Efficiency
Two equations to recall, one calculation pattern that comes up every series — and the sanity check that catches the most common error before it costs you marks.
SPEC 4.1.2.2 • ENERGY — EFFICIENCY
Why This Lesson Matters
Efficiency questions appear on every Paper 1. Usually 3–4 marks. The maths is simple — divide, possibly rearrange, possibly convert to a percentage. But each step has its own way to lose a mark.
⭐
High Priority
2
Equations (given)
0–1
Valid Range
By the end of this lesson
You'll calculate efficiency in either form, rearrange to find a useful output from a given efficiency, switch confidently between decimal and percentage, and spot the error that gives "efficiency = 1.6".
What Efficiency Is
Efficiency is a single number that tells you what fraction of the energy you put in actually does the useful job.
Efficiency
The ratio of useful output to total input. A device that's 0.8 (or 80%) efficient transfers 80% of its input energy to the useful store, and 20% is dissipated to the thermal store of the surroundings.
Connection to lesson 1.05
The "wasted" 20% isn't lost — it's dissipated to the thermal store of the surroundings. Conservation of energy still holds: useful + wasted = total input.
Three Properties Of Efficiency
Three rules that hold for every efficiency value, every question. Memorise these — they double as sanity checks.
PropertyMeaning
1. No unitsEfficiency is a ratio — joules over joules, or watts over watts. The units cancel. Don't write "0.64 J" or "0.64 W".
2. Range: 0 to 1Or 0% to 100% as a percentage. Anything above 1 (or 100%) is wrong — it would mean output exceeded input, breaking conservation of energy.
3. Two valid formsDecimal (0.64) or percentage (64%). They're the same number — just multiply by 100 to convert decimal → percentage.
No machine is 100% efficient
In any real change, some energy is dissipated. Real-world efficiencies: LEDs ~40%, electric motors ~85–95%, petrol engines ~25–30%, filament bulbs ~5%.
The Two Equations
The spec requires you to recall and apply both forms. (Recent exam series have provided them on an equation sheet, but that's not guaranteed — learn them.) The choice of which to use depends on what the question gives you.
Energy Form efficiency = useful output energy transfertotal input energy transfer
Power Form efficiency = useful power outputtotal power input
How to choose
If the question gives you values in joules (J, kJ, MJ) → use the energy form. If values are in watts (W, kW, MW) → use the power form. Both give the same numerical efficiency for the same device.
Worked Example 1 — Calculate Efficiency
The standard pattern: given input and useful output, calculate the efficiency.
A motor is supplied with 500 W of electrical power. It produces 320 W of useful mechanical power. Calculate the efficiency of the motor. 2 MARKS
- EEquation: efficiency = useful power output ÷ total power input
- SSubstitute: efficiency = 320 ÷ 500
- UUnit: none — efficiency is a ratio
- AAnswer: efficiency = 0.64 (or 64%)
Where the marks land
M1 — correct equation chosen. M1 — correct substitution (useful on top, total on bottom — never flipped). A1 — answer in the form the question asks for.
Decimal Or Percentage?
The same efficiency can be written two ways. The question stem tells you which form to give.
Decimal Form
A number between 0 and 1.
efficiency = 0.64
Percentage Form
Multiply the decimal by 100. Add a % sign.
efficiency = 64%
Match The Form To The Question
If the question asks for efficiency "as a percentage", multiplying by 100 is part of the final answer mark. If it asks "as a decimal" (or doesn't specify), leave it as a decimal. Mixing forms — writing "0.64%" or "64.0" with no symbol — loses the answer mark.
Worked Example 2 — Rearrange For Useful Output
The recurring exam pattern: given a known efficiency and the total input, find the useful output. Requires rearranging the equation.
An electric drill has a total power input of 600 W. The efficiency of the drill is 0.75. Calculate the useful power output of the drill. 3 MARKS
- EEquation: efficiency = useful power output ÷ total power input → rearrange: useful power output = efficiency × total power input
- SSubstitute: useful power output = 0.75 × 600
- UUnit: watts (W) — same unit as the total power input
- AAnswer: useful power output = 450 W
Rearrangement Pattern
For these questions, the useful term is always: useful = efficiency × total. If you're asked for the total input instead: total = useful ÷ efficiency.
The Most Common Mistake
Across recent series, mark schemes consistently flag the same calculation error: students flip the fraction. They divide total input by useful output instead of useful output by total input — and end up with an answer above 1.
✗ Wrong
efficiency = 500 ÷ 320
= 1.5625
= 156%
Total on top, useful on bottom — fraction flipped. Result is greater than 1, which is impossible.
✓ Correct
efficiency = 320 ÷ 500
= 0.64
= 64%
Useful on top, total on bottom. Result is between 0 and 1. ✓
The 1-second sanity check
After every efficiency calculation, ask: is my answer between 0 and 1 (or 0% and 100%)? If not, swap the numerator and denominator and recalculate. This catch alone saves the mark.
