Estimating Apple’s iPhone sales has been easy. Just pick a number. However, calculating Apple’s iPhone sales isn’t too hard.

The number of iPhone sold on the first weekend of availability can be estimated by this formula:

N1 = 1800 * P1 + 161 * P2

Where P1 = the number of iPhone placed in each AT&T store prior to 6 PM on June 29th and P2 = the same number for Apple’s 161 U.S. stores. Most stores were sold in a few days.

From information gleaned by iPO staff during the grand opening, the average number for P1 was likely about 80 and probably varried by city. Some large cities probably had a lot more. Some small town stores perhaps 40.

For the Apple stores, estimates on the Internet and guesswork place P2 at about 200. In the bigger cities, the number may have been 300-500. (iPO documented 500 people in line in San Francisco.) In Denver, I counted 176 people in line at one of the Apple stores on June 29th, then queried if they were sold out the next day. They were not.

So day one sales were likely about: 1800 * 100 + 161 + 200. That’s 176,200. Accounting for phones not activated, given as gifts, activated after the chaos, the AT&T number of 146,000 looks pretty good.

Next, the phones sold since then is given by:

N2 = 1800 * R1 * D + 161 * R2 * D

Where R1 is the rate sold per day at AT&T stores, R2 is the number per day sold at the Apple stores, and D = the number of sales days since June 29th, call it 25 since Apple stores are open on Sunday. If we assume R1 = 20 and R2 = 40, then

R2 = 1800 * 20 * 25 + 161 * 40 * 25 = 1.061M.

I’ll make the assumption that the average R1, R2 accounts for the short period of time when some stores were sold out. However, the iPhone has been in stock at most stores for awhile now.

But wait!

Whether these estimates are good or bad for R1 and R2 doesn’t seem as important as the multiplying factor of D. For example, even if R1 and R2 were as small as 10, N2 would still be 490,000 and some change. If R1 and R2 were only 5, the sales since opening day would still exceed N1.

The upshot is that even if the opening day sales were as few as 176,000, the total number of iPhones sold so far in July is probably a much larger number. Unfortunately, we won’t know what that number is for some time.