How do actifit work?

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Almost all smartphones have accelerometer attached on them. Accelerometer is a sensor that senses  axis-based motion which can also be found on fitness trackers. It doesn't need internet connectivity or location tracking to be able to track the number of steps you move

You say "sometimes" on your question. When Actifit fails to detect your movement/steps it has nothing to do with your internet connection or GPS. That's because your phone enters sleep mode due to inactivity (accelerometer detecting motion doesn't prevent phones entering sleep mode). When your phone is on sleep mode processes from all apps deemed not essential by the operating system (Android/iOS) will be partially or fully terminated in order to save battery power and Actifit is included. You may want to "Enable Aggressive Background Tracking" on Actifit setting if sometimes Actifit doesn't track your steps.