"Averaging down" gets talked about a lot -- buy more of a stock after it drops, and your average cost per share goes down with it. That part's true. But a surprising number of people get the actual math wrong, because the intuitive shortcut (just average the two prices) isn't what your broker, or your tax return, actually uses.
It's a weighted average, not a simple one
Say you buy 10 shares at $100, then later buy 10 more shares at $60. It's tempting to average $100 and $60 and land on $80. But because you bought equal quantities at each price here, $80 happens to be correct in this specific case -- the confusion shows up as soon as the share counts differ.
Buy 10 shares at $100, then 30 shares at $60, and your average cost isn't $80. It's:
(10 x $100 + 30 x $60) / 40 shares = ($1,000 + $1,800) / 40 = $70
The average is pulled toward whichever purchase had more shares, not toward the midpoint of the two prices. This is basic weighted-average math, but under time pressure -- watching a position move -- it's an easy thing to eyeball wrong, especially across three or four buys instead of two.
Why this number matters beyond bragging rights
Your average cost per share is your break-even point before fees: the price the stock needs to reach for your total position to be worth what you paid for it. It's also generally the starting point for calculating capital gains or losses when you eventually sell, though the specific accounting method your broker or tax jurisdiction uses (average cost, FIFO, specific lot identification) can change which shares are considered "sold" first. If you've made several purchases at different prices and only sell part of the position, which method applies can meaningfully change your reported gain.
Averaging down lowers your cost, not your risk
This is the part that's easy to lose sight of. Buying more shares as a price drops does lower your average cost and therefore your break-even price -- that's arithmetic, not a strategy. It doesn't change whether the price will keep dropping, and it does increase your total dollar exposure to a position that's already moving against you. Averaging down on a stock because you still believe in the underlying reasons you bought it is a different decision than averaging down because the lower price makes the average look better. The math doesn't distinguish between those two -- only your own reasoning does.
What target-average math looks like in reverse
A related question: if you're holding shares at a loss and want to know how many more shares, bought at the current price, would bring your average down to a specific target, that's the same weighted-average formula solved in reverse. It's useful for deciding how much more capital a "top-up" would actually require, rather than guessing.
Doing the math without spreadsheet errors
None of this is complicated math, but it gets tedious and error-prone once you're tracking four or five separate buys, especially if you're also trying to solve for how many additional shares you'd need to hit a target average. The Stock Average Calculator handles both directions -- your current weighted average across multiple buys, and how many more shares at a given price would bring that average to where you want it.