The Automatic Pro app uses about 5% an hour while driving and no battery when not driving.
The original Automatic app uses about 5% an hour while driving and about 0.25% an hour when you're not driving. It needs Location Services and Bluetooth® to be on, which do use some battery power (these are probably already on if you use other mapping apps or Bluetooth devices).
It's important to understand that in both iPhone and Android if you look at the Battery Usage screen in your Settings, what you see there is the % of battery usage not of the total battery capacity, but of the fraction used since the last charge or in the time period you're viewing. So it's a percentage of a percentage.