# Unit of time

A unit of time or midst unit is any particular time interval, used as a standard way of measuring or expressing duration. The base unit of time in the International System of Units (SI), and by extension most of the Western world, is the second, defined as about 9 billion oscillations of the caesium atom. The exact modern definition, from the National Institute of Standards and Technology is:

The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.[1]

Historically units of time were defined by the movements of astronomical objects.

• Sun based: the year was the time for the earth to revolve around the sun. Year-based units include the olympiad (four years), the lustrum (five years), the indiction (15 years), the decade, the century, and the millennium.
• Moon based: the month was based on the moon's orbital period around the earth.
• Earth based: the time it took for the earth to rotate on its own axis, as observed on a sundial. Units originally derived from this base include the week at seven days, and the fortnight at 14 days. Subdivisions of the day include the hour (1/24th of a day) which was further subdivided into minutes and finally seconds. The second became the international standard unit (SI units) for science.
• Celestial sphere based: as in sidereal time, where the apparent movement of the stars and constellations across the sky is used to calculate the length of a year.

These units do not have a consistent relationship with each other and require intercalation. For example, the year cannot be divided into 12 28-day months since 12 times 28 is 336, well short of 365. The lunar month (as defined by the moon's rotation) is not 28 days but 28.3 days. The year, defined in the Gregorian calendar as 365.24 days has to be adjusted with leap days and leap seconds. Consequently, these units are now all defined as multiples of seconds.

Units of time based on orders of magnitude of the second include the nanosecond and the millisecond.

Visual Gregorian calendar

## Historical

The natural units for timekeeping used by most historical societies are the day, the solar year and the lunation. Such calendars include the Sumerian, Egyptian, Chinese, Babylonian, ancient Athenian, Buddhist, Hindu, Islamic, Icelandic, Mayan, and French Republican calendars.

The modern calendar has its origins in the Roman calendar, which evolved into the Julian calendar, and then the Gregorian.

Horizontal logarithmic scale marked with units of time in the Gregorian calendar

## Scientific time units

• The jiffy is the amount of time light takes to travel one fermi (about the size of a nucleon) in a vacuum.
• Planck time is the time light takes to travel one Planck length. Theoretically, this is the smallest time measurement that will ever be possible. Smaller time units have no use in physics as we understand it today.
• The TU (for Time Unit) is a unit of time defined as 1024 µs for use in engineering.
• The Svedberg is a time unit used for sedimentation rates (usually of proteins). It is defined as 10−13 seconds (100 fs).
• The galactic year, based on the rotation of the galaxy, and usually measured in million years.[2]
• The geological time scale relates stratigraphy to time. The deep time of Earth’s past is divided into units according to events which took place in each period. For example, the boundary between the Cretaceous period and the Paleogene period is defined by the Cretaceous–Paleogene extinction event. The largest unit is the supereon, composed of eons. Eons are divided into eras, which are in turn divided into periods, epochs and ages. It is not a true mathematical unit, as all ages, epochs, periods, eras or eons don't have the same length; instead, their length is determined by the geological and historical events that define them individually.

Note: The light-year is not a unit of time, but a unit of length of about 9.5 trillion kilometres (9,454,254,955,488 kilometres).

## Units of time interrelated

Flowchart illustrating the major units of time

All of the important units of time can be interrelated. The key units are the second, defined in terms of an atomic process; the day, an integral multiple of seconds; and the year, usually 365 days. Most of the other units used are multiples or divisions of these three. The graphic also shows the three heavenly bodies whose orbital parameters relate to the units of time.

## References

1. ^ "Definitions of the SI base units". The NIST reference on Constants, Units, and Uncertainty. National Institute of Standards and Technology. Retrieved 4 March 2016.
2. ^ a b http://starchild.gsfc.nasa.gov/docs/StarChild/questions/question18.html NASA - StarChild Question of the Month for February 2000
3. ^ "It only takes a zeptosecond: Scientists measure smallest fragment of time". RT International. Retrieved 2017-04-20.
4. ^ Milham, Willis I. (1945). Time and Timekeepers. New York: MacMillan. p. 190. ISBN 0-7808-0008-7.
5. ^ "Semester". Webster's Dictionary. Retrieved 3 December 2014.
6. ^ McCarthy, Dennis D.; Seidelmann, P. Kenneth (2009). Time: from Earth rotation to atomic physics. Wiley-VCH. p. 18. ISBN 3-527-40780-4., Extract of page 18
7. ^ Jones, Floyd Nolen (2005). The Chronology Of The Old Testament (15th ed.). New Leaf Publishing Group. p. 287. ISBN 0-89051-416-X., Extract of page 287
Billion years

A billion years (109 years) is a unit of time on the petasecond scale, more precisely equal to 3.16×1016 seconds.

