their own, and an archive of systems withdrawn from use. Each is a separate sheet: definition, dimension, conversion, instruments, writing rules. In 33 languages.

7
base
22
derived
33
languages

Base units

open the passport of the second
s
second
time
m
metre
length
kg
kilogram
mass
A
ampere
electric current
K
kelvin
temperature
mol
mole
amount of substance
cd
candela
luminous intensity

Derived units with names of their own

in terracotta — those whose definition contains the second
Hz 1/s
hertz
frequency
Bq 1/s
becquerel
activity
N kg·m/s²
newton
force
Pa N/m²
pascal
pressure
J N·m
joule
energy
W J/s
watt
power
C A·s
coulomb
charge
V W/A
volt
voltage
Ω V/A
ohm
resistance
F C/V
farad
capacitance
S A/V
siemens
conductance
Wb V·s
weber
magnetic flux
T Wb/m²
tesla
flux density
H Wb/A
henry
inductance
lm cd·sr
lumen
luminous flux
lx lm/m²
lux
illuminance
Gy J/kg
gray
absorbed dose
Sv J/kg
sievert
equivalent dose
kat mol/s
katal
catalytic activity
°C K
degree Celsius
temperature
rad m/m
radian
plane angle
sr m²/m²
steradian
solid angle

Historical systems

archive of notations
1/86400
mean solar
ephem.
ephemeris, 1956
sider.
sidereal
tierce
1/60 of a second
watch
night watch, 3 h
helek
1/1080 of an hour, Talmud

Passport language

33 languages. The symbol s and the formulas are not translated — they are identical in every locale; what is translated is the description, the examples and the writing rules for each script.

EN English
RU Русский DE Deutsch FR Français ES Español PT Português IT Italiano NL Nederlands PL Polski SV Svenska DA Dansk FI Suomi NB Norsk CS Čeština SK Slovenčina RO Română EL Ελληνικά HU Magyar TR Türkçe
AR العربية
FA فارسی
ZH 中文(简) ZH-HANT 中文(繁) JA 日本語 KO 한국어
TH ไทย
VI Tiếng Việt
HI हिन्दी
BN বাংলা
ID Bahasa Indonesia
MS Bahasa Melayu
TA தமிழ்
LA Latina
translated and verified draft translation queued