# How to read such figures with % as “up (by) 120%” and “increased (by) 120%”. Do they mean the same?

There are now 5.7 billion euros, in notes and coins, in circulation, up 120% from December 31 2001,......

Following significant media coverage of the statistics, calls and contacts logged on the following day – 6 April – were up by 120% compared with the previous day.

Plastic bag regulation can have unintended consequences. Sales of small trash can liners increased 120% after bag bans

Rough sleeping has increased by 120% in England but has fallen in Scotland.

Such phrases describing growth rate as in the above examples are very common, but sometimes I'm confused about how to read them correctly.

My understanding is:

• If our 2019 sales are up 120% (or has increased 120%) from year 2018, it means, for instance, US\$ 100 million in 2018, and US\$ 120 million in 2019

• If our 2019 sales are up by 120% (or has increased by 120%) from year 2018, it means, for instance, US\$ 100 million in 2018, and US\$ 220 million in 2019

If the above understanding is correct, then how should I interpret "..... is up 20% from last year"? Is it different from "up 120% from last year"?

Or maybe those expressions include some ambiguities?

• @Takashi As other answers have noted, they do mean the same thing. However, one thing that is not the same is when you say X is 120% of Y. This means that X is 20% more than Y is. In other words, X is six-fifths of Y. – Joe Aug 5 '20 at 23:26

"Increased X%" or "increased by X%" or "up X%" or "up by X%" all mean the same. To increase an amount by a percentage is to take the original amount, and add to it the given percentage of that amount. Thus 'increased by 100%' means the same as 'doubled'. 100 increased by 120% is equal to `100 + (100 x 1.20)` which is 220.

Percentage change calculator

It is common to use everyday fractions for some percentages, e.g. if something is increased by 25, 33.3, 50, or 75 per cent we can say it is increased by a quarter, a third, a half, or three quarters respectively.

My understanding is:

If our 2019 sales is up 120% (or has increased 120%) from year 2018, it means, for instance, US\$ 100 million in 2018, and US\$ 120 million in 2019

Your understanding is not correct. if your sales were \$100 million in 2018 and \$120 million in 2019, then they are up 20% (or have increased 20%) from 2018.

• I agree with this answer, but note that there are plenty of mathematically illiterate journalists writing for our newspapers. It's not uncommon to see "Increased by 20%" used to mean "Changed from 60% to 80%. – James K Aug 5 '20 at 9:38
• @JamesK is perfectly correct and the use of percentage point should be more widespread and perhaps would make a useful edit to the question. 60% to 80% is an increase of 20 percentage points or 33.3% – mdewey Aug 5 '20 at 12:33
• If you wanted to say that it was 100% and is now 120% (not 120% of 100%), you would say that it has increased to 120%, not by 120% or any of those other variants. – Darrel Hoffman Aug 5 '20 at 16:54
• I didn't say "by 20%" was wrong - I said "by 120%" is wrong in that case, but "to 120%" is correct. – Darrel Hoffman Aug 5 '20 at 17:34
• @MichaelHarvey They have: in the first bullet point, the questioner assumes that 100 becoming 120 is "increased 120%" and in this answer, you assert that "by" is equivalent to no preposition – Tim Sparkles Aug 5 '20 at 18:50

From a prescriptivist point of view, "X% increase" means "multiplied by (1+X/100)".

From a descriptivist point of view, "X% increase" is often used to mean "multiplied by X/100". Of course, if X<100, then it can only mean "multiplied by (1+X/100)". This results in the odd situation that "X% increase" suddenly means something different when X reaches 100.

Logically, "increased X times" should also mean "multiplied by 1+X", but its use to mean "multiplied by X" is even more common than "X% increase" as "multiplied by X/100".