It is sometimes abbreviated Gy, Ga ("giga-annum"), Byr and variants. The abbreviations Gya or bya are for "billion years ago", i.e. billion years before present.

The terms are used in geology, paleontology, geophysics, astronomy and physical cosmology.

The prefix giga- is preferred over billion- to avoid confusion in the long and short scales over the meaning of billion; the postfix annum may be further qualified for precision as a sidereal year or Julian year:

1 Gaj=3.15576×1016 s,

1 Gas=3.15581×1016 s (epoch J2000.0).

1 Gas=1×109 yByr was formerly used in English-language geology and astronomy as a unit of one billion years. Subsequently, the term gigaannum (Ga) has increased in usage, with Gy or Gyr still sometimes used in English-language works (at the risk of confusion with Gy as abbreviation for the gray, a unit of radiation exposure). Astronomers use Gyr or Gy as an abbreviation for gigayear.

Chronon

A chronon is a proposed quantum of time, that is, a discrete and indivisible "unit" of time as part of a hypothesis that proposes that time is not continuous.

Day

A day is approximately the period of time during which the Earth completes one rotation around its axis. A solar day is the length of time which elapses between the Sun reaching its highest point in the sky two consecutive times.In 1960, the second was redefined in terms of the orbital motion of the Earth in year 1900, and was designated the SI base unit of time. The unit of measurement "day", was redefined as 86,400 SI seconds and symbolized d. In 1967, the second and so the day were redefined by atomic electron transition. A civil day is usually 86,400 seconds, plus or minus a possible leap second in Coordinated Universal Time (UTC), and occasionally plus or minus an hour in those locations that change from or to daylight saving time.Day can be defined as each of the twenty-four-hour periods, reckoned from one midnight to the next, into which a week, month, or year is divided, and corresponding to a rotation of the earth on its axis. However its use depends on its context, for example when people say 'day and night', 'day' will have a different meaning. It will mean the interval of light between two successive nights; the time between sunrise and sunset, in this instance 'day' will mean time of light between one night and the next. However, in order to be clear when using 'day' in that sense, "daytime" should be used to distinguish it from "day" referring to a 24-hour period; this is since daytime usually always means 'the time of the day between sunrise and sunset. The word day may also refer to a day of the week or to a calendar date, as in answer to the question, "On which day?" The life patterns (circadian rhythms) of humans and many other species are related to Earth's solar day and the day-night cycle.

Exponential growth

Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function of time is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent. Exponential decay occurs in the same way when the growth rate is negative. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay, the function values forming a geometric progression. In either exponential growth or exponential decay, the ratio of the rate of change of the quantity to its current size remains constant over time.

The formula for exponential growth of a variable x at the growth rate r, as time t goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is

${\displaystyle x_{t}=x_{0}(1+r)^{t}}$

where x0 is the value of x at time 0. This formula is transparent when the exponents are converted to multiplication. For instance, with a starting value of 50 and a growth rate of r = 5% = 0.05 per interval, the passage of one interval would give 50 × 1.051 = 50 × 1.05; two intervals would give 50 × 1.052 = 50 × 1.05 × 1.05; and three intervals would give 50 × 1.053 = 50 × 1.05 × 1.05 × 1.05. In this way, each increase in the exponent by a full interval can be seen to increase the previous total by another five percent. (The order of multiplication does not change the result based on the associative property of multiplication.)

Since the time variable, which is the input to this function, occurs as the exponent, this is an exponential function. This contrasts with growth based on a power function, where the time variable is the base value raised to a fixed exponent, such as cubic growth (or in general terms denoted as polynomial growth).

Flick (time)

A flick is a unit of time equivalent to exactly 1/705,600,000 of a second. The figure was chosen so that frequencies of 24, 25, 30, 48, 50, 60, 90, 100 and 120 Hz, as well as 1/1000 divisions of all those, can be represented with integers. The unit was launched in January 2018 by Facebook. A flick is approximately 1.42 × 10−9 s, which makes it larger than a nanosecond but much smaller than a microsecond.

A similar unit for integer representation of temporal points was proposed in 2004 under the name TimeRef, splitting a second into 14,112,000 parts. This makes 1 TimeRef equivalent to 50 Flicks.

Fortnight

A fortnight is a unit of time equal to 14 days (2 weeks). The word derives from the Old English: fēowertyne niht, meaning "fourteen nights".Some wages and salaries are paid on a fortnightly basis; however, in North America it is far more common to use the term biweekly. Neither of these terms should be confused with semimonthly, which divides a year into exactly 24 periods (12 months × 2), instead of the 26 (≈52 weeks ÷ 2) of fortnightly/biweekly.

