The calculations are done for me on my bill. Take a look at the numbers here and see if it helps you with the formula to use.
Things to check for when comparing monthly bills:
1. The billing period. The bill I received at the end of September was actually for the month of August so even though I had turned off everything for nearly the whole month of September, that lesser useage won't be reflected until I get the bill at the end of October.
2. Seasonal rate changes. Here, there are different kilowat charges for the season with the summer rate being higher than the winter rate.
3. There's also a different allowance of kilowat hours before a new level of rates kicks in.
4. Check for new taxes and surcharges. My bill this month has a new Solar surcharge, last month the state surcharge was new. The new year last January brought the new City tax charge.
Okay, let's get to the examples you gave. Let's say that both bills were $150 each and nothing else changed to alter the numbers except for the different number of kilowat hours. No new taxes, surcharges or seasonal rate changes were added.
$150.00 divided by 800 kilowats equals a rate per kilowat hour of $0.1875
$150.00 divided by 1200 kilowats equals a rate per kilowat hour of $0.150
So, if there wasn't a general rate increase then you need to call the utility company and ask for an audit of your bill.