ISO 80000-3

ISO 80000-3:2006 is an ISO standard entitled Quantities and units – Part 3: Space and time, superseding ISO 31-1 and ISO 31-2.[1] It is a part of the group of standards called ISO/IEC 80000, which together form the International System of Quantities.

Contents list

The standard is divided into the following chapters:

  • Foreword
  • Introduction
  1. Scope
  2. Normative references
  3. Names, symbols and definitions
  • Annex A (informative) Units in the centimetre–gram–second system (CGS system) with special names
  • Annex B (informative) Units based on the foot, pound, second, and some other related units
  • Annex C (informative) Other non-SI units given for information, especially regarding the conversion factors

Names, symbols and definitions

Space and time


ISO 80000-3:2006 assigns names and symbols to quantities and units of space and time, and defines these quantities and units. For example,

  • metre (symbol m): "length of the path travelled by light in vacuum during a time interval of 1/(299 792 458) of a second."

Other units of distance defined by the standard are the ångström (symbol Å) (10−10 m) and the nautical mile (1852 m). No symbol is given for the nautical mile.

The are (symbol a) is a unit of area equal to 100 square metres.

The litre (symbol L or l) is a unit of volume equal to 10−3 m3.


ISO 80000-3:2006 assigns names and symbols to quantities and units of space and time, and defines these quantities and units. For example,

  • second (symbol s): "duration of 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"

Other units of time defined by the standard include the minute (1 min = 60 s), the hour (1 h = 60 min) and the day (1 d = 24 h). The year (1 a = 365 d or 366 d) is defined in an informative annex.

  • knot (symbol kn): one nautical mile per hour = 1852/3600 m/s ≈ 0.514 444 m/s.

The standard acceleration of free fall is 9.806 65 m/s2.

Logarithmic quantities and units

Units of level defined by ISO 80000-3:2006 are:

  • neper: 1 Np = ln e = 1
  • bel: 1 B = ln 10 Np ≈ 1.1512925464970228420089957273422 Np
  • decibel: 1 dB = 0.1 B

Annex A (informative)

The following CGS units are deprecated:

Annex B (informative)

The following non-SI units are deprecated by the standard:

  • The inch (Imperial unit of distance, equal to 25.4 mm)
  • The foot (Imperial unit of distance, equal to 12 inches)
  • The yard (Imperial unit of distance, equal to 3 feet)
  • The mile (Imperial unit of distance, equal to 1760 yards)
  • The acre (Imperial unit of area, equal to 4840 square yards)

Annex C (informative)

The following non-SI units are given for conversion. They are not deprecated by the standard:

  • Units of distance: light year (the distance travelled in one year by light in vacuum; abbreviation l.y.; 1 l.y. ≈ 9.460 730 × 1015 m), astronomical unit (the mean distance of the Earth from the Sun, 1 ua ≈ 1.495 978 706 91(30) × 1011 m), parsec (the distance at which 1 ua subtends an angle of 1″ (second of arc); 1 pc ≈ 206 264.8 ua ≈ 30.856 78 × 1015 m)
  • Units of time: year (a), equal to either 365 days or 366 days


  1. ^ "ISO 80000-3:2006". International Organization for Standardization. Retrieved 20 July 2013.
Astronomical unit

The astronomical unit (symbol: au, ua, or AU) is a unit of length, roughly the distance from Earth to the Sun. However, that distance varies as Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once a year. Originally conceived as the average of Earth's aphelion and perihelion, since 2012 it has been defined as exactly 149597870700 metres or about 150 million kilometres (93 million miles). The astronomical unit is used primarily for measuring distances within the Solar System or around other stars. It is also a fundamental component in the definition of another unit of astronomical length, the parsec.

Decade (log scale)

One decade (symbol dec) is a unit for measuring frequency ratios on a logarithmic scale, with one decade corresponding to a ratio of 10 between two frequencies (an order of magnitude difference). It is especially useful when describing frequency response of electronic systems, such as audio amplifiers and filters.

A closely related unit is the octave, which corresponds to a ratio of 2 between two frequencies.


