Estimating crowd sizes can be a very controversial subject. For example Donald Trump claimed there were a "million-and-a-half people" at his inauguration and said that the press were "going to pay a big price" for reporting figures way below his expert opinion.
One way to estimate the size of a crowd is to use maps to calculate the surface area of a crowd and then to multiply that surface area by the estimated density of the crowd. MapChecking is a very simple interactive map tool that can do this for you. It allows you to draw the surface area of your crowd, demonstration, march or gathering on a Google Map. It then allows you to enter an estimate for the number of people per square meter in your crowd. Once you have entered those two variables MapChecking automatically works out the crowd size.
Using a Reuters photo of Trump's inauguration with Map Checking gave me a figure of 357,143 people in the National Mall on January 20, 2017. If anything this might be being a bit generous as I haven't allowed for what look to be sizable gaps in the crowd in the Reuters photograph.
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