# Something increases threefold means it's up 300%, or 200%? **URL:** \ **Category:** Factual Questions\ **Created:** [November 2, 2009, 7:38am UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029 "2009-11-02T07:38:27Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![ColdPhoenix](https://avatars.discourse-cdn.com/v4/letter/c/6bbea6/32.png) [@ColdPhoenix](https://boards.straightdope.com/u/ColdPhoenix)\ **Post date:** [November 2, 2009, 2:31pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/21 "2009-11-02T14:31:13Z")
> [@Joe Frickin Friday](#): > > Why are you treating these two parameters (efficiency and output) differently when used in the same expression? > > “X has increased by 4%” means that the new value of X is 104% of the old value of X, regardless of what you substitute for X. > > Note that in this particular case, the mathematical relationship between output and efficiency does not alter things, either: if you increase output by 4%, you are increasing the numerator in the efficiency calculation by 4%, ergo your efficiency will also increase by 4%. Because in the two expressions we’re talking about percentages of different things. For example assume your putting 100W of power into a machine. If it’s only 42% efficient then the machine’s producing 42W of power. A 4% increase in efficiency is measured against the power put in so 4W. A 4% increase in output is measured againt the 42W and so 1.7W. > [@Mogle](#): > > An increase in output doesn’t neccessarily mean an increase in efficiency, eg stepping harder on the gas pedal will increase an engine’s output but not its efficiency. Fair enough, I was assuming a constant input for purposes of the example. ---
**Author:** ![ColdPhoenix](https://avatars.discourse-cdn.com/v4/letter/c/6bbea6/32.png) [@ColdPhoenix](https://boards.straightdope.com/u/ColdPhoenix)\ **Post date:** [November 2, 2009, 2:32pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/22 "2009-11-02T14:32:53Z")
> [@Joe Frickin Friday](#): > > Why are you treating these two parameters (efficiency and output) differently when used in the same expression? > > “X has increased by 4%” means that the new value of X is 104% of the old value of X, regardless of what you substitute for X. > > Note that in this particular case, the mathematical relationship between output and efficiency does not alter things, either: if you increase output by 4%, you are increasing the numerator in the efficiency calculation by 4%, ergo your efficiency will also increase by 4%. I just reread what you said. The 42% in both cases is the efficiency, as in the original example. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [November 2, 2009, 2:37pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/23 "2009-11-02T14:37:14Z")
> [@ColdPhoenix](#): > > A 4% increase in efficiency is measured against the power put in so 4W. A 4% increase in efficiency is not measured against the power put in; it’s measured against the old value of efficiency. Percent change in X = ( NewX - OldX ) / OldX \* 100% This is true regardless of whether X is efficiency, power, or cheeseburgers. ---
**Author:** ![Animastryfe](https://avatars.discourse-cdn.com/v4/letter/a/8797f3/32.png) [@Animastryfe](https://boards.straightdope.com/u/Animastryfe)\ **Post date:** [November 2, 2009, 2:40pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/24 "2009-11-02T14:40:12Z")
> [@DaveBfd](#): > > I see it as (and Im sure EVERYONE else does) taking 42 and increasing it by 4. If there is a situation where you would need to know what an exact 4% increase of a number is, you had better damn well know you need that exact number. No, not everyone does. I see the distinction between percentage points and just percent most commonly in political and economic contexts, and sometimes scientific ones. ---
**Author:** ![ColdPhoenix](https://avatars.discourse-cdn.com/v4/letter/c/6bbea6/32.png) [@ColdPhoenix](https://boards.straightdope.com/u/ColdPhoenix)\ **Post date:** [November 2, 2009, 2:49pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/25 "2009-11-02T14:49:13Z")
> [@Joe Frickin Friday](#): > > A 4% increase in efficiency is not measured against the power put in; it’s measured against the old value of efficiency. > > Percent change in X = ( NewX - OldX ) / OldX \* 100% > > This is true regardless of whether X is efficiency, power, or cheeseburgers. Efficiency is already a percentage of the power put in. If a machine goes from 42% efficient to 46% efficient then efficiency has increased by 4%. The power output has increased by 9.5%. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [November 2, 2009, 3:01pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/26 "2009-11-02T15:01:14Z")
> [@ColdPhoenix](#): > > Efficiency is already a percentage of the power put in. This is irrelevant. [Don’t make me stay up late.](http://xkcd.com/386/) ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [November 2, 2009, 3:17pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/27 "2009-11-02T15:17:29Z")