Frequency

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second (60 seconds divided by 120 beats). Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.

Hour

An hour (symbol: h; also abbreviated hr.) is a unit of time conventionally reckoned as ​1⁄24 of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions.

The hour was initially established in the ancient Near East as a variable measure of ​1⁄12 of the night or daytime. Such seasonal, temporal, or unequal hours varied by season and latitude. The hour was subsequently divided into 60 minutes, each of 60 seconds. Equal or equinoctial hours were taken as ​1⁄24 of the day as measured from noon to noon; the minor seasonal variations of this unit were eventually smoothed by making it ​1⁄24 of the mean solar day. Since this unit was not constant due to long term variations in the Earth's rotation, the hour was finally separated from the Earth's rotation and defined in terms of the atomic or physical second.

In the modern metric system, hours are an accepted unit of time defined as 3,600 atomic seconds. However, on rare occasions an hour may incorporate a positive or negative leap second, making it last 3,599 or 3,601 seconds, in order to keep it within 0.9 seconds of UT1, which is based on measurements of the mean solar day.

Light-year

The light-year is a unit of length used to express astronomical distances and measures about 9.46 trillion kilometres (9.46 x 1012 km) or 5.88 trillion miles (5.88 x 1012 mi). As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in vacuum in one Julian year (365.25 days). Because it includes the word "year", the term light-year is sometimes misinterpreted as a unit of time.

The light-year is most often used when expressing distances to stars and other distances on a galactic scale, especially in nonspecialist and popular science publications. The unit most commonly used in professional astrometry is the parsec (symbol: pc, about 3.26 light-years; the distance at which one astronomical unit subtends an angle of one second of arc).

Luminosity

In astronomy, luminosity is the total amount of energy emitted per unit of time by a star, galaxy, or other astronomical object. As a term for energy emitted per unit time, luminosity is synonymous with power.In SI units luminosity is measured in joules per second or watts. Values for luminosity are often given in the terms of the luminosity of the Sun, L⊙. Luminosity can also be given in terms of the astronomical magnitude system: the absolute bolometric magnitude (Mbol) of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band.

In contrast, the term brightness in astronomy is generally used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the luminosity of the object and the distance between the object and observer, and also on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness. The distance determined by luminosity measures can be somewhat ambiguous, and is thus sometimes called the luminosity distance.

Metric time

Metric time is the measure of time intervals using the metric system. The modern SI system defines the second as the base unit of time, and forms multiples and submultiples with metric prefixes such as kiloseconds and milliseconds. Other units of time: minute, hour, and day, are accepted for use with SI, but are not part of it. Metric time is a measure of time intervals, while decimal time is a means of recording time of day.

Microsecond

A microsecond is an SI unit of time equal to one millionth (0.000001 or 10−6 or ​1⁄1,000,000) of a second. Its symbol is μs, sometimes simplified to us when Unicode is not available.

A microsecond is equal to 1000 nanoseconds or ​1⁄1,000 of a millisecond. Because the next SI prefix is 1000 times larger, measurements of 10−5 and 10−4 seconds are typically expressed as tens or hundreds of microseconds.

Minute

The minute is a unit of time or angle. As a unit of time, the minute is most of times equal to ​1⁄60 (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a negative leap second, which would result in a 59-second minute, but this has never happened in more than 40 years under this system). As a unit of angle, the minute of arc is equal to ​1⁄60 of a degree, or 60 seconds (of arc). Although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. The prime is also sometimes used informally to denote minutes of time.

A minute is a unit of time in a basketball game. There are forty-eight minutes in each NBA basketball game, excluding overtime. As five people from one team will be on the court at any given time, a total of 240 minutes can be distributed in regulation among a team in an NBA basketball game.

For players, the total number of minutes played in a season—and the average number of minutes played per game—are both tracked as statistics.

Mortality rate

Mortality rate, or death rate, is a measure of the number of deaths (in general, or due to a specific cause) in a particular population, scaled to the size of that population, per unit of time. Mortality rate is typically expressed in units of deaths per 1,000 individuals per year; thus, a mortality rate of 9.5 (out of 1,000) in a population of 1,000 would mean 9.5 deaths per year in that entire population, or 0.95% out of the total. It is distinct from "morbidity", which is either the prevalence or incidence of a disease, and also from the incidence rate (the number of newly appearing cases of the disease per unit of time).

