Going the Extra Mile

It’s time to get a little nerdy with another post inspired but the often quite brilliant web-comic, xkcd … specifically this.

The mouse-over text reads, “and if you drive a typical car more than a mile out of your way for each penny you save on the per-gallon price, it doesn’t matter how worthless your time is to you—the gas to get you there and back costs more than you save”. Seeing as I do drive a bit out of my way each week to get cheaper fuel, it got me wondering – Am I just wasting time and money? Just how far would I have travel before I’d be losing out?

For anyone wanting to play along at home, the formula I used was:

M = L*n / (C*P)

(Where; M is the maximum number of kilometres you can add to your normal journey before you lose money, L is the number of litres you put into your tank on each visit, n is the number of cents cheaper the fuel down the road is, C is the average fuel consumption of your vehicle in L/100 km, and P is the price of the cheaper fuel in dollars.)

First I wanted to verify xkcd’s claim. Apparently a typical car in the USA gets around 23 miles/gallon (10 L/100km) and current prices are somewhere around $3.60/gallon. I also assumed you’d be filling up your tank with about 9 gallons (35 L), which by my calcs means you wouldn’t want to travel any further than 0.9 miles for a 1 cent/gallon drop in price. So the xkcd statement seems a bit conservative, especially if you read it (as I did) as talking about a 2 mile journey (1 mile there, 1 mile back). Still, it kind of helps their point.

But here in Australia, we work on a $/litre price for petrol, and because a litre is much smaller than a US gallon, a 1 cent price drop is more attractive. With my car (which gets around 7 L/100km) it’d be theoretically worth travelling 3.6 km to fill up the whole tank (assuming a $1.40/litre price). Many cars would have higher fuel consumption though, so you can look at the chart below to see how it applies to you (the distance includes your return journey if needed).

If your car uses less than 5 L/100km imagine the curve continuing off to the left. If it uses more than 15 L/100km, now might be a good time to buy a new car.

The petrol station I usually visit always seems to be about 4 cents/litre cheaper than the one on my normal route home from work. It means travelling an extra 4.5 km, but by the method above its well worth it for a big fill-up (even an extra 14 km would be okay).

But, as the comic suggests, there are other factors to be considered. Like how much your time is worth to you, and the fact that the savings you’ll make will be quite small in dollar terms (in my case it’s a bit less than $1 each fill-up). Also, there’s the frustrating inconvenience of lining up with a bunch of other cars all seeking the cheapest fuel.

So is it worth it? Maybe not. I gave myself a rule of thumb that it’s only worth a detour if the money you save is more than twice how much it takes to drive the extra distance, and I made a little spreadsheet to do the calculations for me. By this rule my detour is still worth it but only for 22 L or more, and at 10 L or less I start losing money.

My calculation sheet

All this means is you might want to think twice about going the extra distance for cheaper fuel if;

  • The other station is a decent distance away,
  • The other fuel isn’t that much cheaper,
  • Your car has high fuel consumption,
  • The general price of fuel is high, and/or
  • You’re not planning to put much fuel in the tank.

So whether this is news to you or not, I wish you all good luck in your quest for that smelly stuff we run our cars on!

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This entry was posted in Sort of Science and tagged , , , , , , . Bookmark the permalink.

2 Responses to Going the Extra Mile

  1. olga says:

    I love that you took the time to work this out. Yay xkcd!

  2. Cheers Olga. I have a tendency to waste time on this sort of thing even when I really shouldn’t be. 🙂

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