Weights and Measures

Weights and measures are terms which traditionally referred to standards of mass (or weight), length and volume. Over the past few thousand years such standards have frequently been introduced throughout the world for trading and tax purposes. However, as measurement is one of the most fundamental aspects of science and engineering, the term now embraces a much wider gamut of units.

The development and dissemination of measurement standards has become the science of metrology. To the original basic units of mass and length (volume is a derived unit) have been added other "base units": time, temperature, electric current, luminosity, and the somewhat esoteric amount-of-substance unit. These base units and a large number of derived units are rigorously defined in the International System of Units (Système International d'Unités, or SI), a version of the metric system, formulated by and under the aegis of the International Bureau of Weights and Measures (BIPM). First adopted in 1960, the SI is not invariant but evolves slowly in the interests of greater precision, convenience or internal consistency. Virtually all of the world's scientific work is reported in SI units; construction, engineering and commerce substantially use or will use the system in all major countries except the US and Great Britain, which still largely use the British imperial system.

In 1965 the British government expressed its intention to convert to the SI over a 10-year period; in 1972 the US Senate favoured a voluntary 10-year conversion, but because of a procedural point this suggestion was not endorsed by the House of Representatives. In both countries progress towards metrication has been sporadic and a completion date cannot plausibly be forecast for either. Canada began converting to SI in 1971 and is now officially completely metric.

Canada's former measurement system derived mainly from the imperial system, with some contribution from a French measurement system. The imperial system was codified in its first reasonably "scientific" form in 1838, following a complex history. A number of imperial units (eg, foot, mile) can be traced back to the Roman Empire; however, their magnitude has fluctuated with time and locality. R.E. Zupko's A Dictionary of English Weights and Measures, from Anglo-Saxon Times to the Nineteenth Century contains entries for some 3000 measurement units with 25 000 numerical variations.

In 1884 the UK (hence Canada, as a colony) became an adherent of the Convention of the Metre, by which the BIPM had been established in 1875. The UK was thus a participant in the first distribution by the BIPM of national prototype metre bars and kilogram masses in 1889. Canada became an adherent to the convention in its own right in 1907. From 1929 to 1935, a Canadian, J.C. MACLENNAN, was a member of the International Committee of Weights and Measures (CIPM, now the BIPM). This committee is charged with the direction and supervision of the BIPM, including its metrological laboratories at Sèvres on the outskirts of Paris. There has been a Canadian member of the CIPM continuously since 1951; one of them, L.E. Howlett, served as CIPM president for the period 1964-68. No country is represented on the CIPM; the 18 members (not more than one per country) are elected in a personal capacity. Their task is to monitor and foster metric-based metrology in all nations adhering to the Convention of the Metre (47 in 1988).

Since 1951 Canadian CIPM members have all been members of the NATIONAL RESEARCH COUNCIL. NRC's Division of Physics maintains or realizes the country's primary standards of measurement and many derived standards. Standards disseminated to laboratories and industries requiring the highest precision are calibrated at NRC. The reference standards for trade (periodically calibrated at NRC) are in the custody of the Department of CONSUMER AND CORPORATE AFFAIRS and constitute the legal basis for all local standards employed in the application of the Canadian Weights and Measures Act (1971) to commercial or trade transactions (see CONSUMER STANDARDS). In 1982 Canada joined the International Organization of Legal Metrology (OIML, est 1955). The OIML is concerned only with the application of metrology to trade, eg, in establishing uniformity in international trading practices.

All major industrial countries support national standards laboratories equivalent to that of NRC, eg, the National Bureau of Standards in the US and the National Physical Laboratory in the UK. Elaborate control and comparison procedures ensure measurement consistency among national laboratories. For nations such as Canada, measurement standards are now secure, and adequate monitoring has reduced fraudulent measure to an incidental problem. This achievement eluded all efforts until well into the 20th century. The reasons for failure were many, but the major one was undoubtedly human cupidity. Today's relatively happy situation is one of the benefits of modern technology coupled with a technological infrastructure so pervasive that we now take it for granted.

