Dimensional Analysis

Dimensional analysis helps us check whether equations make physical sense and convert between different unit systems. It is used by physicists all the time!

Every physical quantity has dimensions that describe what type of quantity it is.

Basic Dimensions

We use square brackets to denote dimensions. The three fundamental dimensions are:

• Length: $[d] = L$ (for any distance $d$)
• Time: $[t] = T$ (for any time $t$)
• Mass: $[m] = M$ (for any mass $m$)

When quantities combine these dimensions, we express them as products and quotients. For example, for some physics quantities you may or may not already know:

• Velocity $v = d/t$ has dimensions $[v] = L/T$ (length per time)
• Acceleration $a = v/t$ has dimensions $[a] = L/T^2$

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