> **[Percentage point](https://en.wikipedia.org/wiki/Percentage_point)** > > A percentage point or percent point is the unit for the arithmetic difference between two percentages. For example, moving up from 40 percent to 44 percent is an increase of 4 percentage points (although it is a 10-percent increase in the quantity being measured, if the total amount remains the same). In written text, the unit (the percentage point) is usually either written out, or abbreviated as pp or p.p. to avoid confusion with percentage increase or decrease in the actual quantity. Aft Consi... ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [November 2, 2009, 3:46pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/28 "2009-11-02T15:46:37Z")
[http://www.mathsisfun.com/percentage-points.html](http://www.mathsisfun.com/percentage-points.html) ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [November 2, 2009, 3:47pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/29 "2009-11-02T15:47:41Z")
[http://mathforum.org/library/drmath/view/64433.html](http://mathforum.org/library/drmath/view/64433.html) ---
**Author:** ![ColdPhoenix](https://avatars.discourse-cdn.com/v4/letter/c/6bbea6/32.png) [@ColdPhoenix](https://boards.straightdope.com/u/ColdPhoenix)\ **Post date:** [November 2, 2009, 3:53pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/30 "2009-11-02T15:53:27Z")
I understand what your saying. I know that going from 10% to 12% is a 20% increase. I’m saying that going from 10% efficiency to 12% efficiency is a 2% increase in “efficiency” even though the “efficiency %” has increased 20%. If you don’t see that then we’ll just have to agree to disagree. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [November 2, 2009, 4:07pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/31 "2009-11-02T16:07:52Z")
> [@ColdPhoenix](#): > > I’m saying that going from 10% efficiency to 12% efficiency is a 2% increase in “efficiency” even though the “efficiency %” has increased 20%. The ambiguity embodied in your usage is the kind of thing that crashes rockets; this is why every engineer I’ve ever worked with, for clarity’s sake, sticks to the usage I’ve described. Why do you feel efficiency should be treated differently from any other percentage quantity, such as interest rate, or tax rate, or percentage of the population that are smokers? Not that I regard Wikipedia as the final arbiter of truth, but why do you feel that Wikipedia is just plain wrong in this case? ---
**Author:** ![billfish678](https://avatars.discourse-cdn.com/v4/letter/b/7bcc69/32.png) [@billfish678](https://boards.straightdope.com/u/billfish678)\ **Post date:** [November 2, 2009, 4:55pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/32 "2009-11-02T16:55:12Z")
> [@Joe Frickin Friday](#): > > The ambiguity embodied in your usage is the kind of thing that crashes rockets; this is why every engineer I’ve ever worked with, for clarity’s sake, sticks to the usage I’ve described. IME the really good ones state it in such a way that there CAN BE NO misinterpretation. Assuming anyone on the other end will automatically be Spock is a recipe for disaster. The system efficiency was increased 20 percent, resulting in a overall efficiency of 12 percent rather than the nominal efficieny of 10 percent. Or some such bloviations. ---
**Author:** ![pan1](https://avatars.discourse-cdn.com/v4/letter/p/e495f1/32.png) [@pan1](https://boards.straightdope.com/u/pan1)\ **Post date:** [November 2, 2009, 6:18pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/33 "2009-11-02T18:18:16Z")
> [@Koxinga](#): > > I’m a tad uncertain on this. I’ve always thought that when (say) $100 increases threefold, that’s equivalent to saying it increased to 3 x $100 = $300, which in percent terms would be +200%. But I’ve seen some people (non-native English speakers, FWIW) using a shorthand of “threefold” = “300%”, which of course would yield a dollar figure of $400, not $300. Which is correct? (Or is my math screwed up either way?) Actually both 200% and 300% = threefold - depending on how you apply the math. Threefold $100= $300 = $100 + 200%(of $100) = 300% of $100. ---
**Author:** ![hibernicus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hibernicus/32/2802_2.png) [@hibernicus](https://boards.straightdope.com/u/hibernicus)\ **Post date:** [November 2, 2009, 10:08pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/34 "2009-11-02T22:08:55Z")
> [@ColdPhoenix](#): > > Efficiency is already a percentage of the power put in. > > If a machine goes from 42% efficient to 46% efficient then efficiency has increased by 4%. > > The power output has increased by 9.5%. Not really. Depending on why the efficiency has increased, the power output could have stayed the same, or increased or decreased by some other amount. Until about a year ago I worked in performance testing of power plant. Precisely because of the potential for confusion highlighted in this thread, it is common to express differences in terms of heat rate (effectively, the inverse of efficiency). A 4% improvement in efficiency is ambiguous - a 4% improvement in heat rate is not. ---
