Why mpg is not a scale: 15 to 20 beats 40 to 50
Two cars are traded in. One goes from 15 mpg to 20; the other from 40 mpg to 50. The second looks like the bigger improvement — ten points rather than five, and a higher number to start from.
Over the same distance the first change saves more than three times as much fuel. This is not a trick of the example. It is what happens whenever you treat a per-unit-of-fuel measure as if it were a scale of consumption.
The units are inverted
Miles per gallon is distance divided by fuel. What you buy is fuel, so the quantity that governs the bill is the other way up:
fuel used = distance ÷ mpg
Because mpg sits in the denominator, equal steps along it do not produce equal savings. Steps low down the scale are worth far more than steps high up.
The arithmetic, over 12,000 miles
Twelve thousand miles is chosen purely to keep the numbers clean; substitute whatever distance you actually drive.
- 15 mpg:
12,000 ÷ 15 = 800gallons - 20 mpg:
12,000 ÷ 20 = 600gallons - 40 mpg:
12,000 ÷ 40 = 300gallons - 50 mpg:
12,000 ÷ 50 = 240gallons
Now the two improvements:
- 15 to 20 mpg:
800 − 600 = 200gallons saved - 40 to 50 mpg:
300 − 240 = 60gallons saved
200 ÷ 60 = 3.33. The five-point improvement on the thirsty car saves more than three times the fuel of the ten-point improvement on the efficient one, over identical mileage. Multiply by whatever fuel costs where you are — a figure that varies by country and by week, so use your own — and the same ratio carries straight into money.
The version that really lands
The 40 mpg car uses 300 gallons over those 12,000 miles. That is everything it consumes, so 300 gallons is the absolute ceiling on what any improvement to it could ever save, even an impossible one.
Improving the 15 mpg car to 20 saves 200 of the 300 gallons that scrapping the 40 mpg car entirely would save. One modest change to the worst vehicle is worth two thirds of perfection applied to the good one.
L/100km is the right way up
Fuel per distance behaves the way people expect a scale to behave. Converting with the tool's factor, L/100km = 235.214583 ÷ mpg:
- 15 mpg =
15.681L/100km - 20 mpg =
11.761L/100km - 40 mpg =
5.880L/100km - 50 mpg =
4.704L/100km
The improvements are 15.681 − 11.761 = 3.920 and 5.880 − 4.704 = 1.176. Their ratio is 3.920 ÷ 1.176 = 3.33 — the same 3.33 as the gallons, and necessarily so, because differences in fuel-per-distance are proportional to fuel used over a fixed distance. Differences in mpg are not proportional to anything useful.
That is the practical argument for the metric unit: a one-unit change in L/100km means the same amount of fuel wherever you are on the scale. A one-unit change in mpg does not.
Where the conversion factor comes from is no mystery: a US gallon is 3.785411784 litres and a mile is 1.609344 km, so 3.785411784 ÷ 1.609344 × 100 = 235.214583.
A homemade version of the same idea
If you would rather stay in gallons, invert it yourself: gallons per 10,000 miles is 10,000 ÷ mpg. That gives 666.67, 500, 250 and 200 for the four cars above. Same shape, same conclusion, no metric units required.
One more trap: two different gallons
An imperial gallon is larger than a US one, so the same car scores higher in UK mpg. The tool multiplies by 1.20095: a car at 30 US mpg is 30 × 1.20095 = 36.03 UK mpg. Comparing a US-quoted figure against a UK-quoted one directly overstates the difference by about a fifth, which is more than most model-to-model differences you would be comparing.
Running the numbers
The free Fuel Economy converter takes a US mpg figure and returns L/100km, km per litre and UK mpg, so you can put two differently quoted cars on one scale before comparing them. It converts the rating; the fuel saved is the division above, using your own annual distance and your own fuel price.
And a rating is a rating. What a car does on your commute, with your right foot, in your weather, is a different number — but the shape of the arithmetic does not change: fix the worst number on your driveway before polishing the best one.