Dimensional Analysis: Checking Equations With Units

Dimensional analysis ensures equations make sense by comparing their units.
Every physical quantity—like velocity, force, or energy—can be expressed in base dimensions.
Common base dimensions include length (L), mass (M), and time (T).
If two sides of an equation don’t match in dimensions, the equation is wrong.
It helps scientists catch mistakes without solving the full problem.
Dimensionless numbers, like the Reynolds number, reveal hidden patterns in physics.
Scaling laws from dimensional analysis predict how systems change with size.
Engineers use it to design models and prototypes before building real systems.
It provides quick estimates when exact solutions are too hard to find.
At its heart, dimensional analysis is physics’ reality check, keeping math grounded in units.