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According to one of the questions already asked on EL&U, “E = mc²” is read as

E equals M C squared.

How do we read “E = (mc)²” so that it is not mistaken for “E = mc²”?

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I believe someone just went through a downvoted every answer to this question as well as the question itself. That seems mature ... –  Macro Jun 14 '12 at 20:07
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Yep. Took 'em 31 seconds. Though the question was downvoted approximately 10 minutes before the answers. Those votes should be caught; if they're not, we may have to get meta. –  Daniel Jun 14 '12 at 20:10
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@Hugo: I think the real question here is: "How could you read xy² and (xy)² so they aren't confused?" I agree with you, using E = (mc)² as an example makes the question seem a bit contrived, but there's nothing wrong with the overarching question of how to keep the two "mathematical homophones" unambiguous. –  J.R. Jun 14 '12 at 21:00
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How about E equals M squared C squared –  jasssonpet Jun 15 '12 at 2:31
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Wouldn't this be a better fit @ math.stackexchange.com ? But I might read that "E equals the square of mc" –  TecBrat Jun 15 '12 at 10:41
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26 Answers 26

As a member of the mathematics community for many years, I'd say the standard pronunciation is:

E equals the quantity MC squared

Also, as pointed out by Mark Adler in the comments, this is the standard pronunciation used when recording mathematics textbooks for the blind (thanks for the info Mark!).

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This is what I was taught to say in algebra. If you wanted to be extra diligent, E equals the product of MC, squared. –  choster Jun 14 '12 at 19:38
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Well then how would you say E = (MC² + X)²? Take that, math community. –  Phillip Schmidt Jun 14 '12 at 20:14
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E equals M C squared plus X, all squared. –  ThePopMachine Jun 14 '12 at 20:21
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I've also heard "E equals MC quantity squared" –  MrZander Jun 14 '12 at 23:54
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I used to record textbooks for the blind, and this answer is exactly correct. There most certainly is value in having an unambiguous scheme for rendering equations to speech. –  Mark Adler Jun 17 '12 at 8:25
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Trying to swap things around to make it the least ambiguous possible and still sound light:

E equals the square of MC

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What's to stop one from interpreting this as "E equals the square of M, C" do you have to say "MC" really fast or something? An answer based on a subtle issue of vocalization like that seems to be missing the point. I'm surprised to see this as the top voted answer since it's more ambiguous than many of the answers in this thread. My point is more one of clarity than mathematical convention but I think it is also worth mentioning that this is discordant with convention in the mathematical community. –  Macro Jun 17 '12 at 23:58
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Hi Marco. I agree that from a purely mathematical standpoint, the possibility is there, but it's unlikely for ordinary human interpretation in my opinion. Obviously, based on the upvotes on this variation, a great amount of individuals here don't feel the ambiguity you're referring to. My gut tells me it's because an average English speaker wouldn't consider as far as such alternate meaning. This is afterall an English QA, not a Mathematics one. I think your solution is mathematically perfectly unambiguous, but I think that my current variation is "humanly" readable and unambiguous. –  Wadih M. Jun 18 '12 at 0:55
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Well, I do think that the interpretation "E equals the square of M, C" would be extremely unnatural for a human to perform. For example if I wanted to say "E equals the square of M, C", I would have said "E equals the square of M times C", which I think is also "humanly" readable. Ultimately, I think it's about making the most people understand what you're saying without hammering the auditory's minds with precedence enforcing syntax. English language was never the select medium to perfectly communicate mathematical formulas because of it's openness and "style". –  Wadih M. Jun 18 '12 at 1:28
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I find "E equals the square of MC" easier to consume in a listener's mind. I think even mathematically savvy listeners would have no problem understanding this. –  Wadih M. Jun 18 '12 at 1:52
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Hi Marco, ultimately it's a human brain that generates English language and that and consumes it, and not a computer. In the current context, the square of MC IS clearer than MC squared, especially since the formula ends there. Though if I had to pick, I'd go with choster's "E equals the product of MC, squared". Again, the point here is that it's an English language QA, we're looking for the fine line between elegance and unambiguity. If you want the mathematical answer, I suggest opening another version of this question there. At any rate, I think we killed it to death already! –  Wadih M. Jun 18 '12 at 2:11
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The word all can be used to indicate the grouping that is shown in print by brackets, so this could be read as

E equals M C all squared

In this specific example that’s probably sufficient for a listener to realise you’re saying something different from the more common “E equals M C squared”, and the correct meaning ought to be clear because it’s a simple expression with no other plausible interpretation – but in the general case it can be extremely difficult to express the precise meaning of an arbitrarily complex equation using a natural language in place of a symbolic one.

