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 It was superseded in 2006 by ISO 80000-3.


Its definitions include:

Quantity Unit Remarks
Name Symbol Name Symbol Definition
(plane angle)
α, β, γ, ϑ, φ radian rad 1 rad = 1 ​mm = 1
degree ° 1° = ​π180 rad There is no space between the number and these superscript-style unit symbols. Decimal subdivision of degrees is preferable (i.e., 12.5° instead of 12°30′)
minute 1′ = (​160
second 1″ = (​160)′
solid angle Ω steradian sr 1 sr = 1 ​ = 1
length l, L metre m The metre is the length of the path travelled by light in vacuum during a time interval of ​1299 792 458 of a second; see speed of light
breadth b
height h
thickness d, δ
radius r, R
diameter d, D
length of path, (linear) displacement vector s, s
distance d, r
cartesian coordinates x, y, z
radius of curvature ϱ
curvature ϰ reciprocal metre m−1 ϰ=​1ϱ
area A square metre The units are (1 a = 100 m²) and hectare (1 ha = 100 a) are used for agrarian areas.
volume V cubic metre
litre L, l 1 L = 1 dm³ The capital L is preferred as the small l can be indistinguishable from the number 1 in some fonts.
time, time interval, duration t second s The second is the 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 Representations of time of day are defined in ISO 8601.
minute min 1 min = 60 s
hour h 1 h = 60 min = 3 600 s
day d 1 d = 24 h = 86 400 s
angular velocity ω radian per second rads ω=​dφdt
angular acceleration α radian per second squared rad α=​dωdt
velocity v (general symbol),
v (velocity vector),
c (propagation speed of waves),
u, v, w (components of a velocity c)
metre per second ms
kilometre per hour kmh
acceleration, acceleration vector a, a metre per second squared m g = 9.80665 ​m
acceleration of free fall, acceleration due to gravity g

Annex A

Annex A of ISO 31-1 lists units of space and time based on the foot, pound, and second.

Annex B

Annex B lists some other non-SI units of space and time, namely the gon, light year, astronomical unit, parsec, tropical year, and gal.

Foot (unit)

The foot (pl. feet; abbreviation: ft; symbol: ′, the prime symbol) is a unit of length in the imperial and US customary systems of measurement. Since 1959, both units have been defined by international agreement as equivalent to 0.3048 meters exactly. In both systems, the foot comprises 12 inches and three feet compose a yard.

Historically the "foot" was a part of many local systems of units, including the Greek, Roman, Chinese, French, and English systems. It varied in length from country to country, from city to city, and sometimes from trade to trade. Its length was usually between 250 mm and 335 mm and was generally, but not always, subdivided into 12 inches or 16 digits.

The United States is the only industrialized nation that uses the international foot and the survey foot (a customary unit of length) in preference to the meter in its commercial, engineering, and standards activities. The foot is legally recognized in the United Kingdom; road signs must use imperial units (however distances on road signs are always marked in miles or yards, not feet), while its usage is widespread among the British public as a measurement of height. The foot is recognized as an alternative expression of length in Canada officially defined as a unit derived from the meter although both the U.K. and Canada have partially metricated their units of measurement. The measurement of altitude in international aviation is one of the few areas where the foot is used outside the English-speaking world.

The length of the international foot corresponds to a human foot with shoe size of 13 (UK), 14 (US male), 15.5 (US female) or 46 (EU sizing).


The gradian is a unit of measurement of an angle, equivalent to



{\textstyle {\frac {1}{400}}}

of a turn,



{\textstyle {\frac {9}{10}}}

of a degree, or



{\textstyle {\frac {\pi }{200}}}

of a radian. The gradian is defined as



{\textstyle {\frac {1}{100}}}

of the right angle (in other words, there are 100 gradians in the right angle), which implies a full turn being 400 gradians.It is also known as gon (from Greek γωνία/gōnía for angle), grad, or grade. In continental Europe, the French term centigrade was in use for one hundredth of a grad. This was one reason for the adoption of the term Celsius to replace centigrade as the name of the temperature scale.


An hourglass (or sandglass, sand timer, sand clock or egg timer) is a device used to measure the passage of time. It comprises two glass bulbs connected vertically by a narrow neck that allows a regulated trickle of material (historically sand) from the upper bulb to the lower one. Factors affecting the time it measured include sand quantity, sand coarseness, bulb size, and neck width. Hourglasses may be reused indefinitely by inverting the bulbs once the upper bulb is empty. Depictions of hourglasses in art survive in large numbers from antiquity to the present day, as a symbol for the passage of time. These were especially common sculpted as epitaphs on tombstones or other monuments, also in the form of the winged hourglass, a literal depiction of the well-known Latin epitaph tempus fugit ("time flies").

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

ISO 31 (Quantities and units, International Organization for Standardization, 1992) is a deprecated international standard for the use of physical quantities and units of measurement, and formulas involving them, in scientific and educational documents. It is superseded by ISO/IEC 80000.

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. It is a part of the group of standards called ISO/IEC 80000, which together form the International System of Quantities.


The inch (abbreviation: in or ″) is a unit of length in the (British) imperial and United States customary systems of measurement. It is equal to ​1⁄36 yard or ​1⁄12 of a foot. Derived from the Roman uncia ("twelfth"), the word inch is also sometimes used to translate similar units in other measurement systems, usually understood as deriving from the width of the human thumb. Standards for the exact length of an inch have varied in the past, but since the adoption of the international yard during the 1950s and 1960s it has been based on the metric system and defined as exactly 25.4 mm.


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

Philosophy of physics

In philosophy, philosophy of physics deals with conceptual and interpretational issues in modern physics, and often overlaps with research done by certain kinds of theoretical physicists. Philosophy of physics can be very broadly lumped into three main areas:

The interpretations of quantum mechanics: Concerning issues, mainly, with how to formulate an adequate response to the measurement problem, and understand what the theory tells us about reality.

The nature of space and time: Are space and time substances, or purely relational? Is simultaneity conventional or just relative? Is temporal asymmetry purely reducible to thermodynamic asymmetry?

Inter-theoretic relations: the relationship between various physical theories, such as thermodynamics and statistical mechanics. This overlaps with the issue of scientific reduction.

Term (time)

A term is a period of duration, time or occurrence, in relation to an event. To differentiate an interval or duration, common phrases are used to distinguish the observance of length are near-term or short-term, medium-term or mid-term and long-term.

It is also used as part of a calendar year, especially one of the three parts of an academic term and working year in the United Kingdom: Michaelmas term, Hilary term / Lent term or Trinity term / Easter term, the equivalent to the American semester. In America there is a midterm election held in the middle of the four-year presidential term, there are also academic midterm exams.

In economics, it is the period required for economic agents to reallocate resources, and generally reestablish equilibrium. The actual length of this period, usually numbered in years or decades, varies widely depending on circumstantial context. During the long term, all factors are variable.

In finance or financial operations of borrowing and investing, what is considered long-term is usually above 3 years, with medium-term usually between 1 and 3 years and short-term usually under 1 year. It is also used in some countries to indicate a fixed term investment such as a term deposit.

In law, the term of a contract is the duration for which it is to remain in effect (not to be confused with the meaning of "term" that denotes any provision of a contract). A fixed-term contract is one concluded for a pre-defined time.

International standards
Obsolete standards
Time in physics
Archaeology and geology
Astronomical chronology
Other units of time
Related topics
ISO standards by standard number

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