180 classes a week adds up to over 20 classes a day. ?? I am wondering if there is a typo there. Or perhaps you coordinate for several physical locations? I looked for your profile to see geographically where you were, but the profile won’t pull up.
Nancy is right that although the standard is to have the instructor take a count it is useful to have someone in charge of taking an official count. This is partly because people might inflate if they felt pressured, but also because it can be hard to count in a big class, especially in a place where people can wander in after the class has started.
In a place where people pay per class Mind Body is a good program. I will give you a count and keep statistics, as well as member data.