# ISO 80000-1

ISO 80000-1:2009 is a standard describing scientific and mathematical quantities and their units. The standard, whose full name is Quantities and units Part 1: General was developed by the International Organization for Standardization (ISO), superseding ISO 31-0. It provides general information concerning quantities and units and their symbols, especially the International System of Quantities and the International System of Units, and defines these quantities and units. It is a part of a group of standards called ISO/IEC 80000.

## Contents list

The standard is divided into the following chapters:

• Foreword
• Introduction
1. Scope
2. Normative references
3. Terms and definitions
4. Quantities
5. Dimensions
6. Units
7. Printing rules
• Annex A (normative) – Terms in names for physical quantities
• Annex B (normative) – Rounding of numbers
• Annex C (normative) – Logarithmic quantities and their units
• Annex D (informative) – International organizations in the field of quantities and units

## Scope

ISO 80000-1 gives "general information and definitions concerning quantities, systems of quantities, units, quantity and unit symbols, and coherent unit systems, especially the International System of Quantities, ISQ, and the International System of Units, SI."

## Terms and definitions

The standard includes the following definitions.

• quantity: property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed by means of a number and a reference
• kind of quantity: aspect common to mutually comparable quantities
• system of quantities: set of quantities together with a set of non-contradictory equations relating those quantities
• base quantity: quantity in a conventionally chosen subset of a given system of quantities, where no quantity in the subset can be expressed in terms of the other quantities within that subset
• derived quantity: quantity, in a system of quantities, defined in terms of the base quantities of that system
• International System of Quantities: system of quantities based on the seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity
• quantity dimension: expression of the dependence of a quantity on the base quantities of a system of quantities as a product of powers of factors corresponding to the base quantities, omitting any numerical factor
• quantity of dimension one: quantity for which all the exponents of the factors corresponding to the base quantities in its quantity dimension are zero
• unit of measurement: real scalar quantity, defined and adopted by convention, with which any other quantity of the same kind can be compared to express the ratio of the second quantity to the first one as a number
• base unit: measurement unit that is adopted by convention for a base quantity
• derived unit: measurement unit for a derived quantity
• coherent derived unit: derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units with no other proportionality factor than one
• system of units: set of base units and derived units, together with their multiples and submultiples, defined in accordance with given rules, for a given system of quantities
• coherent system of units: system of units, based on a given system of quantities, in which the measurement unit for each derived quantity is a coherent derived unit
• off-system measurement unit: measurement unit that does not belong to a given system of units
• International System of Units: system of units, based on the International System of Quantities, their names and symbols, including a series of prefixes and their names and symbols, together with rules for their use, adopted by the General Conference on Weights and Measures (CGPM)
• multiple of a unit: measurement unit obtained by multiplying a given measurement unit by an integer greater than one
• sub-multiple of a unit: measurement unit obtained by dividing a given measurement unit by an integer greater than one
• quantity value: number and reference together expressing magnitude of a quantity
• numerical quantity value: number in the expression of a quantity value, other than any number serving as the reference
• quantity calculus: set of mathematical rules and operations applied to quantities other than ordinal quantities
• quantity equation: mathematical relation between quantities in a given system of quantities, independent of measurement units
• unit equation: mathematical relation between base units, coherent derived units or other measurement units
• conversion factor between units: ratio of two measurement units for quantities of the same kind
• numerical value equation: mathematical relation between numerical quantity values, based on a given quantity equation and specified measurement units
• ordinal quantity: quantity, defined by a conventional measurement procedure, for which a total ordering relation can be established, according to magnitude, with other quantities of the same kind, but for which no algebraic operations among those quantities exist
• quantity-value scale: ordered set of quantity values of quantities of a given kind of quantity used in ranking, according to magnitude, quantities of that kind
• ordinal quantity-value scale: quantity-value scale for ordinal quantities
• conventional reference scale: quantity-value scale defined by formal agreement
• nominal property: property of a phenomenon, body, or substance, where the property has no magnitude

## Quantities

### International System of Quantities (ISQ)

The special choice of base quantities and quantity equations, given in ISO 80000 and IEC 80000 defines the International System of Quantities, denoted “ISQ” in all languages. Derived quantities can be defined in terms of the base units by quantity equations. There are seven base quantities in the ISQ: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.

## Units

Section 6.5 of the standard describes the International System of Units including SI prefixes and IEC binary prefixes kibi- to yobi-.

## Printing rules

Section 7.3.2 states that the decimal mark is either a comma or a point on the line and further states that whichever decimal mark is used, that same mark should be consistently used. This is in agreement with prior ISO standards and revisions, notably resolution 10 of the 22nd CGPM, 2003.

## Annex A (normative) – Terms in names for physical quantities

According to Annex A, "[t]he logarithm of the ratio of a quantity, Q, and a reference value of that quantity, Q0, is called a level". For example LP = ln(P/P0) is the level of a power quantity P.

## Annex C (normative) – Logarithmic quantities and their units

Annex C introduces the concepts of power quantities and root-power quantities, and deprecates field quantity.