So I did the cost-of-gas analysis last week and now I got to wondering if the cost of natural gas was high enough to justify electric heat. I first heard about this from someone who was building a workshop. They were trying to figure out if they should bother to install a gas furnace or if electric heat would be cost-effective — so I got the bug in my head about the conversion between the heat energy in natural gas and that in electricity.

So here's the deal: like last week, we have the cost of gas heat (C_g) and the cost of electric heat (C_e) which, at the break-even point will be the same:

C_g = C_e

And what we want to end up with is a break-even point where the price of a unit of natural gas (P_g) is some constant multiplied by the price of a unit of electrical energy (P_e). This is where it gets a little funny because I'm just going to assume the efficiency of a gas furnace is 80% and that an electric heater is 95%. In other words, the total heat in a cubic-foot of natural gas has a certain amount of chemical energy that can be converted to heat, but a furnace is not perfectly efficient at recovering that heat as usable heat in your house (i.e. some necessarily needs to go up the chimney to get rid of the carbon dioxide). Electric heaters are much more efficient as the easiest thing you can do with electric current is to turn it into heat — it's more like 100% efficient, but I'll assume there's some cable losses in the house and maybe it has a fan that does non-heating work.

It also gets a little funny because when I talk about the total cost of heating, for purposes of determining the conversion factor between prices-per-unit, it doesn't matter how much heat — just that it's the same amount. So let's say it's 2000 Calories — like kilocalories or the Calories in terms of food. Trust me. It'll be a fun result.

So now what we've got is that the cost is the unit price * 2000 Calories:

2000 Calories * P_g = 2000 Calories * P_e

Obviously the 2000 Calorie factor cancels out — but I'll leave it there for a while.

Now let's turn to the electricity. We pay for electricity in kilowatt-hour blocks. If I go to Google, I see that 2000 Calories is 2.324 kilowatt-hours. If I factor in that 95% efficiency, I'll need 2.447 kilowatt-hours to make 2000 Calories of heat.

Now gas gets kind of weird [great, more weird, right?] because it's delivered in hundreds of cubic feet (ccf) but billed as therms (100,000 British Thermal Units or 100,000 BTUs). RG&E does the conversion on the bill: 1.0136 therm is 1 ccf. Again turning to Google, 2000 Calories is 0.0793 therms. If I factor in that 80% efficiency, I'll need 0.0991 therms to make 2000 Calories of heat.

So now what I have is:

0.0991 therms * P_g = 2.447 kilowatt-hours * P_e

And since P_g is in dollars/therm and P_e is in dollars/kilowatt-hour, it all works out to dollars-equals-dollars which is perfect.

Moving stuff around, that's:

P_g = 2.447 kilowatt-hours * P_e / 0.0991 therms
P_g = 24.69 kilowatt-hours/therm * P_e

In other words, if you take the price-per-kilowatt of electricity, and multiply it by 24.69, you get the price-per-therm of gas for the same amount of heat.

I had signed up for ConEdison Solutions GreenPower (which is all renewable wind and hydroelectric) so there's separate sections for how much electricity costs. On the last bill I used 363 kwh and paid ConEdison $36.12 and RG&E another $20.93 (-$19.38 in fixed charges for the privilege of being a customer), so that's a total of $37.67 in charges based on a per-kwh rate. Dividing the total by 363, I get an overall cost of $0.104/kwh.

Doing the conversion, if my gas cost is higher than 24.69 * $0.104 = $2.57/therm, then it's cheaper to run electric heat.

I used 157.1 therms of gas, but 3 therms are included for "free" in my $14.38 customer charge and $0.62 "bill issuance charge" — $15.00 total. I paid $209.20 for gas with all the surcharges and such, so removing the $15.00 fixed charge, that's $194.20. Dividing by the 154.1 therms used, that's $1.26/therm — just about half the cost of heating with electricity.

But hey, now you can do the math yourself with your own bill. If it's easier, you can round up the conversion to 25 — so the break-even point is when the cost of a therm of gas is 25 times the cost of a kilowatt-hour of electricity.

Oh yeah, but what about the fun with the 2000 Calorie number? That's about a day's worth of food, right? So if I ran on electricity, it would cost 2.447 kilowatt-hours * $0.104/kwh = $0.25, or if I ran on natural gas, that would be 0.0991 therms * $1.26/therm = $0.12.