Energy at home · Quantitative
Calculating energy transferred
An electric shower is rated 8500 W and you are in it for ten minutes. Someone leaves a 60 W lamp on for a full day. Which one transferred more energy?
Start here
Ten minutes against twenty-four hours.
An electric shower is rated 8500 W. You are in it for ten minutes. Someone else in the house leaves a 60 W lamp on all day — twenty-four hours.
Commit. Which transferred more energy?
The shower gives 5.1 MJ, against the lamp's 5.2 MJ. They are almost identical, which nobody guesses. Ten minutes of shower and a full day of forgotten lamp cost the same, and the only way to know that is to do the multiplication.
One relationship, one line of working, and one trap. The relationship is energy = power × time. The trap is units: watts want seconds, kilowatts want hours, and mixing them is the single most common way to be wrong by a factor of 3600.
Writing it down · the shape of this relationship
Energy = power × time
W with s gives J
kW with h gives kWh
and no other pairing is legal
The triangle
Cover the one you want
Energy is alone at the top. Cover it and the other two sit side by side — multiply.
Power sits underneath with energy above it. Cover it and you are left with E over t — divide.
Time sits underneath with energy above it. Cover it and you are left with E over P — divide.
Two things side by side means multiply. One thing over another means divide. And there are exactly two legal unit pairings: watts × seconds gives joules; kilowatts × hours gives kilowatt-hours. Watts × minutes is always wrong.
The appliance bench · set it up and price it
Two units, one answer.
Pick an appliance, set a realistic time, and read the same energy in both legal unit pairings — with what it costs beside them.
Commit first. A 2000 W kettle runs for 3 minutes. Which calculation gives the energy in joules?
In joules
In kilowatt-hours
At 27p per kWh (2026)
The fridge — 90 W, the second-lowest rating on the bench — gets through more energy in a day than the kettle does, because it keeps coming back on all day and night. Its motor does not run flat out the whole time; it runs in bursts, for about half the day. Nothing about its rating hints at that.
Key fact
E = P × t, with the power in watts and the time in seconds. Converting the time is part of the calculation, not an afterthought — minutes and hours never go into the formula as they stand.
Five lines, every time · CFIFA
A 60 W lamp is left on for 300 s. How much energy does it transfer?
Step 0 of 5
Convert
60 W stays 60 W · 300 s stays 300 s
A watt is a joule each second, and the time is already in seconds, so there is nothing to convert.
Formula
E = P × t
Cover E on the triangle: P sits beside t, so you multiply.
Insert
E = 60 W × 300 s
The seconds on the bottom of the watt cancel the seconds of the time.
Fine-tune
60 × 300 = 18 000
Watts times seconds gives joules.
Answer
E = 18 000 J
Eighteen thousand joules, which is 18 kJ.
Five lines, every time · CFIFA
A 2000 W kettle runs for 3 minutes. How much energy does it transfer?
Step 0 of 5
Convert
3 min × 60 = 180 s
A watt is a joule each second, so the minutes have to become seconds before anything multiplies.
Formula
E = P × t
Cover E on the triangle: P sits beside t, so you multiply.
Insert
E = 2000 W × 180 s
The converted time goes in. The 3 never does.
Fine-tune
2000 × 180 = 360 000
Watts times seconds gives joules.
Answer
E = 360 000 J
Insert 3 instead of 180 and the answer comes out 6000 J — sixty times too small. That is the mistake at the top of the next section.
Think again
“A 2000 W kettle for 3 minutes: 2000 × 3 = 6000 J.”
The time is in minutes and the watt is defined per second. Three minutes is 180 seconds, so the answer is 360 000 J — sixty times what was written.
There is a check that catches this every time, and it costs you five seconds: ask whether the answer is a sensible size. 6000 J is about what it takes to carry yourself up three flights of stairs. It could not possibly boil a litre of water. When your answer is absurd, suspect the units before you suspect the physics.
The safest habit is to convert on the Insert line, never later — write “180 s” into the working rather than converting the answer afterwards. Two consistent pairs exist and no others: watts with seconds gives joules; kilowatts with hours gives kilowatt-hours.
“A joule is a decent amount of energy, so 6000 J for a kettle sounds about right.”
A joule is tiny. Lifting an apple from the floor to a table takes about one; a single AA cell holds around 10 000. A kettle boiling a full litre needs about 360 000 J, which is why the answers in this lesson run into hundreds of thousands and why kilojoules and megajoules exist at all. If a kettle calculation comes out in the thousands, the time was almost certainly left in minutes.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Recall
A 1200 W microwave runs for 90 seconds. How much energy does it transfer?
Rung 2 · The one that catches people
A 2000 W kettle runs for 3 minutes. A student writes 2000 × 3 = 6000 J. What is wrong?
Rung 3 · Explain
An 8500 W shower runs for 10 minutes and a 60 W lamp is left on for 24 hours. Show that they transfer almost the same energy, and explain what this tells you about judging appliances by their rating.
Rung 4 · Take it somewhere new
A household wants to cut its electricity bill and has a 2200 W oven used 45 minutes a day, a 90 W fridge whose motor runs in bursts for about 12 hours a day, and eight 9 W LED lamps on about 5 hours a day. Work out which costs most per day and advise them, using numbers.
Key note
E = P × t. Convert the time on the Insert line, not afterwards. Watts with seconds, or kilowatts with hours — and always ask whether the answer is a sensible size.
Going further
Unit slips of exactly this kind are not confined to homework. In 1999 NASA lost the Mars Climate Orbiter — a spacecraft that took nine months to arrive — because one team supplied thrust figures in pound-force seconds and the receiving software expected newton seconds. Nobody made an arithmetic mistake. Every number was correct in its own units, and the craft entered the atmosphere about 170 km lower than intended and was destroyed. The discipline you are being asked for here, of writing the unit next to every number in the working, is the same discipline that would have saved a $327 million mission.
Before this lesson
At GCSE this becomes
- Energy transferred by an appliance, efficiency calculations, and the cost of electricity.
Where to next
Ask Mr Badmus AI
Answer coming out sixty times too small?
Lesson content © MrBadmusAI.