There are four ways of counting audiences at events: from ticket sales, manual counting, automatic counting, and aerial photography. The choice of method depends on the budget available, the importance of accuracy, whether the event is indoors or outdoors, and whether people pay to attend.
Measuring an audience at an event is simple. As long as all of these statements are true, all you need to do is count the number of tickets sold:
Perhaps you can see already that there are many exceptions: complimentary tickets, "no-shows" (people who buy tickets but don't turn up), and the circus tradition of children wriggling under the edge of the tent, or attaching themselves to large groups of strangers.
The lowest-tech method is to have a person at each entry point, with a piece of paper and a pencil. Every time somebody comes through the entry, the counting person makes a mark on the paper. At the end of the day, these marks are counted. If all goes well, the number of marks is the number of people attending. In practice, it tends to be lower. The work is so boring that the counters become distracted, and forget to enter some people entering.
A slightly less manual method is to use a tally counter. This is a small hand-held machine with two buttons and a counter rather like the odometer in a motor vehicle's speedometer. One button zeroes the tally, and the other adds one, every time it is pressed.
Automatic counters work by breaking a beam of light. Though they tend to undercount (e.g. when two people go through the beam at the same time) automatic counters are still more reliable than using people to do the counts - even if those people have automatic clickers. The narrower the entrance, the less error.
Another type of automatic counter is used for counting vehicles. It's a rubber tube that runs across a roadway. At the end of the tube is a box containing a counter. Every time a heavy enough wheel crosses the tube, it is squeezed, and an impulse (air or electrical) increments the counter. These are fine for vehicles, but no good for people on foot (who step over the tube). Because they count axles, not vehicles, and some vehicles have more than 2 axles, you need to make an estimate of the average number of axles per vehicle, and divide the total count by that.
A clicker is a device with a button that a staff member presses every time somebody passes - they used to be manual, but these days are more often electronic. This is just a slightly easier way of making a manual count, and is subject to the same measurement errors.
As the price of automatic counters has been steadily falling, and they don't rely on people remembering to press a button, we recommend using automatic counters - either continuously at every entrance to the event, or (if the price is a problem) rotating between entrances at random.
The third option - useful for very large events, and those without clearly defined entries and exits - is aerial photos, usually taken from small aircraft flying at about 3000 feet, which is close enough to count heads, but far enough to include a lot of heads. The photos are divided into grids, and the number of visible heads in randomly selected grid cells is counted manually, then multiplied by the ratio of total cells to sampled cells. This method tends to under-count in wet weather, when many people are using umbrellas. And it doesn't work well at night. An example from the San Francisco Chronicle.
The previous section was all about counting people - but that's only the beginning of event research. More often, the organizers know how many are there, but want to get their opinions.
The page on Visitor surveys (from Know Your Audience provides a lot of information on this, but there are other methods too.
See the page on event evaluation for a good method of getting detailed feedback on a public event - though it applies more to seminars than to artistic performances.
In the rich countries, more and more use is being made of electronic devices that audiences can use to evaluate events. For example, the US organization FMR Associates has developed a high-quality method called EARS (Electronic Attitude Research System). This is used mainly for measuring audience reactions to music - though it can be used for any type of radio program or speech. Up to 100 people sit in a room and listen to abbreviated programs, and press buttons on devices similar to TV remote controls. A receiving unit picks up all the signals and converts them into a second-by-second average. We commissioned FMR for some work for the Australian Broadcasting Corporation in the 1990s, and the system worked very well indeed.
As events are usually one-off, there's no standardized method of presenting audience sizes. Often, only a single cumulative figure is presented, not stating any margin of error or range. A more honest approach is to include some estimate of error (which can be derived by using several methods to make the same estimate), and attendance (or at least entry) figures for each day, or each hour (for a one-day event).
All of the above methods tend to produce counts that are too low. Humans forget to mark the forms, automatic counters miss people when several enter together, and aerial photos, unless taken from exactly overhead, miss people who are not visible behind other people.
For more on counting crowds with aerial photography, there's an interesting article in the Poynter Ethics Journal for 27 February 2003, including several links to follow.