Energy at home · Quantitative
Reading a fuel bill
A real electricity bill lists “units used: 412” and charges 27p for each one. Nowhere on the page does it say what a unit is. What have you been buying?
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412 of something, at 27p each.
A real electricity bill lists “units used: 412” and charges 27p for each one. Nowhere on the page does it say what a unit is — the word appears eleven times and is never defined. The prices on this page are 2026 ones, and the cap that sets them moves every three months.
Commit. A unit on an electricity bill is one…
One kilowatt-hour — the energy a 1 kW appliance transfers in one hour, which is 3 600 000 joules. It is a unit of energy, not power, despite starting with the word kilowatt. Every fuel bill in the country is written in it and almost none of them explain it.
This lesson is the one place where the arithmetic of the last two lessons meets money. A bill is a list of products — power times time, appliance by appliance — added together. That structure matters, because it is a sum of products, and the way you write it down has to show both.
What one unit actually is
One kilowatt-hour, four ways
The same amount of energy, spent four different ways. Pick each one and watch the product come out the same.
Four different shapes, one area. That area is the unit you are billed for.
Key fact
One unit on a bill is one kilowatt-hour: 3 600 000 J. It is an amount of energy, not a power. Cost = units × price per unit.
Build the bill · a sum of products
Set the household's habits and watch the total.
Five appliances, five sliders. Each row is a product; the bottom line is their sum, plus a standing charge that no slider can touch. The hours are the hours a thing is drawing power — a fridge is plugged in all day, but its motor only runs a few hours of it.
Commit first. In a typical UK home, which of these is usually the largest single item on the electricity bill?
| Appliance | Power | Hours per day | Units in 30 days | Cost |
|---|---|---|---|---|
| Electric shower | 8500 W | |||
| Oven and hob | 2200 W | |||
| Kettle | 2000 W | |||
| Fridge-freezer | 90 W | |||
| Lighting, whole house | 72 W | |||
| Standing charge · 30 days | ||||
| Amount due | ||||
Every row responds to its slider. The standing charge does not respond to anything.
Writing it down · two shapes in one calculation
amount due = (row + row + row + row + row) + standing charge
each row is power in kilowatts × time in hours — a product
the amount due is every row added — a sum
no single diagram does both jobs, so the drawing does both
Read it as a balance: everything on the left pan, added, equals the amount due on the right. Change any one row and the beam stays level — the total simply follows. This is the same shape you met for conservation of energy, and for the same reason: whenever the top-level relationship is an addition, a triangle would teach you a relationship that does not exist.
Five lines on one row · CFIFA
An oven rated 2.0 kW runs for 1.5 hours. How many units does it use?
Step 0 of 5
Convert
2.0 kW stays 2.0 kW · 1.5 h stays 1.5 h
A unit is a kilowatt-hour, and the rating is already in kilowatts and the time already in hours, so there is nothing to convert.
Formula
units = power in kW × time in hours
Two quantities multiplied — one row of a bill.
Insert
units = 2.0 kW × 1.5 h
The kilowatt and the hour are what make the answer a kilowatt-hour.
Fine-tune
2.0 × 1.5 = 3.0
Kilowatts times hours leaves kilowatt-hours.
Answer
units = 3.0 kWh
Three units, which at 27p each is 81p.
Five lines on one row · CFIFA
A 120 W fridge compressor runs for 4.0 hours a day. How many units in a day?
Step 0 of 5
Convert
120 W ÷ 1000 = 0.120 kW
A unit is a kilowatt-hour, so a rating printed in watts has to become kilowatts first.
Formula
units = power in kW × time in hours
Two quantities multiplied — one row of a bill.
Insert
units = 0.120 kW × 4.0 h
The converted rating goes in. The 120 never does.
Fine-tune
0.120 × 4.0 = 0.48
Kilowatts times hours leaves kilowatt-hours.
Answer
units = 0.48 kWh
Insert 120 instead of 0.120 and the fridge comes out using 480 units a day — more than the whole house uses in a month.
Think again
“A kilowatt-hour is a measure of power — it has kilowatt in the name.”
The “hour” on the end is the giveaway: a time has already been multiplied in, which turns a rate into a total. A kilowatt is a rate. A kilowatt-hour is a rate multiplied by a time, and a rate times a time is always an amount.
It is worth saying what the amount is. One kilowatt-hour is 1000 W × 3600 s = 3 600 000 J. Bills are written in it rather than in joules for the same reason shopkeepers do not price flour by the grain.
“Switch everything off and the bill goes to zero.”
The units do; the standing charge does not. It is a fixed daily amount for being connected to the network — around 53p a day here in 2026, or about £16 a month — and it is on the bill whether you use one unit or a thousand. That is why the cheapest month is never free, and why comparing suppliers on unit price alone is not enough.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Recall
One unit on an electricity bill is one…
Rung 2 · The one that catches people
A 2.2 kW oven runs for 45 minutes a day for 30 days, at 27p a unit. What does it cost?
Rung 3 · Explain
A household uses 412 units in 30 days at 27p a unit, plus a standing charge of 53p a day. Work out the bill, and explain why cutting their usage by half would not halve what they pay.
Rung 4 · Take it somewhere new
A family is told to “switch off lights to save money”. Using the bill you built, say whether that is the best advice available to them, and justify your answer with numbers.
Key note
A unit is a kilowatt-hour, which is energy, not power. Cost = units × price. A bill is a sum of products — triangle for a row, balance for the total. And a standing charge is owed whether you use anything or not.
Going further
The standing charge is the line people argue about, and it is worth understanding why it exists rather than just resenting it. The cables, substations, meters and the crew who come out when a line goes down all cost the same whether your house draws 400 units a month or none — so that cost is billed per day rather than per unit. It has a consequence that catches people out: a household that cuts its usage in half does not halve its bill, because a fixed portion never moves. If you ever want to work out what a genuine saving would be worth, the standing charge has to come out of the calculation first, and it is the one row on the bill that no change in behaviour will touch.
Gas is the other half of most fuel bills, and its meter counts volume, not energy: the number in the little window is cubic metres of gas that have gone past, and that is not the number you are billed for. The bill converts it with a formula printed on every UK gas bill — kWh = m³ × 1.02264 × 39.5 ÷ 3.6. The 1.02264 is a volume correction factor, fixed by the regulator, bringing the measured volume to a standard temperature and pressure. The 39.5 is the calorific value in megajoules per cubic metre — how much energy that gas carries. The network measures it and prints it on the bill, and it does vary, roughly 37.5 to 43.0, with where the gas came from. Dividing by 3.6 turns megajoules into kilowatt-hours, because one kilowatt-hour is 3.6 MJ. So 100 m³ gives 100 × 1.02264 = 102.264, then × 39.5 = 4039.4 MJ, then ÷ 3.6 = 1122 kWh. Domestic energy is charged VAT at 5 per cent, not the standard 20. The unit at the end is the same kilowatt-hour the electricity side is billed in — which is what lets you compare the two halves of a bill.
Before this lesson
At GCSE this becomes
- Domestic energy costs, and the National Grid's role in matching supply to demand.
Where to next
Ask Mr Badmus AI
Still unsure whether kWh is power or energy?
Lesson content © MrBadmusAI.