Market capitalisation is the share price multiplied by the number of shares outstanding: what it would cost to buy every share at the current price. It is the standard measure of company size and the basis of most index weightings.
It is not what a company is worth to an acquirer, who also has to settle the debt and gets the cash. That figure is enterprise value, market cap plus net debt, and for a heavily indebted company the two can differ by more than the market cap itself.
Multiplying is trivial; knowing what to multiply is not. A company with more than one class of share, such as Berkshire, Alphabet and many family-controlled businesses, has a price for each class and a share count that may be reported in units of only one of them. Combining the wrong pair produces a number wrong by the conversion ratio between the classes, which can be a factor of a thousand or more.
US-listed foreign companies bring a second version of the same trap. An American depositary share represents a fixed number of ordinary shares, commonly five, four or eight to one, and the company reports its share count in ordinary shares while the price you see is per depositary share. Multiply those together and the answer is too large by exactly the depositary ratio.
Neither error announces itself. The result is a plausible-looking number in the right units, which is why a market cap is worth checking against something independent: the company reported equity, its revenue, or simply whether the ranking it produces makes sense.
Shares outstanding is every share in existence. Free float excludes those not really available to trade, such as founder and family stakes, government holdings and cross-shareholdings, and it is what index providers usually weight by, so a company index weight can sit well below its headline size.
Fully diluted counts add the shares that would exist if options and convertible instruments were exercised. For a company that pays heavily in equity the diluted count can be materially higher, and it is the more honest denominator for anything expressed per share.
On the S&P 500 heatmap, tile area is the square root of market cap rather than market cap itself. The range within the index is enormous, the largest constituent being worth thousands of times the smallest, so at true proportion a handful of megacaps would fill the screen and several hundred companies would be invisible.
The square root compresses that while preserving the ordering, and a floor keeps the smallest tiles clickable. It is a deliberate distortion: judging what share of the index a sector represents by eye will understate the giants and overstate the tail.