Why No Machine Is 100% Efficient
This is where Lesson 1.05 connects to this one. Every real device dissipates some energy — so efficiency is always less than 1.
The conservation link
total input = useful output + dissipated energy
The dissipated energy is "wasted" — it goes to less useful stores, almost always the thermal store of the surroundings. Conservation still holds; the energy isn't destroyed, just transferred to a store you can't use.
DeviceUseful transferWhere waste goes
Electric motorElectrical → kinetic storeThermal store (friction in bearings, heating in coils)
Filament bulbElectrical → light (radiation)Thermal store (~95% of input)
Petrol engineChemical → kinetic store of carThermal store (exhaust gases, engine block)
Increasing Efficiency HT ONLY
Higher Tier students must be able to describe ways of increasing the efficiency of a device. Five common methods — each one targets a different dissipation pathway.
🛢️
Lubrication
🧣
Insulation
✈️
Streamlining
⚡
Low-R Wires
💡
LEDs
HT — Mark-Scheme Pattern
Each method must be linked to what it reduces AND what dissipation pathway it cuts. "Lubrication" alone is not enough — you need "lubrication reduces friction so less energy is dissipated to the thermal store".
How Each Method Works HT ONLY
Each method on its own line, with the mechanism. Memorise the linking phrase — that's where the marks live.
MethodWhat it reducesHow it raises efficiency
LubricationFriction between moving partsLess energy dissipated to thermal store of moving parts
Thermal insulationEnergy transfer by conductionLess thermal energy dissipated to surroundings (links to RP2)
StreamliningAir or water resistance (drag)Less work done against drag → less energy dissipated to thermal store
Lower-resistance wiresHeating in wires (P = I²R)Less electrical energy dissipated to thermal store of wires
LED replacementWasted thermal output of filament bulbsLEDs convert a far higher fraction of input to light (radiation)
Vague vs Mark-Scheme Language HT
Examiner reports flag the same vague phrases every series on efficiency-improvement questions. Replace each one with a precise mechanism.
✗ Vague — REJECTED
"Saves energy"
"Uses less energy"
"Energy efficient appliances waste no energy"
"No energy is wasted"
"Rotates faster"
"Rotates more smoothly"
✓ Precise — CREDITED
"Less energy is dissipated to the thermal store"
"Reduces friction so less energy is transferred to the thermal store of the moving parts"
"Less heating in the wires" (for low-R wires)
"Greater fraction of input transferred to useful store"
Two Recurring Pitfalls
Absolute statements — "no energy is wasted" — contradict conservation. Always say "less", never "no".
Missing mechanism — "rotates more smoothly" doesn't earn a "less friction" mark on its own. State the cause AND the effect.
Practice Question
1500 W
600 W
Calculate the efficiency of the wind turbine. Give your answer as a percentage. 3 MARKS
E
Equation: efficiency = useful power output ÷ total power input
S
Substitute: efficiency = 600 ÷ 1500 = 0.40
U
Unit: none (ratio) — but the question asks for a percentage, so multiply by 100
A
Answer: efficiency = 0.40 × 100 = 40%
Sanity check: 40% is between 0% and 100%. ✓ The fraction is the right way up. M1 (equation) · M1 (correct substitution) · A1 (answer with % as required).
Lesson Summary
Definition & Properties
Efficiency = useful output ÷ total input
No units · range 0 to 1 (or 0% to 100%) · multiply decimal by 100 → percentage
No real machine is 100% efficient — some energy is always dissipated to the thermal store of the surroundings
The Two Equations (both for recall)
Energy form: efficiency = useful output energy transfer ÷ total input energy transfer
Power form: efficiency = useful power output ÷ total power input
Rearranged: useful = efficiency × total | total = useful ÷ efficiency
HT Methods To Increase Efficiency
Lubrication · Thermal insulation · Streamlining · Lower-resistance wires · LEDs instead of filament bulbs
Each method must be linked to a specific dissipation pathway — not just "saves energy"
The 1-second sanity check
Is your answer between 0 and 1 (or 0% and 100%)? If yes, you've got the fraction the right way up. If no, swap numerator and denominator.
Checkpoint
You should now be able to…
Recall and apply both efficiency equations (energy form and power form)
Choose the correct equation based on whether the question gives energies or powers
Calculate efficiency from input and useful output
Rearrange the equation to find useful output (or total input) given an efficiency
Convert between decimal and percentage, matching the form to the question
Spot when an efficiency answer is impossible (greater than 1) and self-correct
HT: describe and justify common methods to increase efficiency, linking each to a specific dissipation pathway
Up Next — Lesson 1.07
National and global energy resources. The eight named resources, renewable vs non-renewable, reliability — and the recurring 6-mark evaluation question on trade-offs.
Next: Why This Lesson Matters