Core Concept

Dimensional analysis (also called factor-label method or picket fence)  is a method used to convert between units, perform unit conversions, and check the correctness of mathematical equations. 

It relies on the principles of dimensional consistency, which states that physical quantities being added, subtracted, multiplied, or divided must have the same dimensions or units.

The process of dimensional analysis involves using conversion factors, which are ratios of equivalent quantities expressed in different units, to convert from one set of units to another. 

Here's a step-by-step approach to using dimensional analysis:

1. Identify the given quantity: Identify the quantity you have, along with its unit.

2. Determine the desired unit: Determine the unit you want to convert the given quantity to.

3. Set up conversion factors: Find or derive the appropriate conversion factors that relate the given unit to the desired unit. Conversion factors often come from conversion tables, unit equivalencies, or relationships derived from mathematical formulas.

4. Construct conversion factor chains: Use multiple conversion factors as needed to create a chain of ratios that cancel out unwanted units and leave you with the desired unit. Each conversion factor should be chosen in a way that the units cancel out appropriately.

5. Perform the calculation: Multiply the given quantity by the conversion factors, making sure that units cancel out correctly. The final result will be the desired quantity expressed in the desired unit.

Metric Conversions

A base unit is the basis of measurement in the sciences. The most commonly used base units are liters (L) for liquids, grams (g) for mass, and meters (m) for distance. Metric base units can be converted to other useful quantities by adding a prefix (see the common metric conversions table below). The base unit does not have a prefix, and these prefixes are not used in any other measuring system.