# Dimensional Analysis

Dimensional analysis might sound like an intimidating scientific term, but it’s a powerful tool that helps us make sense of the world around us. Dimensional analysis can be used to solve a wide range of problems in a variety of disciplines, from chemistry and physics to cooking and construction.It is a technique used to convert from one dimension (or unit) to another dimension (or unit). It is sometimes referred to as the factor-label method or the unit-factor method, but regardless of what it’s called, its purpose is the same.Dimensional analysis uses conversion factors. Conversion factors are used to change one set of units into an equivalent set of units of another type, like pounds to kilograms or inches to feet. They are equalities, which means that one thing is equal to another thing in algebraic equations.For example, a conversion factor for inches and centimeters is 1 in = 2.54 cm. In dimensional analysis, these equalities are written as a fraction, which has a total value of 1. The inches to centimeter conversion written as a fraction would be  or .

There are several steps that can be used to solve a dimensional analysis problem.

Sometimes you can use intrinsic properties of substances as conversion factors. For example, you may use density to convert between mass and volume.

Example problem: I have 0.6 kilograms (kg) of aluminum (Al). What volume of aluminum do I have?

You know you have 0.6 kg of Al, which is .

You know you want to find volume, which is expressed as cm3.

You need to convert from kg to cm3.

You need the density of Al, which is and the conversion factor  .

Note: these conversions can be flipped so that you are able to eliminate your units as needed.

Now you need to solve your problem.

Next, multiply across the top and then multiply across the bottom.

Then, divide as needed.

You may also use balanced chemical equations and molecular weights as conversion factors. In the balanced chemical equation for the production of water (2H2 + O2 → 2H2O), you know that for every 1 molecule of oxygen (O2), 2 molecules of water (H2O) are produced, so this is an equality you can use. You also know that every mole of oxygen (O2) is 32.0 g.

Example: If you have 64 grams of oxygen, how many grams of water are produced?

You know you have 64 g of O2; .

You know you need grams of water (g H2O).

You need to covert from grams of O2 to grams of H2O.

You know you need the conversion factors: .

Note: these conversions can be flipped so that you are able to eliminate your units as needed.

Now you need to solve your problem.

Next, multiply across the top and then multiply across the bottom.

Then, divide as needed.

Regardless of why you’re using dimensional analysis, the tool can help you move from one set of units to another.