[Any Language] fitting products into a shipping box

This is a problem I've been recently wrestling with: when a user places an order through Site X, I need to be able to determine whether a certain shipping box will accommodate the products in the order, in terms of volume, and 3 sides.

Is there an algorithm to do this, or could someone point me in the right direction of where to go with this? I have my own theories, but while I'm competent with math, I'm not a math genius either...

I'll definitely take examples in whatever language you want to give them to me in. PHP is preferable, but since this is pretty much only math operations, any other coding language is readable to me.

Thanks!

What is the unit volume of each products and what is the geometric shape of each product.

I think you understand what i am asking, but of course you will not find any optimized formula in math, if you need to calculate how many onion you can put in a 20 cubic ft. box.