Lessons · Electrical · energy and the bill (kWh)
Watts are a rate; the bill is watts times hours
Power is how fast energy is used; energy is power multiplied by time, and the meter on the house counts it in kilowatt-hours.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A customer asks whether the new heater in the back room is why the bill jumped. Watts alone cannot answer that; hours can. A heater on eight hours a day is a very different bill from the same heater on for ten minutes.
How to think about it
Convert watts to kilowatts by dividing by 1000, multiply by the hours it actually runs, and you have kWh. Multiply by the price per kWh and you have money. Write the units at each step so a watt never gets billed as a kilowatt.
Worked example
1200 W = 1.2 kWKilo means a thousand. The bill is in kilowatt-hours, so start there.
1.2 kW × 6 h = 7.2 kWhOne day. Kilowatts times hours is kilowatt-hours; the kW and the h stay stuck together in the unit.
7.2 kWh × 30 days = 216 kWhA month.
216 kWh × $0.15 = $32.40At fifteen cents a kilowatt-hour. That is the number the customer was asking for.
Your turn
A 100 W lamp on for 5 hours a day. Write the line that gives one day's energy.
0.1 kW × h = 0.5 kWh
Solve one, graded on the server
The trap
Multiplying watts by hours and calling it kWh. 1200 W × 6 h is 7200 Wh, which is 7.2 kWh; forgetting the thousand makes the bill a thousand times too big, and it still looks like a real number.