**Author:** ![Irishman](https://avatars.discourse-cdn.com/v4/letter/i/b487fb/32.png) [@Irishman](https://boards.straightdope.com/u/Irishman)\ **Post date:** [November 2, 2009, 10:31pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/35 "2009-11-02T22:31:43Z")
**billfish678** said: > [@](#): > > IME the really good ones state it in such a way that there CAN BE NO misinterpretation. This. Percentages are already something that is not intuitive to most people. Add to that the ambiguity of the language, and you have a recipe for disaster. Why talk about a percentage increase of a percentage value? Are you talking about the value increasing by a certain number, or changing by a percentage of the value it was at? Why risk someone misinterpreting? State the original value and the final value, and don’t worry about how much “percentage change” that is. Because if you state percentage change, 99% of the time the person is just going to need to convert that to the final value anyway. Skip the confusion, state the result. “We were running at 42% efficiency, but we increased to 46%.” ---
**Author:** ![Cardinal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cardinal/32/4000_2.png) [@Cardinal](https://boards.straightdope.com/u/Cardinal)\ **Post date:** [November 3, 2009, 8:38pm UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/36 "2009-11-03T20:38:24Z")
Does anyone know if the California car registration was increased by Grey Davis by a factor of 3 or 4? The goofball news media around here reported it as both a 3x increase and a 300% increase. I can’t decide which way they misinterpreted it. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [November 4, 2009, 7:58am UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/37 "2009-11-04T07:58:51Z")
> [@Irishman](#): > > **billfish678** said: > > This. Percentages are already something that is not intuitive to most people. Add to that the ambiguity of the language, and you have a recipe for disaster. > > Why talk about a percentage increase of a percentage value? Are you talking about the value increasing by a certain number, or changing by a percentage of the value it was at? Why risk someone misinterpreting? > > State the original value and the final value, and don’t worry about how much “percentage change” that is. Because if you state percentage change, 99% of the time the person is just going to need to convert that to the final value anyway. Skip the confusion, state the result. > > “We were running at 42% efficiency, but we increased to 46%.” In advertising and politics, sometimes confusion is the point. In these cases, pick the choice that shows the presenter in the worst light. ---
**Author:** ![Superhal](https://avatars.discourse-cdn.com/v4/letter/s/b4bc9f/32.png) [@Superhal](https://boards.straightdope.com/u/Superhal)\ **Post date:** [November 4, 2009, 10:30am UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/38 "2009-11-04T10:30:55Z")
> [@Koxinga](#): > > I’m a tad uncertain on this. I’ve always thought that when (say) $100 increases threefold, that’s equivalent to saying it increased to 3 x $100 = $300, which in percent terms would be +200%. But I’ve seen some people (non-native English speakers, FWIW) using a shorthand of “threefold” = “300%”, which of course would yield a dollar figure of $400, not $300. Which is correct? (Or is my math screwed up either way?) If something triples in size, it’s now 200% bigger than it used to be. ---
**Author:** ![Koxinga](https://avatars.discourse-cdn.com/v4/letter/k/4af34b/32.png) [@Koxinga](https://boards.straightdope.com/u/Koxinga)\ **Post date:** [November 4, 2009, 10:41am UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/39 "2009-11-04T10:41:14Z")
My question was more one of English usage than of math per se. I’m just wondering how “a threefold increase” is commonly understood. Myself, I tell people it’s up 20,000 basis points. ---
**Author:** ![amarone](https://avatars.discourse-cdn.com/v4/letter/a/e0b2c6/32.png) [@amarone](https://boards.straightdope.com/u/amarone)\ **Post date:** [November 4, 2009, 10:42am UTC](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029/40 "2009-11-04T10:42:58Z")
> [@BigT](#): > > In advertising and politics, sometimes confusion is the point. In these cases, pick the choice that shows the presenter in the worst light. Absolutely. The party raising taxes from 30% to 33% will say they are raising by 3%; their opponents will say they are raising taxes by 10% [Previous page](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029.md?page=1) [Next page](https://boards.straightdope.com/t/something-increases-threefold-means-its-up-300-or-200/516029.md?page=3)