Definition
Active users are the distinct people who used a product meaningfully in a period. Daily, weekly and monthly active users (DAU, WAU and MAU) use a day, 7 days and 30 days.
Defining "active"
The definition matters more than the number. Opening the app is a weak signal; doing what the product exists for is a strong one. Write down which actions count, and keep it stable.
Formula
Active users = count of distinct users with at least one qualifying event in the period. Count distinct people over the whole period: adding up seven daily counts doesn't give a weekly count.
How to measure it
Send events with a user ID. In LogZuno, mark the project's active events, then chart unique users, or weekly and monthly active users as rolling windows. See DAU, WAU and MAU.