On the left of Board 1 are two input cards: Power (1,000 W) and Time per use (10 min). Price (assumed), at the top right, is $0.20 per kWh, and Days used, at the bottom right, is 30. The other four cards are calculation cards: Hours (the minutes converted to hours), Energy per use, Cost per use and Cost over the days. Changing an input updates the cards connected to it. How formulas are written is covered in the usage guide, under Writing formulas and functions.
The price per kWh differs from one contract to another, so the $0.20 on Board 1 is an assumed value. The actual price is on your own electricity bill, and typing it into the price field gives a figure closer to your own contract.
What does a 1,000 W hair dryer cost for 10 minutes?
In this example, about 3.3 cents. Board 1 works it out in three steps, from the top.
- Convert 10 minutes to hours: 10 ÷ 60 = 0.166667 hours, a sixth of an hour. This is the value of the Hours card.
- Work out the energy: 1,000 W × 0.166667 h ÷ 1,000 = 0.166667 kWh (about 0.1667 kWh).
- Work out the cost: 0.166667 kWh × $0.20 per kWh = $0.033.
That is one use. Used every day for 30 days, it comes to $1.00, the value of the Cost over the days card.
With Days used set to 365, a year of daily use comes to $12.17. With Days used back at 30, it is $1.00.
Energy is power × hours ÷ 1,000
The watt (W) is the unit for the rate at which a device uses electricity; the power printed on an appliance is in W. The kilowatt-hour (kWh) is the unit for the amount of electricity used, and the cost is worked out from it. The prefix k stands for 1,000, so 1 kW = 1,000 W.
A 1,000 W device that runs for one hour uses exactly 1 kWh. With Time per use set to 60 on Board 1, Energy per use is 1 kWh and Cost per use is $0.20. Ten minutes is a sixth of an hour, so at 10 minutes the energy and the cost are a sixth of the 60-minute values. With Time per use back at 10, they are 0.166667 kWh and $0.033.
Energy (kWh) = power (W) × hours used ÷ 1,000
Power × hours gives watt-hours (Wh), and dividing by 1,000 gives kWh. Here 1,000 W × 0.166667 h = 166.667 Wh, and dividing by 1,000 gives 0.166667 kWh. The hours come from dividing the minutes by 60; converting between minutes and hours is also covered in the unit conversion article.
Cost = energy (kWh) × price ($ per kWh)
Written with units, kWh × $/kWh = $. The price says how much one kWh costs, so multiplying the energy by it gives an amount of money.
Changing the numbers
Each row of the table below changes only the value named, starting from the starting values on Board 1.
| Changed value | Energy per use | Cost per use | Cost over the days |
|---|---|---|---|
| (starting values) | about 0.1667 kWh | $0.033 | $1.00 |
| Power 500 W | about 0.0833 kWh | $0.017 | $0.50 |
| Power 2,000 W | about 0.3333 kWh | $0.067 | $2.00 |
| Time per use 20 min | about 0.3333 kWh | $0.067 | $2.00 |
| Price $0.40 per kWh | about 0.1667 kWh | $0.067 | $2.00 |
| Days used 365 | about 0.1667 kWh | $0.033 | $12.17 |
Doubling the power, the time or the price doubles the cost, because they are linked by multiplication. Halving any of them halves it.
Because it is a product, doubling one factor and halving another brings the amount back. From the starting values, with the power at 2,000 W and the time at 5 minutes, the energy is still 0.1667 kWh and the cost is still $0.033.
Which appliance drives the monthly amount?
Lining several appliances up shows which of them matters most for the month. Board 2 adds up the monthly energy of three appliances and shows the shares as a pie chart.