On the nRF51822 Is it possible to check the battery level using the on-board AD, software connected internally, avoiding external resistor divider.
If not what is the best method, hardware and software?
If you have a battery that has a nominal voltage above the maximum supply current of 3.6V, then you will have to add an external voltage divider in order to measure the battery voltage, as described in this blog post.
If the batter has a nominal voltage below 3.6V then you can use the ADC measure the battery voltage directly, see this github repo for ADC examples for the nRF51 series.
Take a look at the graphs in this post to see why!