Vacuum cleaner power rating does not match line voltage and current rating
There are many unknown factors. Both power and current will vary with load and there is only one way to find out how they relate: measure them.

One of the most important properties of AC power you neglected is the power factor cos(φ) with inductive loads:

\$P = U \cdot I \cdot \cos(\varphi)\$

\$\begin{align} \cos(\varphi) &amp; = \dfrac{P}{U \cdot I} \\ &amp; = \dfrac{1300\text{W}}{120\text{V} \cdot 12\text{A}} \\ &amp; \approx \boxed{0.9} \end{align}\$

which sounds about what I'd expect for a vacuum cleaner.

Check this Wikipedia article on electric power for more background details.