How do I know if I need a sub woofer?

A subwoofer's job isn't only shoringup bass. 

Room bass management of nodes and anti nodes because... Physics of sound vant be circumvented is why one needs a subwoofer or two.

Has nothing to do with playing low alone even though that is a key objective

Depends on what your listening objectives are.  Home theater- subs can come in handy.  Mostly 2-channel music, you would be better served by using speakers that can supply ample bass bandwidth.  

The sad reality is that unless you have full range speakers (usually very large $) AND sufficient current (not just watts) to drive them you need subs.  Sigh. 

You will know, if, you are not happy with the low frequencies your speakers put out.

First, you want at least two subs, and second there are very few systems that wouldn’t benefit significantly from subs.  Anyone who tells you differently hasn’t heard decent subs properly set up and dialed in.  Not only will your in-room bass improve but also imaging and an expanded 3D soundstage.  Once you listen with good subs you won’t wanna listen without them.