Dimensional Analysis
Definition
Checking physics with units — a powerful method to verify formulas, catch errors, and even guess new ones.
Technical definition
The technique of tracking base dimensions (M, L, T, etc.) through equations. Both sides of a valid equation must have identical dimensions. It can derive formula forms up to dimensionless constants (e.g., pendulum period must go as √(L/g)).
Example
Checking v = at: [L/T] = [L/T²]·[T] = [L/T] ✓ — dimensions match, so the formula is at least plausible.
Common confusion
Dimensional analysis cannot find dimensionless constants (like 2π) or tell + from −. It validates the shape of a formula, never the exact numerical factors.