How do I know if I need a sub woofer?

It can be difficult. You don't know what you are missing if you can't hear it.

I had a nice pair of ADS L-810II speakers that I purchased new in the late 70's. They were a "full range" speaker and really nice example for that era, still in use by my little brother. With my present, way short of state of the art system, I am frequently shocked by low frequency information that I never knew existed.

I presently have a pair of KEF R3 Meta bookshelf speakers with dual HSU subs. Those subs are essentially flat to around 20hz. I hear (and feel) low frequency music that just was never there before, even on decent headphones,

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. 

I agree with soix.

Agree all systems benefit from an appropriate pair of subs...

you can't sleep at night!

There are all kinds of technical reasons, but the ultimate answer is, What do you hear, or miss?

Go to a live performance of chamber music and listen to an acoustic bass (instrument). Chamber, because there is more chance to hear the bass by itself. Acoustic, to get a direct feel for how an unadulterated bass instrument sounds and feels.

Then listen to similar music on your system. You will hear the bass differently. If the bass lacks depth, or floats strangely around the room, *and if you want to try to improve those shortcomings*, then you might try subs.

Cheers.

Thanks everyone. You have given me a lot to think about....I hope this doesn't keep me awake tonight.  Elliot what should I do if I have trouble sleeping...

The room will have a big influence on wether you need subs or not. 

Seems most add subwoofers for the following reasons:

• fill in bass for standmount speakers 
• adding more bass energy 
• Improving fidelity- seamlessly fills in bottom end and supports up to midrange 

Sound meter app + streamed white noise will inform you for certain.