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International System of Quantities (ISQ): Part 1 - Introduction

This post starts a series of articles about the International System of Quantities (ISQ). In this series, we will describe:

  • What is ISQ?
  • Which engineering problems does ISQ help to solve and how?
  • How to model and implement it in the programming language?
  • What is missing in the ISQ, and why is that a problem?

Articles from this series

Terms and Definitions

From our experience, many people, including experts in the domain, often tend to name things differently, or sometimes they use the same term while having a different meaning in mind. This is why it is essential to stick to one well-defined glossary of terms for metrology.

The mp-units project consistently uses the official metrology vocabulary defined by the ISO and BIPM:

The above are identical and contain the same set of definitions. We provide both to point out that the biggest institutions in standardizing metrology agree on the same vocabulary.

Systems of Quantities vs Systems of Units

Here are the official definitions from our vocabulary:

System of quantities

A system of quantities is a set of quantities together with a set of noncontradictory equations relating those quantities.

System of units

A system of units is a 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.

From the definition above, we can find out that the systems of quantities and units form a hierarchy:

flowchart TD
    system_of_quantities["System of Quantities"]
    system_of_quantities --- system_of_units1[System of Units #1]
    system_of_quantities --- system_of_units2[System of Units #2]
    system_of_quantities --- system_of_units3[System of Units #3]

System of quantities defines quantities commonly used in engineering (e.g., length, time, mass, speed, energy, power, etc.) and relations between them. It does not assign any specific units to those quantities, though.

Systems of units are the ones that assign units of measurement to quantities from a specific system of quantities they chose to model. Different systems of units are free to chose whatever they find suitable for specific quantities and do not have to be consistent/compatible with other such systems. For example:

  • SI decided to measure length in meters, mass in kilograms, and time in seconds,
  • CGS decided to measure length in centimeters, mass in grams, and time in seconds.

Both systems of units above agree on the unit of time, but chose different units for other quantities. In the above example, SI chose a non-prefixed unit of metre for a base quantity of length while CGS chose a scaled centimetre. On the other hand, SI chose a scaled kilogram over the gram used in the CGS. Those decisions also result in a need for different coherent units for derived quantities. For example:

Quantity SI CGS
length metre (m) centimetre (cm)
mass kilogram (kg) gram (g)
time second (s) second (s)
force newton (N) dyne
energy joule (J) erg
pressure pascal (Pa) barye

Often, there is no way to state which one is correct or which one is wrong. Each system of units has the freedom to choose whichever unit suits its engineering requirements and constraints the best for a specific quantity.

ISQ vs SI

Some of the systems of quantities and units have been used more over the years and have become more popular than others. Here are the official descriptions of the most popular systems used in engineering today:

International System of Quantities (ISQ)

The International System of Quantities (ISQ) is a system of quantities based on the seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.

International System of Units (SI)

The International System of Units (SI) is a 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).

The International System of Quantities (ISQ) standardization

The set of quantities constituting the ISQ is defined in the series of ISO 80000 and IEC 80000 standards under the general title "Quantities and units".

ISO 80000:

  • Part 1: General
  • Part 2: Mathematical signs and symbols to be used in the natural sciences and technology
  • Part 3: Space and time
  • Part 4: Mechanics
  • Part 5: Thermodynamics
  • Part 7: Light
  • Part 8: Acoustics
  • Part 9: Physical chemistry and molecular physics
  • Part 10: Atomic and nuclear physics
  • Part 11: Characteristic numbers
  • Part 12: Condensed matter physics

IEC 80000:

  • Part 6: Electromagnetism
  • Part 13: Information science and technology
  • Part 15: Logarithmic and related quantities, and their units
  • Part 16: Printing and writing rules
  • Part 17: Time dependency

To be continued...

In the next part of this series, we will describe typical issues with libraries that do not model systems of quantities.

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