Units and the discipline of checking them

A quantity in engineering is a number and a unit, and the two are inseparable: "1000" is not a flow, "1000 kg/h" is. Most of the order-of-magnitude errors that reach a design are unit errors — a factor of a thousand from grams against kilograms, of 3600 from seconds against hours, of the density bridge between a mass basis and a volume basis. Treating units as part of the quantity, and carrying them through every line, is the cheapest and most reliable error check the discipline has.

Dimensional homogeneity: the free check

Every valid equation is dimensionally homogeneous — both sides reduce to the same units. That fact is a check you get for nothing: write the units alongside the numbers, cancel them as you go, and if the units of your answer are not the units you expected, the calculation is wrong before you have even examined the arithmetic. A heat duty that comes out in kilograms, a velocity in seconds, a concentration that will not reduce to mass over volume — each is the units telling you a term is inverted, a factor is missing, or two quantities on different bases have been added. The habit is to treat units as algebra: multiply the conversion factors as fractions, let the unwanted units cancel, and read the result.

The conversion engine

This site is built around exactly this discipline: a conversion engine spanning thousands of unit conversions across the quantities a process engineer meets — flow, pressure, density, energy, power, concentration and the rest. The point of a cited, consistent conversion factor is that the bridge between units is not re-derived from memory each time, where the slips happen, but applied from a single audited source. Browse the conversion families to convert a value cleanly, and use the calculators below when the conversion is itself a small computation — turning a solute mass and a volume into a concentration, or stepping a stored strength down to a working one.

The audit-trail habit

The deeper discipline is the audit trail: a calculation written so each step shows its inputs, its relation and its units, so that another engineer — or you, six months on — can follow it and find the error. A bare answer cannot be checked; a worked line carrying its units can. This is the house method behind every calculator here, and it is why the worked examples quote their numbers to a named source rather than asserting a result. Carry the units, show the working, cite the number — the three together are what makes engineering arithmetic trustworthy.

A note on framing and the sister path: units are framing-neutral — a flow in kilograms per hour means the same thing in any industry — so this page does not re-teach the concentration and slurry units a specific industry leans on. The hydrometallurgy path treats those in depth in its "The units of the trade" topic (wt%, g/L, kg/t and percent solids, with the density bridge worked through); read that for the industry-specific dialect. Here the lesson is the general one: units are part of the quantity, and checking them is the discipline.