Circuit Bytes · Episode 8 · Circuit basics · Energy
Watts vs kilowatt-hours
Watts measure how fast something uses energy; your power bill charges for the total energy, in kilowatt-hours. Run 1,000 watts for one hour and you've used one kilowatt-hour.
Power is a rate, energy is a total
Think of a car. Its speed tells you how fast it's going right now; the distance tells you how far it went in total. Watts are like speed: a measure of power, how fast energy is being used at this moment. Energy is like distance: the total you used over time.
The two are linked the same way: distance = speed × time, and energy = power × time.
What a kilowatt-hour is
A kilowatt (kW) is 1,000 watts. Run something that uses 1,000 W for one hour and you've used one kilowatt-hour:
1,000 W × 1 h = 1 kW × 1 h = 1 kWh
In physics units, one kilowatt-hour is 3.6 million joules. Power companies use kWh because joules are far too small for a whole month of use.
The heater, two hours
The 1,500 W space heater from the last episode is 1.5 kW. Run it for two hours:
1.5 kW × 2 h = 3 kWh
To work out the cost, multiply the energy by your rate. With an example rate of 15 cents per kWh:
3 kWh × $0.15 = $0.45
A 60 W bulb uses energy 25 times more slowly, so it needs 50 hours to use the same 3 kWh: 0.06 kW × 50 h = 3 kWh.
Try it yourself
Pick a device with a wattage label, such as a hair dryer, kettle or TV. Divide the watts by 1,000 to get kW, multiply by the hours you use it in a day, and you have kWh per day. Then find the price per kWh on your power bill and multiply. What does that device cost you each month?
Good to know
- Watts measure power (energy per second); a kilowatt-hour is energy: 1 kWh = 1,000 W for one hour = 3.6 million joules.
- The speed and distance comparison is exact in form: energy = power × time, just as distance = speed × time.
- Fifteen cents per kWh is a round example. Real rates vary a lot by province, state and time of day: the US residential average has been roughly 15 to 17 cents in recent years, and many Canadian provinces are lower, around 7 to 13 cents.
- Bills also add fixed charges, delivery fees and taxes, and some commercial customers pay separately for peak demand in kW.
- The heater math assumes it runs at its full 1,500 W the whole time. Thermostats cycle heaters on and off, so real use is often lower.
- A typical US home uses about 900 kWh a month (EIA, 2022 average).
Test your knowledge
Quick quiz: Watts vs kilowatt-hours
4 multiple-choice questions. Pick one answer for each, then check how you did.
Sources
- OpenStax (Rice University), College Physics, "20.4 Electric Power and Energy": E = Pt; a kilowatt-hour is 3.6 million joules; cost = energy in kWh times the rate per kWh
- US Energy Information Administration, "Electricity explained: Measuring electricity": kilowatts as power, kilowatt-hours as the energy on bills
- US Department of Energy, Energy Saver, "Estimating Appliance and Home Electronic Energy Use": watts × hours used ÷ 1,000 = kWh; multiply by your utility rate for the cost
- US Energy Information Administration, "How much electricity does an American home use?": about 899 kWh a month in 2022
Video transcript
Your power bill doesn't charge you for watts. It charges for something else.
Watts tell you how fast something uses energy, right now. Like a car's speed. Your bill cares about the total, like the distance you drove.
That total is the kilowatt-hour. A kilowatt is a thousand watts. Run 1,000 watts for one hour, and you've used one kilowatt-hour.
Remember the 1,500-watt heater from last time? Run it for two hours. One and a half kilowatts times two hours is three kilowatt-hours.
Say your rate is 15 cents per kilowatt-hour. That's 45 cents. The 60-watt bulb would need 50 hours to use the same energy.
That's your bite. Next: why touching two wires together makes sparks.