# Is "600% smaller" correct use of percentages?

"600% smaller when compared to GIF"

This doesn't make sense. I can understand 600% larger (it is 6 times larger), but not 600% smaller. If it is acceptable English, what does it mean? 1/6 the size? I am seeing this construct more and more often.

• Saying "600% larger" should generally be avoided. Something that is 90% larger than 100 is 190, not 90. By induction, something that is 600% larger than 100 is 700, not 600. 600 is six times as large as 100, not six times larger than 100. Commented Dec 28, 2021 at 15:27

This statement is likely correct about whatever file format you're talking about. To understand why, you have to look at the savings as a ratio.

Imagine you have a file that is 1,000,000 bytes of raw data, and you compress it with GIF, and the result were 900,000 bytes of compressed data. Now, imagine the other file format takes the same 1,000,000 bytes and outputs 400,000 bytes of compressed data.

The original GIF encoding saved 100,000 bytes, the new file format saved 600,000 bytes of data. As such, the new file format saved 600% space compared to the 100% space saved by GIF.

Note, we're not talking about the reduction in file size as a percentage of the original size, we're talking about the amount of space we saved in two different formats, which is a gain in efficiency, and that gain can be expressed as a ratio, and ratios can be expressed as percentages.

• Then the description should have said thet the compression was 600% better, not that the file was 600% smaller. Commented Aug 31, 2021 at 17:28
• @TimRandall I agree with that statement. The original claim, by the way, appears to be from Lottie, which actually says "600% smaller" in a title section without a lot of space. I think they were simply trying to be efficient at a minor cost of grammatical accuracy. "Better" would have been a better word choice, but the target audience, programmers (like myself) would have understood it equally well either way. Commented Aug 31, 2021 at 17:39

It is meaningless. Something cannot be more than 100% smaller.

It would be like having a pint glass full of beer and then pouring away 6 pints of it!

• But if Alice owes Bob \$1, and Carol owes Alice \$5, then Alice's debt to Carol is 600% smaller than her debt to Bob. Commented Dec 28, 2021 at 15:14
• 80% smaller I think.
– Nemo
Commented Dec 29, 2021 at 17:22
• No, because Alice's debt to Carol is minus five dollars, which is 600% smaller than one dollar. Commented Dec 29, 2021 at 21:44

It doesn't make that much sense, but it often means "six times smaller" than a reference item. If a deer is 600% larger than a dog, then some people might imagine that a dog is 600% smaller than a deer, if they don't fully understand how percentages work.

600% smaller when compared to GIF

It doesn't make a lot of intuitive sense, but I assume the authors here are merely just trying to create an effect on the reader. This is slightly off-topic for English Stack Exchange, but from a mathematical perspective:

If you've got 100\$ in the bank, you could be down by 600% the next month if you are in a debt of 500\$. Here's the math:

^For those who are suspicious of the math

• I'd say that you got the English right but the math wrong. I'd say that "six hundred percent smaller" would be dividing by 600% (or, in other words, dividing by six). Commented Aug 31, 2021 at 7:02
• I don't think I'm wrong: see this calculatorsoup.com/calculators/algebra/… Commented Aug 31, 2021 at 7:16
• The maths is correct but the point is that a file cannot have a negative size.
– Nemo
Commented Aug 31, 2021 at 7:26
• @Shane There's a difference between 600% smaller (where the sign must remain the same) and 600% less. Commented Aug 31, 2021 at 7:27
• @nick012000 something that is 25% larger (or smaller) may be calculated by multiplying by a factor of 1.25 (or 0.75), calculated as 100% plus (or minus) 25%. By extension, something that is 600% larger (or smaller) may be calculated using a factor of 700% (or -500%). If you try to calculate something 25% smaller using your logic, you get something that is 4 times as large. For example, 15 kg divided by 25% yields 60 kg. Commented Dec 28, 2021 at 15:19

Avoid %smaller/ larger like the plague. Here's why:

1. Logic 1: x% smaller = (100-x)% the size of the original. "Sounds good" for x <100. Eg 20% smaller -> 80% of the original.

2. Logic 2: x% smaller = (100/x)% the size of the original. "Sounds good" for x >200. Eg 500% smaller -> 5 times smaller -> 20% of the original.

