This simple app can help you increase the standby time of your device: WiFi Automatic automatically disable your WiFi radio when you don't need it and thereby lowers the battery consumption.

You can also specify to automatically turn on WiFi again if you turn on your device or when you enter a specified location (requires a cell radio and therefore does not work on WiFi-only tablets!). Also the app can regularly scan for available networks to connect to and re-disable WiFi if no suitable network is found. This way you are always connected to your WiFi network when using the device.

WiFi Automatic is open source: https://github.com/j4velin/WiFi-Automatic

A WiFi connection generally uses less power than a mobile data connection so on your phone it makes sense to keep the WiFi radio active whenever a WiFi network is in range


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Permissions:
RECEIVE_BOOT_COMPLETED - is required to start the service again when rebooting your device

The following permissions are required to observe and change the WiFi state:
CHANGE_WIFI_STATE
ACCESS_NETWORK_STATE
ACCESS_WIFI_STATE

The following permissions are required to the "turn on WiFi when entering these locations" feature:
INTERNET
WRITE_EXTERNAL_STORAGE
ACCESS_COARSE_LOCATION
ACCESS_FINE_LOCATION
BILLING