Calculating the Cost of Electricity

Units of Power & Energy

The Kilowatt

The kilowatt (kW) is a unit of power
Kilowatts are used mostly in the context of domestic power use

$P = \frac{E}{t}$

Therefore:

1 kW = 1000 W = 1000 J/s

The Kilowatt Hour

The kilowatt hour (kWh) is a unit of energy
Kilowatt hours are the units of energy used by domestic energy providers
The kilowatt hour is defined as:

A unit of energy equivalent to one kilowatt of power expended for one hour

$E = P t$

Therefore:

1 kWh = 1 kW × 1 hour

Appliances are given power ratings, which tell consumers the amount of energy transferred to the device every second

Power Rating of a Kettle

This kettle has a power rating of between 2500 and 3000 W, which means that 2500 - 3000 J of energy are transferred to the kettle every second

Energy suppliers calculate the cost of gas and electricity used by:

Units of energy used (kWh) = power used (kW) × time (hours)

Then the cost of that energy use can be calculated:

Cost (£) = units used (kWh) × cost per unit (£ per kWh)

Suppliers have different price plans called tariffs
Different tariffs will have slightly different prices for:
- Cost of electricity per kWh
- Cost of gas per kWh
- Standing charges for electricity and gas
After the bill has been calculated, the total amount will be subject to the standard rate of VAT tax (approximately 20%)

Worked example

In the month of January, a 3 bedroom household used 284 kWh of electricity, and 1366 kWh of gas.

The household's tariff details are listed below.

Electricity unit price: 26.47 p/kWh
Electricity standing charge: 51.38 p/day
Gas unit price: 7.00 p/kWh
Gas standing charge: 26.16 p/day

Calculate the total price of the energy bill for the month of January.

The month of January has 31 days. Ignore the cost of VAT tax.

Answer:

Step 1: List the known quantities

Electricity used = 284 kWh
Electricity unit price = 26.47 p/kWh
Gas used = 1366 kWh
Gas unit price = 7.00 p/kWh
Electricity standing charge = 51.38 p/day
Gas standing charge = 26.16 p/day

Step 2: Write out the equation for calculating the cost of energy

Cost = units used × cost per unit

Step 3: Calculate the cost of the electricity used

$cost of electricity = 284 \times 26.47$

$cost of electricity = 7517.48 p$

Convert pence (p) to pounds (£) by dividing by 100 and rounding to the nearest pence

$cost of electricity = \frac{7517.48}{100} = £ 75.17$

Step 3: Calculate the cost of the gas used

$cost of gas = 1366 \times 7.00$

$cost of gas = 9562 p$

$cost of gas = \frac{9562}{100} = £ 95.62$

Step 4: Calculate the total standing charge for electricity

total standing charge electricity = standing charge per day × number of days

$total standing charge electricity = 51.38 \times 31$

$total standing charge electricity = 1592.78 p$

$total standing charge electricity = \frac{1592.78}{100} = £ 15.93$

Step 5: Calculate the total standing charge for gas

$total standing charge gas = 26.16 \times 31$

$total standing charge gas = 810.96 p$

$total standing charge g a s = \frac{810.96}{100} = £ 8.11$

Step 6: Add all the individual costs together to find the total cost of the bill

Total cost of bill = cost of electricity + cost of gas + total standing charge electricity + total standing charge gas

$total cost = £ 75.17 + £ 95.62 + £ 15.93 + £ 8.11$

$total cost = £ 195.47$

Exam Tip

The price per unit is given in pence (p), but the total amounts are billed in pounds (£). Unless the exam question tells you otherwise, you should convert your answer into pounds and round to the nearest pence.

Calculating the Cost of Electricity (WJEC GCSE Physics)

Revision Note

Units of Power & Energy

The Kilowatt

The Kilowatt Hour

Power Rating of a Kettle