The decibel (symbol: dB) is a unit of measurement used to express the ratio of one value of a power or field quantity to another on a logarithmic scale, the logarithmic quantity being called the power level or field level, respectively. It can be used to express a change in value (e.g., +1 dB or −1 dB) or an absolute value. In the latter case, it expresses the ratio of a value to a fixed reference value; when used in this way, a suffix that indicates the reference value is often appended to the decibel symbol. For example, if the reference value is 1 volt, then the suffix is "V" (e.g., "20 dBV"), and if the reference value is one milliwatt, then the suffix is "m" (e.g., "20 dBm").Two different scales are used when expressing a ratio in decibels, depending on the nature of the quantities: power and field (root-power). When expressing a power ratio, the number of decibels is ten times its logarithm to base 10. That is, a change in power by a factor of 10 corresponds to a 10 dB change in level. When expressing field (root-power) quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The decibel scales differ by a factor of two so that the related power and field levels change by the same number of decibels in, for example, resistive loads.

The definition of the decibel is based on the measurement of power in telephony of the early 20th century in the Bell System in the United States. One decibel is one tenth (deci-) of one bel, named in honor of Alexander Graham Bell; however, the bel is seldom used. Today, the decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels.

In the International System of Quantities, the decibel is defined as a unit of measurement for quantities of type level or level difference, which are defined as the logarithm of the ratio of power- or field-type quantities.

Field, power, and root-power quantities

A power quantity is a power or a quantity directly proportional to power, e.g., energy density, acoustic intensity, and luminous intensity. Energy quantities may also be labelled as power quantities in this context.A root-power quantity is a quantity such as voltage, current, sound pressure, electric field strength, speed, or charge density, the square of which, in linear systems, is proportional to power. The term root-power quantity was introduced in the ISO 80000-1 § Annex C; it replaces and deprecates the term field quantity.

It is essential to know which category a measurement belongs to when using decibels (dB) for comparing the levels of such quantities. A change of one bel in the level corresponds to a 10× change in power, so when comparing power quantities x and y, the difference is defined to be 10×log10(y/x) decibel. With root-power quantities, however the difference is defined as 20×log10(y/x) dB. In linear systems, these definitions allow the distinction between root-power quantities and power quantities to be ignored when specifying changes as levels: an amplifier can be described as having "3 dB" of gain without needing to specify whether voltage or power are being compared; for a given linear load (e.g. an 8 Ω speaker), such an increase will result in a 3 dB increase in both the sound pressure level and the sound power level at a given location near the speaker. Conversely, when ratios cannot be identified as either power or root-power quantities, the units neper (Np) and decibel (dB) cannot be sensibly used.

In the analysis of signals and systems using sinusoids, field quantities and root-power quantities may be complex-valued.

Gal (unit)

The gal (symbol: Gal), sometimes called galileo after Galileo Galilei, is a unit of acceleration used extensively in the science of gravimetry. The gal is defined as 1 centimeter per second squared (1 cm/s2). The milligal (mGal) and microgal (µGal) refer respectively to one thousandth and one millionth of a gal.

The gal is not part of the International System of Units (known by its French-language initials "SI"). In 1978 the CIPM decided that it was permissible to use the gal "with the SI until the CIPM considers that [its] use is no longer necessary". However, use of the gal is deprecated by ISO 80000-3:2006.

The gal is a derived unit, defined in terms of the centimeter–gram–second (CGS) base unit of length, the centimeter, and the second, which is the base unit of time in both the CGS and the modern SI system. In SI base units, 1 Gal is equal to 0.01 m/s2.

The acceleration due to Earth’s gravity (see standard gravity) at its surface is 976 to 983 Gal, the variation being due mainly to differences in latitude and elevation. Mountains and masses of lesser density within the Earth's crust typically cause variations in gravitational acceleration of tens to hundreds of milligals (mGal). The gravity gradient (variation with height) above Earth's surface is about 3.1 µGal per centimeter of height (3.1×10−6 s−2), resulting in a maximal difference of about 2 Gal (0.02 m/s2) from the top of Mount Everest to sea level.Unless it is being used at the beginning of a sentence or in paragraph or section titles, the unit name gal is properly spelled with a lowercase g. As with the torr and its symbol, the unit name (gal) and its symbol (Gal) are spelled identically except that the latter is capitalized.

ISO/IEC 80000

ISO 80000 or IEC 80000 is an international standard promulgated jointly by the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC).

The standard introduces the International System of Quantities (ISQ). It is a style guide for the use of physical quantities and units of measurement, formulas involving them, and their corresponding units, in scientific and educational documents for worldwide use. In most countries, the notations used in mathematics and science textbooks at schools and universities follow closely the guidelines in this standard.The ISO/IEC 80000 family of standards was completed with the publication of Part 1 in November 2009.