I think people will use these two terms mainly on the conditions I mention. The ambiguousness, of course, is infuriating. I'd stick to saying "x% of the original" and, on the unfortunate cases where people use such terms, assume logic 1 for x<100, logic 2 for x>200 (and even >100 with a heavy heart).

• +1 "X is N% of Y" is, I think, the only rigorous usage. I agree that people who say "N% bigger" probably mean "N/100 times bigger", but I don't think a statistician would use it and I'll bet many of those who do use it, get it wrong (they'll say 200% bigger when they mean 200% of the size, ie 100% bigger. "N% smaller" means, mostly, "I suck at math and you can't believe numbers from me", but to the extent it means anything, "600% smaller" is probably an attempt at saying 1/6th. Do not accept this in any context where accuracy is needed, like a contract or a specifications document.
– CCTO
Commented Aug 31, 2021 at 13:47

No, it is not a correct usage.

Calculating percentages is taught in primary school. It is not a matter of subjective interpretation, and does not depend on language. If GIF is 600% larger than X, then GIF's size is 700% of X: 100% of the original size of X, plus 600% the size of X; in other words, 700% or 7 times larger than X. Then, X is:

100% - (1/7 × 100%)

smaller than GIF, or in simpler terms, about 86% smaller than GIF.

"600% smaller when compared to GIF" sounds like the author wanted to sound smarter than he/she really is, went a bit above his/her educational and/or intellectual "pay-grade", and voiced out a statement that makes no sense.

Such a statement might have made sense in some context where negative values were valid; however, the size of computer files is not such a context because their size is never negative. In this case, no matter of creative misinterpreting coupled with Olympic level mental gymnastics could make sense of that statement.

This doesn't make sense. I can understand 600% larger (it is 6 times larger),

Mathematically, 600% larger is 7 times the size, or 6 times larger. This is so because 100% larger means double the size. Double the size is 1 time larger. (Two times larger would be triple the size. Two times the size would be double the size.)

However, English isn't math, and some people understand "600% larger" to mean 6 times larger and some people understand "600% larger" to mean 5 times larger (thus 6 times the size).

Style guides strongly suggest not using constructs like "X% larger" if X is greater than 100 because it is not consistently understood by English speakers.

but not 600% smaller. If it is acceptable English, what does it mean? 1/6 the size? I am seeing this construct more and more often.

It might be understood to mean 1/6th the size. But I think many English speakers would find it confusing. No editor or proofreader would permit such a construct to pass unless it was in a mathematical context where its meaning was clear.

If x is K% "smaller" or "bigger" means that it is |K%| "lesser than" or "greater than" it was before, i.e. "K% less" or "K% more", i.e. x becomes "x minus K% of x" (subtraction) or "x plus K% of x" (addition); not division or multiplication (which could be stated as "x [shrunk or grew] to [|K%|<1 or |K%|>1]" of its original size).

In the case of the question, "600% smaller" := "600% lesser" = "x -600% of x" = x-6x = -5x.

One confusing matter is the use of 'smaller' instead of 'lesser' in the question: Whereas 'small' and 'large' lend themselves to the notion of magnitude (absolute value close to zero versus greatly positive), 'lesser' and 'greater' than denote the distance to the left versus right on a number line. As such, the former lends itself more to a multiplication interpretation than does the latter which is a simple addition. That said, there are much clearer ways to express a shrinking or growing in "in scale" instead of linearly (e.g. simply "shrunk to one-sixth of its size"). If wanting to express a scaling-down or up sense in terms of a percentage, then to say that "x became 600% smaller" (instead of "x loss 600%" reversing sign). I'm not sure, but I think it doesn't make sense without comparing it to a preceding reference rate. "x shrank to 1/6" which equates to "x became 16.666..7% x" or "x↦0.16666..7 (x)" as a decimal. As used colloquially, "600% smaller" likely is intended by the person to mean "six-times smaller", which could be taken to mean the inverse of "six-times larger", i.e., one-seventh the original.

As others have pointed out, '600%' here means something like '6 times', and '6 times times as small as ...' would have been a slightly better phrase, IMO; or much better '1/6 as big as ...'

