A utility does not sell power. It sells energy — power multiplied by the time you kept drawing it. $E = P t$, read aloud E equals P t: $E$ is the energy, $P$ the constant power draw and $t$ the running time. Keep $P$ in kilowatts and $t$ in hours and $E$ lands directly in kilowatt-hours, the unit on every bill on earth.

Then the money: $C_e = E \, p_e$ — C-e equals E p-e — where $C_e$ is the cost in dollars, $E$ the energy in kilowatt-hours and $p_e$ the rate in dollars per kilowatt-hour. A tariff quoted as 12 ¢/kWh is $p_e = 0.12$; reading the 12 straight into the multiplication inflates the bill a hundredfold, and it is the error this lesson exists to kill.

The other trap is the unit itself. A kilowatt-hour is an ENERGY, not a rate: kW is how fast, kW·h is how much. “Kilowatts per hour” is a phrase you will hear on the news and should never write. And the hour is already inside the unit, so converting to seconds is a second helping of a conversion you already made.

Worth knowing where the money actually goes: a 15 kW compressor left running two hundred hours a month costs about as much as a small car payment, and the audit that finds it takes twenty minutes with these two relations.