# Ratios below 1:1 called "negative"

**URL:** <https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040>\
**Category:** Factual Questions\
**Created:** [April 18, 2013, 3:45pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040 "2013-04-18T15:45:23Z")\
**Posts on this page:** 18\
**Page:** 1

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**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\
**Post date:** [April 18, 2013, 3:45pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/1 "2013-04-18T15:45:23Z")

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I’m reading a report right now which deals with some ratios, and when the ratios are below 1:1, it refers to them as negative, with ratios above 1:1 being referred to as positive. (For example, a ratio of .96 is referred to as negative, and a ratio of 1.02 is referred to as positive.)

I understand the intended meaning of this, and the rationale for using these terms, but my question is, is this an established usage?

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**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\
**Post date:** [April 18, 2013, 3:51pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/2 "2013-04-18T15:51:29Z")

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That’s a really bad convention. What do they do for ratios that are actually negative numbers, like -3:2?

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**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\
**Post date:** [April 18, 2013, 3:58pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/3 "2013-04-18T15:58:18Z")

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If a “negative” ratio pertains to a trend line, it would indicate a diminishing progression, hence, negative increase.

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**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\
**Post date:** [April 19, 2013, 11:34am UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/4 "2013-04-19T11:34:20Z")

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> [@Frylock](#):
>
> I’m reading a report right now which deals with some ratios, and when the ratios are below 1:1, it refers to them as negative, with ratios above 1:1 being referred to as positive. (For example, a ratio of .96 is referred to as negative, and a ratio of 1.02 is referred to as positive.)
> 
> I understand the intended meaning of this, and the rationale for using these terms, but my question is, is this an established usage?

It is common usage when its a Ratio of X to X. ! (eg money in the bank..)

When its a slope, its height to width.. thats NOT X to X ,and so its not common usage for that.

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**Author:** ![Dog80](https://avatars.discourse-cdn.com/v4/letter/d/6bbea6/32.png) [@Dog80](https://boards.straightdope.com/u/Dog80)\
**Post date:** [April 19, 2013, 11:58am UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/5 "2013-04-19T11:58:34Z")

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When a ratio is expressed as a logarithm (for example when measuring power in dB), a negative number means a ratio smaller than 1:1

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**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\
**Post date:** [April 19, 2013, 3:34pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/6 "2013-04-19T15:34:47Z")

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Context is everything. What is the subject of the report and what are the ratios measuring?

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**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\
**Post date:** [April 19, 2013, 3:49pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/7 "2013-04-19T15:49:10Z")

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Meh, I was just asking if it’s ever in line with any convention. I don’t really know much about the details here–this is just something I saw in passing while working on something tangentially related.

These are financial ratios (I don’t actually know exactly what that means, but I _think_ it represents growth. But I don’t know.)

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**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\
**Post date:** [April 19, 2013, 5:27pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/8 "2013-04-19T17:27:34Z")

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> [@Frylock](#):
>
> These are financial ratios…

I know of no example where a ratio \<1 is called negative. An engineer, scientist, or mathematician would not use that convention but finance people and accountants just have a different way of thinking.

A P/E ratio can be negative if the company is losing money, but that does not mean the ratio is \<1, it means it’s \<0.

There is something in accounting called the _current ratio_ (current assets:current liabilities). You want it to be \>1 but it can never be negative.

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**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\
**Post date:** [April 19, 2013, 11:15pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/9 "2013-04-19T23:15:05Z")

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> [@CookingWithGas](#):
>
> A P/E ratio can be negative if the company is losing money, but that does not mean the ratio is \<1, it means it’s \<0.

Never heard of a negative P/E. Earnings are dividends or other disbursements from the issuer, not speculative gains or losses. Do companies actually demand payment as a condition of being a shareholder when they are losing money?

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**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\
**Post date:** [April 20, 2013, 2:41am UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/10 "2013-04-20T02:41:37Z")

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> [@For You](#):
>
> Never heard of a negative P/E. Earnings are dividends or other disbursements from the issuer, not speculative gains or losses. Do companies actually demand payment as a condition of being a shareholder when they are losing money?

The earnings in a P/E ratio has nothing to do with dividends or other distributions; it is net earnings (earnings before such distributions). It is not speculative, it is plainly stated on financial statements (P&L). When P/E is negative, it is generally not reported but still exists theoretically.

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**Author:** ![Absolute](https://avatars.discourse-cdn.com/v4/letter/a/b2d939/32.png) [@Absolute](https://boards.straightdope.com/u/Absolute)\
**Post date:** [April 20, 2013, 4:45am UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/11 "2013-04-20T04:45:46Z")

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As an engineer, if pressed to express that in words instead of numbers, I’d probably go with “less than unity”. Negative makes no sense.

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**Author:** ![Qadgop\_the\_Mercotan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/qadgop_the_mercotan/32/83_2.png) [@Qadgop\_the\_Mercotan](https://boards.straightdope.com/u/Qadgop_the_Mercotan)\
**Post date:** [April 20, 2013, 9:28am UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/12 "2013-04-20T09:28:33Z")

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Are we talking about medical titers here?

