3.3v switching regulator

You need to check the mAh rating of the battery (milliamp hours) you want to use.

For example, using a battery rated 1000mAh, with a load of 100mA, will be good for 10 hrs, (more or less - probably on the less side.) But it's a good starting estimate. The same battery with a load of 1Amp will only be good for 1hr. These are just optimistic estimate times because there will be other losses/efficiency involved so real world usage will be lower. Also, don't forget temperatures... when it's too cold outside and your batteries are not insulated, they'll run out of juice faster and you'll end up with a dead battery sooner.