ISO 31-1

ISO 31-1 is the part of international standard ISO 31 that defines names and symbols for quantities and units related to space and time. It was superseded in 2006 by ISO 80000-3.

Knot (unit)

The knot () is a unit of speed equal to one nautical mile per hour, exactly 1.852 km/h (approximately 1.15078 mph). The ISO standard symbol for the knot is kn. The same symbol is preferred by the Institute of Electrical and Electronics Engineers (IEEE); kt is also common, especially in aviation where it is the form recommended by the International Civil Aviation Organization (ICAO). The knot is a non-SI unit. Worldwide, the knot is used in meteorology, and in maritime and air navigation—for example, a vessel travelling at 1 knot along a meridian travels approximately one minute of geographic latitude in one hour.

Etymologically, the term derives from counting the number of knots in the line that unspooled from the reel of a chip log in a specific time.


The abbreviation kyr means "thousand years".

Kyr was formerly common in some English language works, especially in geology and astronomy, for the unit of 1,000 years or millennium. The "k" is the unit prefix for kilo- or thousand with the suffix "yr" simply an abbreviation for "year".

Occasionally, the "k" is shown in upper case, as in "100 Kyr"; this is an incorrect usage. "kyr" itself is often considered incorrect, with some preferring to use "ky".

ISO 80000-3 recommends usage of ka (for kiloannum), which avoids the implicit English bias of "year" by using a Latin root.

Level (logarithmic quantity)

In science and engineering, a power level and a field level (also called a root-power level) are logarithmic measures of certain quantities referenced to a standard reference value of the same type.

A power level is a logarithmic quantity used to measure power, power density or sometimes energy, with commonly used unit decibel (dB).

A field level (or root-power level) is a logarithmic quantity used to measure quantities of which the square is typically proportional to power, etc., with commonly used units neper (Np) or decibel (dB).The type of level and choice of units indicate the scaling of the logarithm of the ratio between the quantity and it reference value, though a logarithm may be considered to be a dimensionless quantity. The reference values for each type of quantity are often specified by international standards.

Power and field levels are used in electronic engineering, telecommunications, acoustics and related disciplines. Power levels are used for signal power, noise power, sound power, sound exposure, etc. Field levels are used for voltage, current, sound pressure.


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).


The abbreviation myr, "million years", is a unit of a quantity of 1,000,000 (i.e. 1×106) years, or 31.6 teraseconds.


The neper (symbol: Np) is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. The unit's name is derived from the name of John Napier, the inventor of logarithms. As is the case for the decibel and bel, the neper is a unit defined in the international standard ISO 80000. It is not part of the International System of Units (SI), but is accepted for use alongside the SI.

Positive real numbers

In mathematics, the set of positive real numbers, , is the subset of those real numbers that are greater than zero. The non-negative real numbers, , also include zero. The symbols and are ambiguously used for either of these, so it safer to always specify which.

In a complex plane, is identified with the positive real axis and is usually drawn as a horizontal ray. This ray is used as reference in the polar form of a complex number. The real positive axis corresponds to complex numbers with argument .


Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions.Time has long been an important subject of study in religion, philosophy, and science, but defining it in a manner applicable to all fields without circularity has consistently eluded scholars.

Nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems.Time in physics is unambiguously operationally defined as "what a clock reads". See Units of Time. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities. Time is used to define other quantities – such as velocity – so defining time in terms of such quantities would result in circularity of definition. An operational definition of time, wherein one says that observing a certain number of repetitions of one or another standard cyclical event (such as the passage of a free-swinging pendulum) constitutes one standard unit such as the second, is highly useful in the conduct of both advanced experiments and everyday affairs of life. The operational definition leaves aside the question whether there is something called time, apart from the counting activity just mentioned, that flows and that can be measured. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy.

Temporal measurement has occupied scientists and technologists, and was a prime motivation in navigation and astronomy. Periodic events and periodic motion have long served as standards for units of time. Examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the international unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms (see below). Time is also of significant social importance, having economic value ("time is money") as well as personal value, due to an awareness of the limited time in each day and in human life spans.

Turn (geometry)

A turn is a unit of plane angle measurement equal to 2π radians, 360 degrees or 400 gradians. A turn is also referred to as a cycle (abbreviated cyc), revolution (abbreviated rev), complete rotation (abbreviated rot) or full circle.

Subdivisions of a turn include half turns, quarter turns, centiturns, milliturns, points, etc.


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. The current year is 2019.

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.

ISO standards by standard number

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