riddle - Before the Ides of March

If I lost a leg I'd be twice the size
When grown up I cause many multiplies
Maybe mistaken for a fifth in Rome
Or for twelve thirteenths in a modern home

What am I?

Answer

You are

$\pi$

If I lost a leg I'd be twice the size

By removing one vertical line from $\pi$ we get $\tau$, which is a standard mathematical notation for $2\pi$; see for example the links http://www.thepimanifesto.com/ and https://xkcd.com/1292/

When grown up I cause many multiplies

$\prod$ is used as symbol for products in mathematical equations.

Maybe mistaken for a fifth in Rome

Aicient Greek (not sure what this has to do with Rome) notation for 5 was something that resembles as PI. . Thanks to Jan Ivan

Or for twelve thirteenths in a modern home

I got nothing here. Still looking for something that matches.

Bonus (Before the Ides of March)

Happy Pi day. March 14. The Ides of March was March 15th in Rome.