Dimensional Analysis

Dimensional analysis checks whether an equation or estimate makes sense by verifying that the units on both sides match. If you're calculating cost per customer and your answer comes out in "dollars per square metre," something is wrong — regardless of whether the arithmetic looks right. The method originated in physics and engineering, where mixing up units has caused real disasters (the Mars Climate Orbiter was lost because one team used metric and another used imperial). As a thinking tool, dimensional analysis is a fast, low-cost sanity check that catches errors before they compound into bad decisions.

Before trusting any calculation, check the units. Write out what each variable represents and trace the units through each step. If the output units don't match the question's units, there's an error in the logic — even if the arithmetic is correct. This is especially valuable for Fermi estimates and financial models, where a single unit mistake can produce answers that are off by factors of 10 or 100.

Dimensional analysis checks that the units of an answer match the question. It's a fast, low-cost sanity check that catches logical errors before they compound into bad decisions. If the units don't match, the answer is wrong.