International System of Units (SI)

The following descriptions of the 7 SI base units and the 2 SI supplementary units include 1987 estimates of reproducibilities. These estimates are based on measurements of the highest quality made at various places and times, and are applicable to measurements at unit magnitude. Imprecision will increase at substantially greater or smaller magnitudes; thus, while a mass of one kilogram can be determined to within about 2 parts in 109, masses of a gram can be determined only to within 3 parts in 10 million (3 in 107); those of a tonne, to within one part per million (1 in 106).


When adopted in 1799, the metre (m) was fixed as one ten-millionth part of a quadrant of the Earth's meridian. In 1983 it was defined as the distance light travels in a vacuum in one 299 792 458th of a second. Reproducibility is 2 parts in 1011.

Non SI Length Units converted into Metric

Unit Definition SI Value
nautical mile air & sea measure 1.852 km
furlong 220 yd 201.2 m
mile 1760 yd 1.609 km
arpent 180 Paris feet 58.47 m
yard 3 feet 0.9144 m
foot 12 inches 0.3048 m
inch 1/36 yard 25.4 mm


The unit of mass is the kilogram (kg), not the gram (g). When adopted in 1799, the kilogram was defined as the mass of a cubic decimetre of water. Since 1889 it has been the mass of the international prototype kilogram, a platinum-iridium artifact kept at Sèvres. Reproducibility is 2 parts in 109.


The second (s), traditionally one 86 400th of a mean solar day, was established in 1960 as one 31 556 925.9744th of the tropical year 1900. In 1968 it was defined in terms of the frequency radiated from the transition between specified energy levels of the cesium-133 atom. Measurement accuracy is 5 parts in 1014.

Electric Current

The ampere (A) was defined in 1881 in terms of the force between magnetic poles (a purely theoretical concept); in 1908 as a more reproducible "international ampere" in electrolytic terms. Since 1948 the "absolute ampere" has been defined in terms of the force between parallel, current-carrying conductors. However, in practice electric units are maintained in terms of the ohm and the volt. Reproducibility is 1 part in 107.


(kelvin, K) is the only base unit that is "intensive" rather than "extensive" (ie, 2 temperatures cannot be added together to give their sum). This characteristic presents certain measurement difficulties. The present International Practical Temperature Scale of 1968 evolved from the "hydrogen temperature scale" of 1889, superseded by the International Temperature Scale of 1990 (ITS-90). Measurements are accurate to within 0.0002 K at room temperature. Significant celsius equivalents are 273.15 K = 0°C and 373.15 K = 100°C.

° Fahrenheit = (Celsius x 1.8) + 32 ° Celsius = (Fahrenheit - 32) x 5/9

Amount of Substance

The mole (mol) is a quantity which serves to connect the macroscopic SI units to measurements used in chemistry and atomic physics. A 1902 convention using oxygen-16 as a standard was superseded in 1960-61 by one using carbon-12; the latter standard was incorporated into the SI in 1971. The mole is the amount of substance which contains as many elementary particles (atoms, molecules, ions, etc; the precise ones under consideration must be specified) as there are atoms in 0.012 kg of carbon-12. In some circumstances, relative atomic weights can be determined to one part in 107. The absolute value of the mole is known to about 1 part per million (1 in 106).

Luminous Intensity

The candela (cd) is one of various "standard candles" which have been in use since before 1800. The candela (then called "new candle") was first defined in 1946 in terms of the freezing temperature of platinum. The present definition is a monochromatic (f = 540 x 1012 Hz) radiant intensity of 1/683 watt per steradian. Reproducibility is 3 parts per thousand.

Plane Angle

The radian (rad) is the plane angle between 2 radii of a circle that cut off (from its circumference) an arc equal in length to the radius. Thus a full circle (360 arc degrees) is an angle of 2 rad. Measurement accuracy is 5 x 10min7 rad or 0.1 arc second.

Solid Angle

The steradian (sr) is the solid angle which, having its vertex at the centre of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere. Thus the solid angle of an entire sphere is 4 pi sr.

The SI is essentially a decimal system, ie, units are related by factors of 10, expressed in prefixes attached to the unit name. Many quantities derived from the base units and which could be expressed in terms of those units are more conveniently designated by special names and symbols. Some non-SI units are used with the SI because they are in worldwide use (eg, hour, knot, nautical mile). Others, eg, the hectare, tonne and litre are not SI units but are used conjointly with the SI for convenience.