RV folks often wonder which source of energy is more costly to use. Keep in mind that in many RV parks the site includes electricity so those situations make it pretty clear since they don't include propane. But when you stay for longer periods, then most parks charge a monthly rate, plus electricity. Here are a few facts that with simple math should allow you to compare the two and get your answer.
Remember that the rate charged by RV parks for electric power varies widely. Escapee parks do not add any profit margin to the bill that they pay, but many parks do this. I have seen rates in the past year that ranged from a low of $0.09 to as much as $0.21 per kilowatt hour. Keep in mind that these numbers are for the portable electric heaters that we use in our RVs or for electric baseboard heat that some owners have added.
This is in no way applicable to a heat pump because that is not electric heat, but simply a device that collects heat energy from the outside are and sends it inside. It is impossible to give an efficiency for an RV heat pump because there are several manufacturers and they will vary. In addition, the efficency of a heat pump ranges very widely from warm temperatures where it can supply a great deal of heat with little power, while as the temperature falls below 35 degrees or so, the heat pump becomes very inefficient.
This information also would not apply to the heat strips found in some RV air conditioners, because the fan motor for it is outside of the RV and so heat lost from it is not supplied to the interior, and so that kind of electric heat is less than 100% efficient, probably more like 90% or a bit less, but I am only guessing on that one.
Some facts to compare propane and electricity:
One kW hour of electricity is 3,412 Btu's.
One gallon of propane is 91,502 Btu's.
One pound of propane is 21,548 Btu's.
Comparing cost of propane to cost of electricity:
Multiply the propane price per gallon by 0.037 to give the equivalent price per kilowatt hour of electricity, ignoring the efficiency factors.
Multiply the electricity price per kWh by 27.0 to give the equivalent price per gallon of propane ignoring efficiency.
For those who pay for propane by the pound/bottle:
The typical 20# tank holds 4.7 Gallons of propane.
A 30# holds 7 Gallons of propane.
Fuel efficiencies for each:
For heating applications we can consider electricity as 100% efficient. For each Kwh you get 3412 Btu's of energy 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 perhaps as little as 50% efficiency. Never assume any more than 70%.
Modern water heaters are a bit higher, but I doubt if any will be better than 70% efficiency and would consider that to be generous.
The refrigerator is probably the highest, approaching 80-90% due to the enclosed space in the chimney.
In my mixed usage, I would allow an overall efficiency a 70%, no more. This means, that a gallon of propane instead of 91,502 Btu's only delivers a usable 64,051 Btu's due to the losses in the appliances.
In other terms, the 20# bottle you just had filled only gives you 14# of usable Btu's or the motorhome bottle that took 15 gallons will actually supply 10.5 gallons of usable energy. A better way to look at this when comparing the cost of each is to consider each at it's usable energy level.
Effective energy comparisons:
One kW hour of electricity is 3,412 Btu's.
One gallon of propane is 91,502 X 70% efficiency equals 64,051 Btu's.
One pound of propane is 21,548 X 70% efficiency equals 15,083 Btu's.
Volume comparisons allowing for efficiency:
One gallon of propane is equal in useful energy to 18.8 KWh of electricity.
One pound of propane is equal in useful energy to 4.4 KWh of electricity.
Multiply the propane price per gallon by 0.0259 to give the equivalent price per kilowatt hour of electricity, considering the efficiency factors.
Multiply the electricity price per kWh by 18.8 to give the equivalent price per gallon of propane, considering efficiency.
Multiply propane cost per pound by .226 to determine equivalent price per kilowatt hour.
Multiply the cost per kilowatt hour by 4.4 to determine equivalent price per pound of propane.