Primary Dimensions and SI Units

Quantification is essential to the understanding of both continuous and discontinuous media. The first issue is determining the dimension or dimensions to be measured. Seven “primary” dimensions are recognized: mass [M], length [L], time [T], amount of a substance [N], electric current, temperature, and luminous intensity. Square brackets at this website are used to indicate dimensions of a variable, and only the four dimensions whose abbreviations are shown in such brackets will be used extensively. “Secondary” or “derived” dimensions are made up of primary dimensions. Velocity, for example, is distance (length) per unit of time [L T-1].

An "N" in square brackets [N] is not standard notation and is included here as a primary dimension to deal with some cruder measures than are typically needed in laboratory physics and chemistry. In aquatic environments, e.g., for purposes of estimating encounter rates, one may often be interested in number concentrations of organisms or inanimate particles. In general, this website uses [N] for countable entities, and does not restrict its use to elementary entities that could be properly counted in moles. A chemist would cringe at the thought of a mole of (furry) moles, but this website would sanction the idea of Avogadro's number of bacteria as a legitimate treatment of countable entities, including both the strict chemist's moles and numbers of any countable entity under the primary dimension [N].

Other than this site-specific artifice for countable entitites, this site uses SI units (Système International d’Unités) for all calculations. Serious mischief can occur if systems of units are mixed: NASA lost the 125 million-dollar Mars Climate Orbiter because one development team used SI, whereas another used English, units. If you have obtained measurements in one set of units and have trouble remembering how, a number of helpful websites can help you make the necessary conversions, and Google’s calculator can now help directly. If you have the name of a measurement unit but don’t recognize it, you can probably find it in an online dictionary. Be especially careful not to mix two different subsets of metric conventions, so called mks (for meter, kilogram second; which conform to SI) with cgs (centimeter, gram, second; which in general require conversion to SI). This site does use grams and centimeters when they are convenient, but not in formulas or calculations. If you need a refresher on acceptable prefixes (e.g., to find out how many grams in a petagram), visit the table of SI prefixes at the NIST (U.S. National Institute of Standards and Technology) site. NIST has useful help on all aspects of SI units and physico-chemical constants.

Try to stick with or convert to the following:

  • kilogram (kg) [M] — Appropriately for this site, the original definition was the mass of water filling a volume of 1 cubic decimeter. The present definition is the mass of a prototype kilogram mass of platinum-iridium kept at the International Bureau of Weights and Measures. Beware of confusing mass with weight. The mass of an object is a measure of its amount of matter, independent of where the mass is located. Weight is a force (a mass times and acceleration). On earth a mass m has weight m x g, where g is the acceleration constant due to Earth's gravitation attraction. Mass [M], but not weight [M L T-2] constitutes a primary dimension.
  • meter (m) [L] — The original meter was intended to be one ten-millionth of the north-south distance through Paris from the North Pole to the equator, and a prototype of this calculated length was made of platinum-iridium. Despite the fact that the calculated distance was in error, the prototype was retained as a standard, though the definition was modified several times to include the temperature, atmospheric pressure and even the means of support of the bar when measured. The meter is now defined as the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 second.
  • second (s, not sec) [T] — The original definition was 1/86,400 of a “mean solar day.” The definition was plagued by variations in the rate of Earth’s rotation. The second is now defined as 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 cesium 133 atom.
  • mole (mol) [N] — Reviewing the history of the mole would add confusion. The current definition has two pieces that reflect historical disgreements between chemists and physicists, now settled. By current definition, (1) the mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; (2) when the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. It is understood that the referenced carbon 12 atoms are unbound, at rest and in their ground states.

If you need more information on dimensions, units or physical constants, the U.S. National Institute of Standards and Technology maintains one of the most useful sites.