The McDonald’s Fries Theorum

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Everyone's Favourite Jim had a lot of work to do, so naturally chose to ignore it all and do something silly instead. Are McDonald's fries a con? Only one way to find out.
The McDonald's Fries Theorum

As a family, we don’t get McDonald’s that often, mainly because I think it’s shit and there are better life choices to be made, but occasionally it will magically appear at our door, often when we’re feeling lazy.

However, there was something different about this particular order, the presence of medium fries.

When asked about it, my wife responded “Because there’s not actually any more chips in them, it’s a con!”

Me being me, I couldn’t take that at face value and decided to test it.


There are more fries in a large. Job done.

But, the fries are in a larger box.

So I zero out the scales with a bowl and weigh the chips.


There are more fries in a large. Job done.

18g more, to be precise. Which interestingly (excuse my fast and loose usage of ‘interestingly’) means that the large has 2g of extra cardboard.

Here’s what 18g of fries looks like.

With this myth conclusively proven to be incorrect, science has won the day yet again.


A large has 116% of the fries of a medium, but, at £2.29 vs £1.79, is 128% of the price. Surely, then, there is a point where it’s cheaper to buy more medium portions than large portions.

Turns out, there is. And it’s not as many as you might think.

I wanted to find the crossover point where buying just one more portion of medium fries made it more cost-effective than buying large fries. And here are the results.


If you buy five portions of medium fries, it’s cheaper than four portions of large fries by 21p and you get 37g more fries!


This works up to 7 mediums vs 6 large where you get 1 gram extra of fries for £1.21 less! After that, it gets cheaper but you do get fewer fries.


If you were following this thread on twitter, that’s where we got to, but I since thought we could go deeper.

So, I turned to my AI friend, ChatGPT, and we had a little conversation about the whole thing.

Yes, you are correct…

(I love being validated.)

At some point, buying more portions of medium fries will become cheaper than buying one fewer portion of large fries.

To find the point where this happens, we can set up the following equation:

Price of n medium portions = Price of (n-1) large portions and weight of n medium portions >= weight of (n-1) large portions

£1.79n = £2.29(n-1) and 109n >= 127(n-1)

Solving for n:

£1.79n = £2.29n – £2.29 £0.50n = £2.29 n = £2.29 / £0.50

n = 4.58

Since you cannot buy a fraction of a portion, you would need to buy 5 medium portions, which would cost £8.95 and weigh 545g.

Buying 4 large portions would cost £2.29 x 4 = £9.16 and weigh 508g. Therefore, buying 5 medium portions at a total cost of £8.95 and weight of 545g is cheaper and heavier than buying 4 large portions at a total cost of £9.16 and weight of 508g.

Now, I’m no mathematologist, so all I can say is ‘good bot!’

However, ChatGPT did have one caveat:

Note that the equation above assumes that the prices of the large and medium portions of fries remain the same, and does not take into account any promotions or discounts that may be available.

Weird that the AI feels he has to make a statement so he doesn’t get sued. Anyway…

At this point, I had already expanded my table to see where the crossover happened if you bought two more medium portions than large portions…

The McDonald's Fries Theorum

But essentially, this all boils down to Cost Per Gram.

The CPG for a large portion is £0.0180315.

The CPG for a medium portion is £0.01642202.

So beyond a few, it will always be more cost-effective to buy more medium portions than large portions, but how many exactly?

It occurred to me that, because my AI buddy now understood the concept, instead of infinitely expanding my table, I could get him to write some code.

Ladies and gentlemen, I would like to present:

McDonald’s Fries Calculator

So there we have it. I think I’ve taken this as far as it will go. I appreciate this is only a small sample size, and you’re more than welcome to conduct your own experiments and report back. I’d genuinely be interested in how you get on, so comment below or catch me on Twitter.

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