In the generic form, mortality rates are calculated as:

${\displaystyle d/p*10^{n}}$

where d represents the deaths occurring within a given time period and p represents the size of the population in which the deaths occur.

Planck time

In quantum mechanics, the Planck time (tP) is the unit of time in the system of natural units known as Planck units. A Planck time unit is the time required for light to travel a distance of 1 Planck length in a vacuum, which is a time interval of approximately 5.39 × 10 −44 s. The unit is named after Max Planck, who was the first to propose it.

The Planck time is defined as:

${\displaystyle t_{\mathrm {P} }\equiv {\sqrt {\frac {\hbar G}{c^{5}}}}}$

where:

ħ = ​h2π is the reduced Planck constant (sometimes h is used instead of ħ in the definition)
G = gravitational constant
c = speed of light in vacuum

Using the known values of the constants, the approximate equivalent value in terms of the SI unit, the second, is

${\displaystyle 1\ t_{\mathrm {P} }\approx 5.391\,245(60)\times 10^{-44}\ \mathrm {s} ,}$

where the two digits between parentheses denote the standard error of the approximated value.

Rate (mathematics)

In mathematics, a rate is the ratio between two related quantities in different units. If the denominator of the ratio is expressed as a single unit of one of these quantities, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable.

The most common type of rate is "per unit of time", such as speed, heart rate and flux. Ratios that have a non-time denominator include exchange rates, literacy rates and electric field (in volts/meter).

In describing the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate (for example a heart rate is expressed "beats per minute"). A rate defined using two numbers of the same units (such as tax rates) or counts (such as literacy rate) will result in a dimensionless quantity, which can be expressed as a percentage (for example, the global literacy rate in 1998 was 80%) or fraction or as a multiple.

Often rate is a synonym of rhythm or frequency, a count per second (i.e., Hertz); e.g., radio frequencies or heart rate or sample rate.

Second

The second (symbol: s) is the base unit of time in the International System of Units (SI), commonly understood and historically defined as ​1⁄86400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each. Analog clocks and watches often have sixty tick marks on their faces, representing seconds, and a "second hand" to mark the passage of time in seconds. Digital clocks and watches often have a two-digit seconds counter. The second is also part of several other units of measurement like meters per second for velocity, meters per second per second for acceleration, and per second for frequency.

Although the historical definition of the unit was based on this division of the Earth's rotation cycle, the formal definition in the International System of Units (SI) is a much steadier timekeeper: it is defined by taking the fixed numerical value of the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s−1.

Because the Earth's rotation varies and is also slowing ever so slightly, a leap second is periodically added to clock time to keep clocks in sync with Earth's rotation.

Multiples of seconds are usually counted in hours and minutes. Fractions of a second are usually counted in tenths or hundredths. In scientific work, small fractions of a second are counted in milliseconds (thousandths), microseconds (millionths), nanoseconds (billionths), and sometimes smaller units of a second. An everyday experience with small fractions of a second is a 1-gigahertz microprocessor which has a cycle time of 1 nanosecond. Camera shutter speeds are often expressed in fractions of a second, such as ​1⁄30 second or ​1⁄1000 second.

Sexagesimal divisions of the day from a calendar based on astronomical observation have existed since the third millennium BC, though they were not seconds as we know them today. Small divisions of time could not be counted back then, so such divisions were figurative. The first timekeepers that could count seconds accurately were pendulum clocks invented in the 17th century. Starting in the 1950s, atomic clocks became better timekeepers than earth's rotation, and they continue to set the standard today.

Year

A year is the orbital period of the Earth moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the hours of daylight, and, consequently, vegetation and soil fertility.

In temperate and subpolar regions around the planet, four seasons are generally recognized: spring, summer, autumn, and winter. In tropical and subtropical regions, several geographical sectors do not present defined seasons; but in the seasonal tropics, the annual wet and dry seasons are recognized and tracked.

A calendar year is an approximation of the number of days of the Earth's orbital period as counted in a given calendar. The Gregorian calendar, or modern calendar, presents its calendar year to be either a common year of 365 days or a leap year of 366 days, as do the Julian calendars; see below. For the Gregorian calendar, the average length of the calendar year (the mean year) across the complete leap cycle of 400 years is 365.2425 days. The ISO standard ISO 80000-3, Annex C, supports the symbol a (for Latin annus) to represent a year of either 365 or 366 days. In English, the abbreviations y and yr are commonly used.