Because for many specific medical assays, titers of \< 1:1 are considered negative in that they indicate lack of reaction to the antigen or other substance being tested. Hence _negative_ in this case means a test whose result shows a lack of reaction, not a negative number.

Also in medical nomenclature, a titer of 1:2 is greater than a titer of 1:1. This is due to the fact that a titer measures _dilution_. 1:128 is a greater dilution than 1:64, etc.

Just throwing in my two cents…

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**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\
**Post date:** [April 20, 2013, 11:02am UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/13 "2013-04-20T11:02:44Z")

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Here’s why when I saw the usage I didn’t think it was complete nonsense. Fractions less than one are less than the identity element for multiplication, just as numbers less than zero are less than the identity element for addition. Not that I thought the writer was consciously thinking this and would have explained it in those terms, but it seemed likely to me that he thought of one as a kind of “pivotal” element for ratios in much the same way that zero is a “pivotal” element for sums.

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**Author:** ![Melbourne](https://avatars.discourse-cdn.com/v4/letter/m/b5e925/32.png) [@Melbourne](https://boards.straightdope.com/u/Melbourne)\
**Post date:** [April 20, 2013, 12:22pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/14 "2013-04-20T12:22:30Z")

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You get negative ratios in that sense in the stock market.

I’m talking about the market here, not the stock valuation.

When you’re in negative territory the stock has gone down. This is a “negative ratio” to its previous value. Ratios are sometimes used, particularly in stock speculation, when you are interested in comparing the behviour of two different stocks, or of a particular stock compared to an index, and a comparison of absolute price would not be meaningful.

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**Author:** ![Maserschmidt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/maserschmidt/32/18829_2.png) [@Maserschmidt](https://boards.straightdope.com/u/Maserschmidt)\
**Post date:** [April 20, 2013, 2:07pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/15 "2013-04-20T14:07:17Z")

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> [@CookingWithGas](#):
>
> I know of no example where a ratio \<1 is called negative. An engineer, scientist, or mathematician would not use that convention but finance people and accountants just have a different way of thinking.
> 
> A P/E ratio can be negative if the company is losing money, but that does not mean the ratio is \<1, it means it’s \<0.
> 
> There is something in accounting called the _current ratio_ (current assets:current liabilities). You want it to be \>1 but it can never be negative.

Finance people and accountants don’t do that either that I know of, and I work with them a lot. I’ve called that kind of relationship “sub-unity” before.

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**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\
**Post date:** [April 20, 2013, 2:26pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/16 "2013-04-20T14:26:03Z")

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> [@Melbourne](#):
>
> You get negative ratios in that sense in the stock market.
> 
> I’m talking about the market here, not the stock valuation.
> 
> When you’re in negative territory the stock has gone down. This is a “negative ratio” to its previous value. Ratios are sometimes used, particularly in stock speculation, when you are interested in comparing the behviour of two different stocks, or of a particular stock compared to an index, and a comparison of absolute price would not be meaningful.

Those, again, are trendlines.

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**Author:** ![pinqy](https://avatars.discourse-cdn.com/v4/letter/p/a3d4f5/32.png) [@pinqy](https://boards.straightdope.com/u/pinqy)\
**Post date:** [April 26, 2013, 5:03pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/17 "2013-04-26T17:03:18Z")

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> [@Frylock](#):
>
> I’m reading a report right now which deals with some ratios, and when the ratios are below 1:1, it refers to them as negative, with ratios above 1:1 being referred to as positive. (For example, a ratio of .96 is referred to as negative, and a ratio of 1.02 is referred to as positive.)
> 
> I understand the intended meaning of this, and the rationale for using these terms, but my question is, is this an established usage?

That’s how it’s used for change. If the change in relative prices/wages/etc is \<1 then that’s a negative change. Any change in an index that is \<1 is a negative change.

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**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\
**Post date:** [April 27, 2013, 8:09pm UTC](https://boards.straightdope.com/t/ratios-below-1-1-called-negative/656040/18 "2013-04-27T20:09:15Z")

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> [@Absolute](#):
>
> As an engineer, if pressed to express that in words instead of numbers, I’d probably go with “less than unity”. Negative makes no sense.

In terms of margin over unity, a ratio of \<1:1 can be considered negative. For instance, if the stress on a component loaded in tension exceeds the tensile strength of the material, we would say the component has a negative margin where the margin is calculated as M = strength/stress - 1. This is done to provide a percentage of capability over material strength. Similarly, for margins expressed in logarithmic terms (often used to express power or amplitude factors such as signal gains or vibration and shock environments) an under unity value has a negative logarithm, e.g. log[sub]10/sub \< 0 if A[sub]2[/sub]\<A[sub]1[/sub]. Of course, it should be expressed in these terms so that it is clear that you are talking about a margin against capability rather than just a ratio or capability versus load..

Stranger