Calculator of Alexandria

Electricity cost calculator

What an appliance costs to run from its watts, or volts and amps, hours of use and your price per kWh, with the kilowatt-hour explained.

I know the

On the label or plug. Use the average draw for things that cycle on and off, like fridges.

From your bill. The US average is around 17 cents.

Cost for the period
Energy used (kWh)EE
Cost per day
Power (W)PP

Formula

cost=P×h1000×c\text{cost} = \frac{P \times h}{1000} \times c
How it's derived

The formula

E=P×h1000E = \frac{P \times h}{1000} cost=E×c\text{cost} = E \times c

PP is the power in watts, hh the hours of use, EE the energy in kilowatt-hours and cc your price per kilowatt-hour. If you know the voltage VV and current II instead, P=VIP = VI.

Where it comes from

Power is the rate energy is used: one watt is one joule per second. Energy is power times time. A joule is tiny, so utilities bill in a bigger unit, the kilowatt-hour: one thousand watts running for one hour.

1 kWh=1000 W×3600 s=3.6 MJ1\ \text{kWh} = 1000\ \text{W} \times 3600\ \text{s} = 3.6\ \text{MJ}

So to get kilowatt-hours, multiply watts by hours and divide by 1000. The bill is that number times the price per kWh.

Where does P=VIP = VI come from? Voltage is energy per unit of charge (joules per coulomb), and current is charge per second (coulombs per second). Multiply them and the coulombs cancel, leaving joules per second, which is watts.

Worked example

A 1500 W space heater runs 3 hours a day for 30 days, at 17 cents per kWh:

E=1500×31000×30=135 kWhE = \frac{1500 \times 3}{1000} \times 30 = 135\ \text{kWh} cost=135×0.17=$22.95\text{cost} = 135 \times 0.17 = \$22.95

That’s about 77 cents a day.

Watch out for

  • Label watts are a maximum. Fridges, heaters with thermostats and air conditioners cycle on and off. Their average draw is often a third to a half of the label figure. A plug-in power meter gives the real number.
  • Volts times amps overstates some loads. For motors and some electronics, real power is less than V×IV \times I because of the power factor. The label’s watt figure is better when there is one.
  • Standby power adds up. A device drawing 5 W around the clock uses 44 kWh a year.

Sources

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