## Miles per Gallon vs. Gallons per Mile

Here’s an interesting question.

Suppose you had a household with two cars, and each car needs to be driven 10,000 miles per year. One car consumes 34 MPG, and the other car consumes 18 MPG. Since gas is expensive, you want to replace one car. Because of utility constraints, you have two choices:

• Replace the 34 MPG car with a 50 MPG car — a 16 MPG improvement
• Replace the 18 MPG car with a 28 MPG car — a 10 MPG improvement
• Which car replacement would save you the most gas?

Normally, I consider myself not bad with quantitative comparisons like this, yet initially I picked the answer of replacing the 34 MPG car with the 50 MPG car based on the superior 16 MPG improvement. Another seemingly more analytical approach also leads to the same conclusion: 50 + 18 MPG giving a 34 MPG household average seems more efficient than 34 + 28 MPG giving a 31 MPG household average.

This very interesting article in Science, “The MPG Illusion” by Richard P. Larrick and Jack B. Soll at the Fuqua School of Business in Duke University (Vol 320, June 20, 2008, p. 1593), points out the mathematically obvious truth that gas used per mile is inversely proportional to miles per gallon, which means that you have a steeper slope at lower MPG ratings, and diminishing returns at higher MPG ratings.

(The above image is taken from the article, available here with subscription).

When you run the numbers, replacing the 34 MPG car with a 50 MPG (a 16 MPG improvement) car saves you 94.1 gallons per 10,000 miles, whereas replacing the 18 MPG car with a 28 MPG (a 10 MPG improvement) car saves you 198.4 gallons per 10,000 miles — more than double the savings.

Or, to give an even more clear-cut example, replacing a 5,000 MPG car with a 10,000 MPG car saves you just one gallon of gas, whereas replacing a 1 MPG car with a 2 MPG car saves you 5,000 gallons of gas, using a fixed mileage of 10,000 miles driven for comparison.

There are some important policy implications of this. Relatively small MPG improvements in the most gas-hungry vehicles pay off greater than larger improvements in already efficient cars (hence, it does make sense to offer tax breaks for modest improvements in SUVs versus tax breaks for hybrids, which typically replacing already gas-efficient sedans). Also, personal driving habits, especially for gas-hungry cars, can often times add or subtract a few MPG to a car’s efficiency on average. For example, a car that may get 25 MPG “average highway” will degrade to under 15 MPG if you gun it out of stoplights in city traffic. That’s a huge increase in gas consumed per distance driven, especially for the less efficient cars, whereas for more efficient cars it doesn’t hurt as much to goose the engine a bit.

Apparently the thinking that gas savings is linear with MPG is not uncommon. A survey of college students revealed that a majority of them shares this misconception. I’m not sure what the sociological term is for such a massively accepted factual inaccuracy, but it seems like a textbook case for how common wisdom can fail the common person. It’s also a good example of why you don’t want to put policies to a vote — people just don’t have the time to run the numbers, and simple numbers can be so simply deceptive, even with the best intentions. Good democracies are probably more about the people directly controlling principles (“conserve oil”), rather than the policies (“reward car makers that achieve the greatest fleet MPG delta”). Of course, that doesn’t address the problem of creating accountability between principles, policies, and politicians that make the policies to execute the principles.

### 45 Responses to “Miles per Gallon vs. Gallons per Mile”

1. Of course, out-side of the US, we use l/100km which is the same ‘way-around’ as GPM and is therefore more easily comparable :-)

2. Christian Vogel says:

As Norman Rasmussen already said, here in Europe l/100km is customary and easier to compare with. But maybe we should just go the SI way and specify consumption in square millimeters? {the cross-section of a tube where the flow of fuel consumed runs just as fast as the car…}

3. Hans says:

Norman: It also makes it easier to calculate how much gas you will need for a given distance (e.g. a planned trip). Dividing the distance by 100 is a no-brainer and then multiply it by the liters per 100km. Easy. But dividing the distance through MPG is imho much more complicated.

