Pitching rates

http://www.homebrewtalk.com/f163/why-not-pitch-your-yeast-cake-166221/
http://www.mrmalty.com/pitching.php
http://www.whitelabs.com/beer/homebrew_FAQ.html

For 1.5 Gallons, I need roughly 30-68 billion yeast cells. Dry yeast ranges from 6-20 billion cells per gram. So 4 grams or 1/3 of a dry 11.5g yeast packet.

The standard, according to Fix, Daniels, Bamforth et al., is one million active cells per milliliter of wort per degree Plato. Or:

1,000,000*1ml*1°P

Constants:

• There are 3785 ml per US gallon, or 18,925 ml in 5 US gallons. Round this up to 19,000 (19L) for ease of calculation if you do predominantly 5 gallon batches.
• One °P is roughly equivalent to 4 points of gravity. For an approximation, 1.048 is thus 12°P. This goes askew above around 1.060; in fact, you may find it simpler to consult a chart like this:http://plato.montanahomebrewers.org/ - or use the formula:

{Plato/(258.6-([Plato/258.2]*227.1)}+1 = Specific gravity 

Thus, for 5 gallons of wort at 12°P, we need

1,000,000 * 1 ml * 12°P, or 12,000,000 cells per ml.

12,000,000 * 19,000 = 228,000,000,000 - that's 228 billion cells.

You can expect around 1 billion active cells in a ml of harvested slurry, depending on how much trub and break material makes it into the fermenter. My counts ranged from 0.5 billion to 2 billion, depending on style brewed and brewery practice. 1 billion is a solid average across a dozen different breweries, professional and amateur.