The folks at RV.Net Open Roads Forum: General RVing Issues: Use of Electricity vs propane got to answering the question.
Truckin41 noted that propane isn’t just the per gallon cost but also the delivery costs and these can add up when you take a small RV propane tank a few miles to get filled.
Tonytheobald noted that “1 Kilowatt of electricity equals 3412 BTUH (Cost in our park is about $0.12 ) — 1 Gallon of Propane equals 92,000 BTUH. (Cost varies but I just bought it at $2.23/per gallon.)This would cost about $3.25 if you heated with electricity. ”
Ray,IN cited a rule of thumb: “Since LPG furnaces are not 100% efficient, a formula was devised with that in mind. Find the cost per KWH of electricity and multiply by 22. The result must be less than the price one gallon of LPG for electricity to be cheaper to use.”
In other words, a gallon of propane is equivalent to about 27 KwH of electricity. The 22 number is allowing for propane being 80% as efficient as electricity and that sounds like a good RoT (rule of thumb).
You can find out what the power company is charging you for electricity but you need to be careful of the surcharges, taxes, and other hidden fees. Usually, electricity runs around ten cents per kilowatt hour which means $2.20 per gallon for the propane equivalent in heating.
The 22:1 ratio also means that small changes in the cost of electricity can easily change the balance. That can make you a nervous wreck if you want the cheapest heating and try to figure each and every bill to decide what to do.