4. Don Marti says:

The EPA does manufacturers’ CAFE calculations the right way — they flip the MPG, take the weighted average, and flip back.

Energy Star appliances have a better labeling system than cars, estimated dollars/year.

5. Joel says:

Since you’re going to drive each car the same distance, the change with the greatest percent improvement in MPG will minimize fuel consumption (cost).

If this is a “trick question,” it’s because the “equidistance” stipulation feels unnatural and one tends to “brush it aside.”

6. Craig says:

I’m with Joel.

I just found the household mpg and thought of it going in to 20,000 miles.

So which ever combination of cars had the highest mpg.

Really treating the question as if it’s one car that’s going to do 20,000 rather than 2 cars doing 10,000.

I can not fathom the difference between a 1mpg car vs a 2mpg car, and a 5,000 mpg car vs a 10,000mpg car

aren’t they both double?!?!? ow my head :D

7. Mastro Gippo says:

Answer: electric car and solar panels! Infinite MPG! Do I get the cookie? :)

8. Puyb says:

As a french, this “MPG” thing seems totaly unlogical and conter natural for me. It’s as if the price for potatoes in a store is displayed in kg/€ (or lb/$for imperial system lovers). 9. MikeS says: I think the MPG in the US has the value that a larger number is better. But really, we ought to move it along and go metric already. And while we’re at it can we get rid of pennies and nickels? Not having to haul them around would also save a lot of gas. 10. IIVQ says: In NL, all official bodies use l/100km, but people usually speak about “1 to N” where higher N is better. I manage to get about 1100 km out of a 46 litre tank, which is about 1:24 or 4,2 l/100 km which is fairly good, for a 9 year old car. Another “difficult calculation” I find it to discover how much faster you have to drive to arrive earlier at your destination – it’s something I haven’t managed to do from my head. However, when you – as a joke – do this math, you’ll see that it’s actually near impossible to arrive 10 minutes earlier when your timeframe iss less then an hour – and even then you’ll have to drive mighty fast – accounting that your average has to be a bit higher and thus your peak speed a LOT higher. By the way: Hybrid owners have a great advantage in the city, but on longer runs on the highway the petrol engine is quite efficient and the batteries and power convertors are not used – and thus dead weight. If you’re doing a lot of long-distance driving, a non-hibrid car is usually more efficient than the hybrid version of the same model. 11. […] Bunnie has an interesting write up about AAAS’s Science publication “The MPG Illusion” he writes… Here’s an interesting question. […] 12. Jim says: “whereas replacing the 18 MPG car with a 28 MPG (a 10 MPG improvement) car saves you 198.4 gallons per 10,000 miles — more than double the savings.” SWEET!!! You just bought a new car to save 198.4 *$4.50 = $892.80 a year. No wonder our economy is going down the drain, nobody does basic cost analysis anymore. 13. Bruce says: A good example of overanalysis. Simply take the car with the greatest percentage increase in MPG: 50/34 = 47% 28/18 = 56% • Frank says: Wrong Bruce. A good example of oversimplification (yours) What if the options are 10MPG car improved to 13MPG versus 50MPG car improved to 100MPG? Then the best choice is the first one, but your “rule” would pick the second one… Obviously a bad choice. You didn’t have a good look on the graph. Did you? 14. Sam Liden says: From a “green” point of view you should hang on to your old car as long as possible. I have read that the amount of energy used in making a new car is approximately the same as the energy used in driving an average car for the lifetime of the car. I favor gradually converting to the metric system of weights and measures. It is superior to our English system in every way, including the convention of using liters / 100 km instead of miles / gallon. 15. RoRo says: There is another way to think about this, of course, which puts the mpg rating in the numerator and not the denominator of the calculations. Assuming, as above, that most people have a certain amount they have to drive (to work, for groceries, etc), the above calculation is what needs to happen. However, if you are a person who has a walk or public transportation commute, and you don’t have to drive anywhere (urban living), then mpg makes sense. Theoretically, your car sits in your garage until the end of the month, at which time you have a certain amount of money to go as far as you can make it on that money. The 10 extra miles per gallon are the same 10 miles whether you’re going from 18 to 28 or from 50 to 60. Another similar scenario is that you have a certain amount of gas in your tank, or there is a limited amount of gasoline in the world — how far can you go? Either way, any calculation that assumes money or amount of gas is fixed — as opposed to mileage driven — would do well to keep the current system. 16. Viadd says: Joel, Craig, Bruce, Suppose you have two cars that you drive 10k miles a year each. Using Craig’s numbers, one gets 5000 mpg, the other gets 1 mpg. Your total gas consumption each year is (2 + 10000) = 10002 gallons per year. Replacing the 5000 mpg car with one that’s twice as good saves 1 gallon per year. Replacing the 1 mpg car with one that’s twice as good saves 5000 gallons per year. If the 5000 mpg car is replaced with one that requires no gas at all (infinite mpg! Thank you Mr Fusion) then you save the same amount of gas (2 gallons) as you would if you improved the guzzler by 0.02% 17. Theo says: The other problem is there are two gallons: 1 US gallon = 3.79 litres 1 UK gallon (Imperial gallon) = 4.54 litres So MPG isn’t even comparable between countries! 18. Fred says: Its simply a matter of weight ratios.. O:) It gets better….. Does your car get better gas mileage using the mid grade gas? What is the percent improvement? If the percent improvement is more that the percent cost difference switch to the mid grade gas. Example 300 miles traveled Unleaded regular$4.00 gal / 30 MPG , 10 gal, 300 miles cost $40 Mid grade$4.10 33 MPG , 9.1 gal 300 miles cost $37.31 Key point is to know your MPG for both types of gas. • Terry says: thats a really good point, since 91 octane gas (premium in california) has a 15% higher energy density than 87, there should be a 15% decrease in gallons per mile which means a 15% decrease in$ per mile. Which i think means that as long as 91 is less than 15/85 = 17.6470588% more expensive, it should be cheaper.

