Dimensional analysis is a problem solving technique used in many (perhaps most) chemistry calculations. Converting from one unit to another involves a conversion factor such as 1 pound (lb) = 0.454 kilogram (kg). Various chemical and physical entities such as density (mass/volume), Molarity (moles/Liter), molar mass grams/mol) and some constants such as Planck's constant h (J/Hz) or Avogadro's Number (particles/mole) can be viewed as conversion factors. The mathematical idea is that if the two quantities are equal to each other then if you set up a ratio such as 1lb/0.454kg or 0.454kg/1lb based on the conversion factor then it is as if you are multiplying the starting number by one.
On this page is Javascript calculator that lets you do problems involving this method. In the pink box you type in your starting number and unit. Identifying this starting number is a key step in using dimensional analysis as a problem solving technique. Usually, this number is some measurement and only has one unit. It is not a conversion factor. The you multiply by conversion factors in such a way that the unit in the numerator of the starting number is cancelled out by the unit in the denominator of the conversion factor (or successive conversion factors). At the end of the problem you will have the desired unit and when you perform all the multiplications and divisions, the correct number.
Let's start with a simple example. The average body mass of a human being, globally, was 136 pounds. In North America, which has the highest average body mass of any continent, that number was 178 pounds. What is the average body mass of a North American in kilograms? 1 pound (lb) = 0.454 kilogram (kg)
Upon reading the problem careful we notice that we are given 136 pounds (global average mass), 178 pounds (North American average mass), the conversion factor between pounds and kilograms. A "feature" of many problems is that you are sometimes given irrelevant information. In this case, since the question is about North American body mass, the global average mass (136 pounds) is information not used in this problem. You need to recognize this. One piece of information 178 pounds is not a conversion factor and is a measurement (or the average of measurements). This will be the starting number. You also see that we need the final answer in units of kg.
This is the default problem for the calculator and you will see the starting number, the conversion factor, and the calculated answer. Notice we are only using one conversion factor in this problem. Unused conversion factors in the calculator need to have a 1/1 in the number field and nothing in the units field. Notice the lb unit in the numerator in the starting number. Notice also that the conversion factor puts the lb unit in the denominator so that when you multiply everything out you have lb x 1/lb and so the lb's cancel out. Notice that is it missing from the units of the final answer. (The uncanceled units are shown to the right of the answer in parenthesis. There you still see lb in the numerator and lb in the denominator. The switch button in the calculator lets you switch the numerator and the denominator in case you entered them in such a way the the units don't cancel. Click the the button to see what happens to the answer. Especially notice the units. If you end up with messed up units instead of the one you want, you have probably entered the conversion factor incorrectly. Make sure you switch back for this example. The answer should be 80.8 kg (to 3 significant figures).
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