In astronomy, the Julian year is a unit of time; it is defined as 365.25 days of exactly 86,400 seconds (SI base unit), totalling exactly 31,557,600 seconds in the Julian astronomical year.The word year is also used for periods loosely associated with, but not identical to, the calendar or astronomical year, such as the seasonal year, the fiscal year, the academic year, etc. Similarly, year can mean the orbital period of any planet; for example, a Martian year and a Venusian year are examples of the time a planet takes to transit one complete orbit. The term can also be used in reference to any long period or cycle, such as the Great Year.

Units of time
Unit Length, Duration and Size Notes
Planck time unit 5.39 x 10−44 s The amount of time light takes to travel one Planck length. Theoretically, this is the smallest time measurement that will ever be possible.[3] Smaller time units have no use in physics as we understand it today.
yoctosecond 10−24 s
jiffy (physics) 3 × 10−24s The amount of time light takes to travel one fermi (about the size of a nucleon) in a vacuum.
zeptosecond 10−21 s Time measurement scale of the NIST strontium atomic clock. Smallest fragment of time currently measurable is 850 zeptoseconds.[1][3]
attosecond 10−18 s
femtosecond 10−15 s Pulse time on fastest lasers.
Svedberg 10−13 s Time unit used for sedimentation rates (usually of proteins).
picosecond 10−12 s
nanosecond 10−9 s Time for molecules to fluoresce.
shake 10−8 s 10 nanoseconds, also a casual term for a short period of time.
microsecond 10−6 s Symbol is µs
millisecond 0.001 s Shortest time unit used on stopwatches.
jiffy (electronics) 1/60s to 1/50s Used to measure the time between alternating power cycles. Also a casual term for a short period of time.
second 1 sec SI Base unit.
minute 60 seconds
moment 1/40th of an hour (90 seconds) Medieval unit of time used by astronomers to compute astronomical movements.[4]
ke 14 minutes and 24 seconds Usually calculated as 15 minutes, similar to "quarter" as in "a quarter past six" (6:15).
kilosecond 1,000 seconds 16 minutes and 40 seconds.
hour 60 minutes
day 24 hours Longest unit used on stopwatches and countdowns.
week 7 days Also called "sennight".
megasecond 16,666.6667 minutes About 1 week and 4.6 days.
fortnight 2 weeks 14 days
lunar month 3 weeks 6 days 4 hours 48 minutes–29 days 12 hours Various definitions of lunar month exist.
month 28–31 days Occasionally calculated as 30 days.
quarter and season 3 months
semester an 18-week division of the academic year[5] Literally "six months", also used in this sense.
year 12 months or 365 days
common year 365 days 52 weeks and 1 day.
decade period consisting of ten common years
score period consisting of two decades
century one hundred common years or ten decades or 5 score
millennium one thousand times 365.25 day years
epoch twenty thousand times 365.25 day years
eon one hundred thousand times 365.25 day years
aeon one million times 365.25 day years
tropical year 365 days and 5:48:45.216 hours[6] Average.
Gregorian year 365 days and 5:49:12 hours[7] Average.
sidereal year 365 days and 6:09:09.7635456 hours
leap year 366 days 52 weeks and 2 days.
biennium 2 years
triennium 3 years
olympiad 4 year cycle 48 months, 1,461 days, 35,064 hours, 2,103,840 minutes, 126,230,400 seconds.
lustrum 5 years
indiction 15 year cycle
score 20 years
gigasecond 1,000,000,000 seconds About 31.7 years.
jubilee 50 years
century 100 years
millennium 1,000 years Also called "kiloannum".
terasecond 1 trillion seconds About 31,700 years.
Megannum 1,000,000 (106) years Also called "Megayear." About 1,000 millennia (plural of millennium), or 1 million years.
petasecond 1015 seconds About 31,700,000 years
galactic year Approximately 230 million years[2] The amount of time it takes the Solar System to orbit the center of the Milky Way Galaxy one time.
cosmological decade varies 10 times the length of the previous
cosmological decade, with CÐ 1 beginning
either 10 seconds or 10 years after the
Big Bang, depending on the definition.
aeon 1,000,000,000 years or an indefinite period of time Also spelled "eon"
Day of Brahman
(aka Day of God)
4,320,000,000 years or 4.32 aeon Like the galactic year which measures the time it takes all the solar systems of the Milky Way Galaxy to orbit its central nexus one time, this measurement of time is the presumed length of time it takes all the Galaxies in the Universe to orbit its presumed central nexus (aka "Ground Zero of the Big Bang"), one time. In this context, the "7 Days of Creation" mentioned in the book of Genesis are seen in a much different light, since Earth is estimated to be ~4.3 billion years old, or 1 Day of God according to the Vedic system of time.
exasecond 1018 seconds About 31,700,000,000 years
zettasecond 1021 seconds About 31.7 trillion years
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