What volume of beans yields a tablespoon of ground coffee? I have recently switched from using pre-ground coffee to grinding my own beans.

With the pre-ground, I used 1.5 tbsp per cup, however when i used the equivalent in beans (before grinding) the coffee was noticeably weaker. This makes sense to some degree, since the packing density of beans is lower than ground.

Is there an established ratio of beans-to-ground which I can use to accurately determine what volume of beans I need to grind to produce the same strength I had before?

Apart from the packing density, is there any other reason why the beans would be weaker than ground on a equal mass basis?
Here's an opportunity to start refining your brewing process.

Coffee brewers, including myself, tend to use weight as our measuring unit as opposed to volume since bean sizes vary significantly already without accounting for origin or roast level. All of these factors will change the real amount of coffee you believe you have once ground and also change the extraction parameters needed to make a cup of coffee of the 'same strength'.

From what it sounds, I doubt that the beans you use are of the same variety as the pre-ground coffee you used to use. Not all coffee will taste the same nor brew the same, and the best way to track and refine your brewing to your taste is to measure accurately your bean (origin/blend, roast level, weight used, grind size), water (to coffee ratio, temperature, purity), and extraction time. Depending on what brewing method you use there may be more parameters you will have to account for but ultimately the aforementioned factors will always play a role in any form of coffee brewing.

Start by weighing an amount of pre-ground coffee that you used previously to find out how much coffee you used exactly and start by grinding that much of your new beans to brew.

Good luck!