A friend of mine that is a whole lot smarter than I am gave us these facts.... The bottom line is the part that I understand.

Propane vs Electricity facts:

One kW hour of electricity is 3 412 Btu

One gallon of propane is 91 502 Btu

One pound of propane is 21 548 Btu

Conversion factors:

Multiply the propane price per gallon by 0.037 to give the equivalent price per kilowatt hour of electricity

Multiply the electricity price per kWh by 27.0 to give the equivalent price per gallon of propane

For those of us who pay by the pound/bottle:

The typical 20# tank holds 4.7 Gallons of propane

A 30# holds 7 Gallons of propane

Efficiency:

For heating applications we can consider electricity as 100% efficient.

For each Kwh you get 3412 Btu exchanged to the surrounding medium:

The air in your RV if you use an electric heater, ceramic or other

The water in your hot water heater

The heat tube in your refrigerator

Propane fired appliances of the typical RV variety IMO have very low efficiency.

The hot air furnace is the worst, with, in many cases probably less than 50% efficiency.

Modern water heaters are a bit higher, but I doubt if any will be better than 70% efficiency

The refrigerator is probably the highest, maybe 80-90% due to the enclosed space in the chimney.

I can not proof my hypothesis, but if you put your hand – and be very careful – on the exhaust port of either your furnace or hot water heater while the flames are on, you will find that you are heating a lot of the environment outside of your RV.

In my mixed usage, I would give the overall efficiency a 70%, no more.

This means, that a gallon of propane instead of 91 502 Btu only delivers a usable 64 051 Btu due to the losses in the appliances.

Or in other terms, the 20# bottle you just had filled only gives you 14# of usable Btu

A real $$ world example:

In South Texas, I pay 0.14 USD/Kwh electricity

It costs 27.00 USD to fill a 20# bottle, this is adjusted for efficiency 3.29 gallons. 27 USD / 3.29 gallon is 8.20 USD/gallon.

Apply conversion factor and you get 8.2* 0.037 is 0.30 USD/Kwh

As usual: Your amount of Btus out of a 20# may vary

So, in my case electricity is less than half the cost of propane.