or at least i think so…

20. rageahol says:

suppose you got rid of one car and rode a bike or took public transit?

21. DeNelo says:

In Denmark, we use km per litre – 6 km/l is horrible, 13 km/l is average, 20 km/l is fantastic (and almost only within the reach of diesel-powered cars). We find it easy to calculate with – to travel x km you need (x/mileage) litres. Just thought you might want to know… :o)

22. John says:

Of course, the CORRECT answer is “none of the above”. The 18 MPG vehicle should be replaced by the 50 MPG one. Buying an SUV to save on gas is just plain stupid no matter which way you look at it.

23. Matt says:

An interesting question and fun to illustrate. Assume that a couple, each with a car, commutes 10K miles per year. So the distance is fixed and so is the consumption, no matter what kind of units Theo measures them in.

At a price of $4.50 per gallon (I suppose it could be £4.50 and use UK gallons but it doesn’t really matter for comparison purposes…) we have annual expenses of: Current expenses:$3,824
If you replace the 34 MPG car with the 50 MPG, you drop to $3,400. If you replace the 18 MPG car with the 28 MPG, you drop to$2,931.

And if you take John’s advice and replace the 18 MPG car with the 50MPG car, you drop to $2,224. It’s about percentage improvement and if you think about it that way, it is intuitive. It might be nice to save the planet but if you hope to be economical about it also at the family budget level, gas would have to be about$11/gallon before your gas savings would cover the price of a new car; and we’d have serious economy problems by then anyway.

24. Pete says:

Ah you Europeans and Americans, so logical.