This is a common confusion of the terms 'smaller than ...' and '.. as small as ...' - taken exactly as stated, it isn't actually meaningless as some have suggested, but 'smaller than' means you subtract something - IOW, you have 100% ans subtract 600% and end up with -500%, which is mathematically possible, but perhaps not realistic.

• In the context of the example given, it is impossible to give a negative result. Commented Aug 31, 2021 at 16:38
• @Steve Hence the slightly ironic "... perhaps not realistic". Commented Sep 1, 2021 at 7:24

It could make sense if the scale for some reason could be negative, e.g. a mathematical "size" that doesn't have a unit "the numerator was 600 % smaller than the denominator" (if the denominator is 5, 100 % smaller is 0, 200 % smaller is -5 etc) but in the case of physical items in the real world it is just sloppy language. And even in the case of my example, it is unclear and prone for misinterpretation.

Footnote: 600 % larger is actually 7x times larger. Lets start with 20. 100 % larger is 40 = 2x larger. 200 % larger = 60 = 3x larger. Etc.

There's no way that I can see to describe something as "600% smaller".

I think that even the people who interpret "600% smaller" as "six times smaller" are using a form of words that's meaningless. By this I mean that, if this interpretation is applied consistently, then "100% smaller" means "one times smaller". Does that mean original size? If so, we can all make a lot of money as business consultants by promising clients a 100% reduction in expenses.

TL;DR It's a phrase that is used to make something sound more sensational. In other words, you might call it "Marketing Drivel."

I am an engineer. I do a lot of math. I understand the concept of "600% smaller." The exact definition cannot be pinned down, because the definition of "600% larger" varies.
600% larger could be "6x" or "7x", depending on your reference.

Consider:
My refrigerator has 20 cubic feet of cold storage volume.
Next year, the manufacturer comes out with a new model that is 600% larger. (Note, it is NOT 6 times larger).
Some folks will say the new unit will have 20 x 6 = 120 cubic feet.
Others will say that it has the original space plus 600% more, which is 20 + (20 x 6) = 140 cubic feet.

I have a desktop computer. It has a volume of 3.5 cubic feet.
I replaced it with a cell phone that, according to the manufacturer, is 600% smaller than my desktop computer.

Is my cell phone 1/6th or 1/7th the size of my desktop?
We could argue this until the cows come home.

Since I am in the United States, I could measure the volume of both, compute the difference in size, and if I get a number smaller than 600%, I could sue the manufacturer for false advertising. In that scenario, they would have to prove they were correct. Their math would show that they were right, because there is no specific standard on what 600% smaller means.

What the phrase really means:
It's a whole lot smaller! But, that isn't as exciting in a commercial, so they say:
Our new cell phone is SIX HUNDRED PERCENT smaller than your desktop computer!

In summary, IMHO, it's all nonsense. Don't get caught up in the minutiae of what it actually means. It'll make your head hurt.

\$0.02

### "600% smaller" is the inverse of "600% larger".

In short, "600% smaller" is the inverse of "600% larger", so you perform the same operation in reverse. Since "600% larger" is ambiguous as to whether it means addition or multiplication, "600% smaller" is generally also ambiguous - but in this case, one of those cases is nonsensical, so we know that it means multiplication.

So, to dive into it a bit deeper, there are two possible meanings of "600% larger": either you're adding 600% of the original value to it (i.e. if the original value was x, the final value is x+600%*x), or multiplication, where you're just multiplying the original value by 600% (if the original value is x, the final value is 600% * x).

As a result, "600% smaller" could refer to either subtraction or division. However, when dealing with values greater than 100%, subtraction will yield a negative number, which is often nonsensical. As a result, we know that the meaning of "600% smaller" in this case must mean dividing the number by 600%.

In general, however, you should try to avoid the phrases "percent larger" or "percent smaller", in favor of more specific and less ambiguous verbiage - especially when dealing with percentages that are whole number multiples of 100, since those can simply be expressed as "n times", where n is the whole number multiple in question (e.g. "six times" rather than "600 percent").

• But something that is 60 liters is not six times larger than something that is 10 liters; it is six times as large as it, just as 60 liters is 20% larger than 50 liters and 1.2 times as large as 50 liters. Commented Dec 28, 2021 at 15:24