Dimensional analysis

Dimensional analysis is a method that is used to check if an expression that has been derived could be incorrect. Suppose a problem involves a mass $m$ [kg], a length $L$ [m], a time $t$ [s], and a force $F$ [N]. You are asked to calculate a velocity. The expressions $3L/t$ and $\pi\frac{Ft}{m}$ could possibly be correct because they have the units of [m/s]. The expresions $3Lt$ and $\pi\frac{F}{m}$ must be incorrect because they do not have the units of [m/s].

Whenever you derive an expression, you should check the units. If the units are wrong, you have made a mistake.

The argument of a function such as $\sin$, $\cos$, $\exp$, of $\log$ must be unitless. An expression like $\sin\left(\frac{Ft^2}{mL}\right)$ could be correct while $\sin\left(\frac{Ft}{mL}\right)$ must be wrong.

For reference, there is a table of SI units.