In the UK, we sell our petrol in litres, but measure our fuel efficiency in miles per gallon. We usually use centimetres for small lengths, but when it’s the height of a person, we talk in feet and inches. Our food has to be sold (by law) in grams and kilograms, but we weigh ourselves in stones and pounds.

And of course the Americans call their nice and consistent set of units “English”. If only you knew…

25. Rab says:

Good news Pete, imperial measures are legal again. :o)
Good article, it’s all about ratios eh?
I don’t get the mm squared thing though. Surely it’s about rate that fuel is consumed rather than the diameter of the feed tube because the flow can vary.

26. […] How gas efficient do we need to be? There’s been an interesting meme circulating the internets lately regarding the notion of how fuel efficient our cars need to be, i.e. “Do we all need to go out and buy hybrids?”   So the question goes like this – what is the best thing to do to save the most gas, replace a 35mpg car with a 50 mpg car; or replace a 18mpg SUV with a 28mpg car?  The answer is here, and here.  All started by a paper published in Science by two people from Duke’s Fuqua School.  So, for a policy implication, it may be better for American carmakers to focus on improving  SUV gas mileage by modest amounts than try to convince all Americans to drive small hybrids. […]

27. Janet says:

I posted a blog entry about your blog entry. It’s here, titled “gallons per mile.” http://persistentunwantedthoughts.blogspot.com/

28. Randell Jesup says:

“Common Sense” and probability theory rarely meet…

Witness:
Lotteries
Gambling (“I’ve lost 10 times in a row, I’m due to win!”)
The Price Is Right (see Marilyn vos Savant’s “Game Show Problem”: http://www.marilynvossavant.com/articles/gameshow.html) That one caused Math PhD’s to berate her – incorrectly.)

29. Dan Johnson says:

Don’t forget depreciation and the high cost of replacing that gas guzzler too!

Substantial money can be lost unloading a low MPG vehicle now (low demand) – money that may be better spent on fuel for that vehicle you already own…

For my low mileage lifestyle, I’ve been considering some deeply-depreciated guzzlers with low gas mileage due to the net-savings they may present…

30. nex says:

> “One car consumes 34 MPG”
Well, sure, if you start off assuming that gallons are a fixed factor and that your car is consuming miles, you’re going to get confused quickly.

By the way, just recently I came across an article mentioning 235 MPG cars. Hmm, a curious number … why not 250? It’s not been built yet, so where does that number come from? And how efficient is that actually? To bring this into more familiar territory, I converted it into l/100km, which is how we do it where I live as well, and wasn’t much surprised that it works out to almost exactly 1 litre per 100 kilometres. Someone’s simly translated a press release from Volkswagen, converted the number to MPG and rounded it a bit.

> “The 18 MPG vehicle should be replaced by the 50 MPG one.”
Yeah, sure. So you replace the pickup truck you use to take your tools to your clients, or the van you use to take your family to grandma on weekends, with a subcompact that has room for one passenger and a bag of groceries. That may be feasible for some people, but the scenario described above is also realistic and worth consideration; it’s not a false dilemma.

31. […] 16, 2008 · No Comments Turns out the swapping a car that gets bad gas mileage with one that gets decently good gasmileage is better than replacing a car that gets decently good gas mileage with one that gets outstanding mileage, and the numbers bear it out. This very interesting article in Science, “The MPG Illusion” by Richard P. Larrick and Jack B. Soll at the Fuqua School of Business in Duke University (Vol 320, June 20, 2008, p. 1593), points out the mathematically obvious truth that gas used per mile is inversely proportional to miles per gallon, which means that you have a steeper slope at lower MPG ratings, and diminishing returns at higher MPG ratings. […]

32. Jim van der Vlaan says:

I guess MPG (as opposed to l/100km) has been introduced so that
bigger numbers = better
making it easier to understand for the typical US consumer. Or am I off in this regard?

