per kilowatt-hour

The kilowatt-hour is energy, not power: one kilowatt sustained for one hour, which is exactly 3.6 MJ. That distinction is what makes a utility bill legible. A 1500 W space heater running four hours a day uses 6 kWh a day and 180 kWh a month, so at 15 cents that is $27 a month from one appliance. The general form is simply $\text{cost} = P \times t \times \text{rate}$, and almost every energy saving calculation reduces to it.

Comparing fuels means putting them on a common energy basis, which is exactly what this converter is for. Natural gas sold at $8 per gigajoule is about 2.9 cents per kilowatt-hour of fuel energy, roughly a fifth the price of typical grid electricity per unit of energy. That gap is why gas heating persists, and also why heat pumps change the arithmetic: a unit with a coefficient of performance of 3 delivers three kilowatt-hours of heat per kilowatt-hour of electricity bought, cutting the effective cost per delivered kilowatt-hour to a third. Fuel comparisons also have to account for appliance efficiency, since a gas furnace at 85 percent burns more fuel energy than it delivers as heat while resistance electric heating is 100 percent efficient at the point of use.