Electrical Energy (E = Pt)

Power is the rate at which energy is delivered, so energy is power kept up for a while. That is all $E = Pt$ says, and like every rate-times-time relation it is true by definition rather than by discovery — a watt is a joule per second, so watts multiplied by seconds give joules back. The distinction it enforces is the one people most often lose: power is not energy. A 2000 W heater is not consuming 2000 of anything; it is consuming at a rate of 2000 joules every second, and what it costs depends entirely on how long you leave it on.

Utilities meter in kilowatt-hours because the joule is inconveniently small: 1 kWh is 1000 W sustained for 3600 s, or exactly $3.6 \times 10^{6}$ J. A 1500 W baseboard heater running six hours a day for a thirty-day month uses $1.5 \times 6 \times 30 = 270\ \text{kWh}$; at ten cents a kilowatt-hour that is $27 on the bill. The same 270 kWh would run a 15 W LED lamp continuously for about two years. Energy comparisons like that are the only honest way to judge where a bill actually goes, and they almost always show that the heating and hot water dwarf everything with a screen on it.

The kilowatt-hour is a compound unit of the sort engineers usually avoid, and it survives because it matches how people buy electricity: a rate you can read off a nameplate multiplied by hours you can read off a clock. Watt-hours, ampere-hours and joules all measure the same physical stock of energy in different currencies: $1\ \text{Wh} = 3600\ \text{J}$, and an ampere-hour becomes watt-hours only after you multiply by the voltage. On the site's other pages this same relation appears as work over time in mechanics; there is no separate electrical version of it, only a separate unit.

The assumption doing the quiet work here is constant power, and most real loads are not. A thermostatted heater is either fully on or fully off, so its average power over an hour is the rated power times its duty cycle — a 1500 W baseboard cycling a third of the time is a 500 W load as far as the meter is concerned, and using the nameplate figure triples the estimate. A refrigerator, a well pump and a furnace blower all behave the same way. The other trap is a billing one worth knowing if you read a commercial invoice: those bills carry both an energy charge in kilowatt-hours and a demand charge in kilowatts, set by the highest fifteen-minute average draw in the period. The demand charge is a power charge, this equation does not produce it, and no amount of shortening run times will reduce it — only flattening the peak will.