33. Tom Reingold says:

Jim wrote: “SWEET!!! You just bought a new car to save 198.4 * $4.50 =$892.80 a year. No wonder our economy is going down the drain, nobody does basic cost analysis anymore. ”

I buy used cars only, and the most I’ve ever paid for a car is $12,000. I’m not sure what a typical purchase price for a car is, but assuming$12,000 isn’t insanely atypical, I divide your $900 savings per year over the$12,000 purchase price, and I get a 7.5% yield. Do you know of a security, such as a stock or a bond, that can guarantee that kind of yield? I don’t. So in my view, an investment doesn’t have to pay for itself in the first year or two, especially if it starts paying off immediately.

All the comments here do show an interesting lack of ability to analyze more than a few numbers. This is not so much among the people commenting here but reflecting the public at large, who prove to be fairly innumerate.

Jim van der Vlaan, I don’t know if Americans are more innumerate than Europeans, but I do not believe our backwards fuel efficiency calculations are because of that. So yes, I feel you are off.

Tom Reingold
Noo Joizy, USA

34. Simon Tan says:

@Bunnie: while increasing the efficiencies of inefficient vehicles such as SUVs are good, it would be better if people just purchased efficient vehicles to begin with and tax breaks encourage that.

@Tom Reingold:
you’re numbers don’t include maintenance, gas, insurance, etc; so your 7.5% yield is a bit high. Wow, a used car at \$12,000; must be nice.

@Nex: I agree, all vehicles were designed for a specific purpose. Hopefully, they design them with efficiency in mind rather than throw a couple of wheels and a engine together. I don’t understand when you say “why not 250” MPG. I mean, if they can make a vehicle to run at 250 MPGs, I’m sure they would love to put that in rather than say it only gets 235 MPG. And I believe that number is from scientific estimates from people who have knowledge and experience doing what they do, designing vehicles.

35. Damien R. S. says:

Simon Tan: I think you missed the point. Nex wondered where the 235 — 3 significant digits! — MPG figure would come from, for a car that hadn’t even been built — or designed? — yet. It’s a reasonable question, with the answer that this hypothetical wondercar of the future was from MetricWorld, and had a pipe dream target of 1 l/100km — a nice round number, in those units. Someone dreaming in MPG would probably aim for 100 MPG, or 200, or 1000, not 235.

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38. […] And, There are some important policy implications of this. Relatively small MPG improvements in the most gas-hungry vehicles pay off greater than larger improvements in already efficient cars (hence, it does make sense to offer tax breaks for modest improvements in SUVs versus tax breaks for hybrids, which typically replacing already gas-efficient sedans). Also, personal driving habits, especially for gas-hungry cars, can often times add or subtract a few MPG to a car’s efficiency on average. For example, a car that may get 25 MPG “average highway” will degrade to under 15 MPG if you gun it out of stoplights in city traffic. That’s a huge increase in gas consumed per distance driven, especially for the less efficient cars, whereas for more efficient cars it doesn’t hurt as much to goose the engine a bit. […]

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40. Greg L. says:

This seems disengenous. Yes it is true replacing a car that gets 10 mpg with one that gets 15mgp yields more gpm savings than replacing a 34 mpg car with a 50 mpg car. However:

Wait for it…

Replacing a car that gets 10 mpg with one that get 50 mpg gives you a gpm saving of 800 gallons…so the (real) best choice is getting rid of your hummer and buying a hybrid.

Science can obfuscate as well as illuminate.

• Scott Powell says:

Sure, but often the 10 mpg “car” is really a pickup truck that is used for more than commuting. Granted, many people have a truck or SUV just to have one, but many live where not having 4 wheel drive and good ground clearance can be dangerous. Many also use picks to haul things like lumber, firewood, trailers, whatever (not doing that with a hybrid). Upgrading from a 10mpg to 15mpg is super.

Also, I have 45 mile commute to work. The nearest bus stop is 42 miles away. Please stop pretending everyone lives in the city and can use mass transit. And no, I’m not moving to the city and commuting 42 miles to my farm.

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