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That's how I would say it if I was speaking to someone. –  jhsowter Jun 15 '12 at 3:04
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+1 That's how my maths teacher used to say it. –  Kaz Dragon Jun 15 '12 at 6:58
    
+1 for the last part. Great observation. –  J.R. Jun 15 '12 at 11:00
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To me this sounds like (E = mc)² –  dj18 Jun 15 '12 at 13:09
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E equals open parentheses M C close parentheses square ;) –  Derek 朕會功夫 Jun 15 '12 at 16:31
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As a mathematician, I would say "E equals m c quantity squared".

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This sounds best to me. Using 'the quantity' as above throws off the order of the equation. –  Drew Christianson Jun 15 '12 at 1:02
    
+1 this is the way I was taught to say it also. –  Bill B Jun 17 '12 at 5:00
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This is what I think most mathematicians do, at least in my experience. There's usually a slight pause before and after "m c" to help make it clear that "quantity" refers to "m c". –  David Schwartz Jun 22 '12 at 2:05
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Why does the mathematical notation system exist? It exists because it is an easier way to explain mathematical expressions. Spoken languages have limits. They are not able to perfectly transfer every idea from one person to another, and they are not fully capable of describe feelings and emotions. Don't expect much from spoken language. Don't expect to easily speak everything you want to say. Peoples inner feelings and what they are trying to say usually has a wider meaning then they actually say.

Your question is just an example of the limits of spoken languages. Complex mathematical expressions can not be easily expressed with spoken language. If you want to say them, you need to form long sentences.

For example, A = ((a2b3)2 + 5 - ab2 - (ab)2)3 can be read as "capital A equals, open parenthesis, open parenthesis, a squared times b cube, close parenthesis, square, plus five, minus a times square of b, minus, open parenthesis, a times b, close parenthesis, squared, closed parenthesis, cube".

Talking about mathematical expressions requires a lot of words. Look at this very common dialog below (science students usually explain it this way):
A: ... He completed his homework after reaching the formula "E equals m, c squared".
B: I know it. That famous formula which Einstein found, isn't it?
A: No, this one is different. You take square of both m and c in this one.
B: Oh, I understand.

There is no standard for reading mathematical expressions. Because it is very hard to set a standard for it since the complexity of expressions have no upper bound. In practice, the reader reads the expression without putting any extra afford in it for making it clear (even usually skips the inner parenthesis, etc for simplicity - if he/she reads every detail it becomes a bother for both the reader and listener). Listener knows the subject and recalls the expression in his/her mind as he/she listens to. If the listener cannot remember it, he asks the reader for its details. If it is a conference, the speaker must use a projector, white board, or any other tool for clearly showing the mathematical expression (if he doesn't use any explicit tool and just speak it, then it means that that conference is not well organized; people usually complain after a conference like that).

You should take a pencil and paper with you when you are talking about something related to mathematics. Without using a pencil and paper, you cannot explain the derivation of a mathematical formula to your friend as easily as talking about the summary of a novel or debating about a political matter. This is because, as I stated above, spoken languages are not convenient for expressing mathematical expressions.

Of course, it is easier to read simpler expressions. For the case of E = (mc)2, you can simply read as "E equals the quantity MC squared" as @Macro suggested.

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+1 : the best answer... the problem is with spoken language. –  woliveirajr Jun 15 '12 at 13:50
    
The mathematical notation was invented long before audio tape, mp3 and gramophone, so it might as well have been invented to a) transport a mathematical formula over a long distance without the author traveling along to control the correct submission, and b) to conserve it for the future. By pronunciation (see for example Drews answer) you can express much which isn't easily writable. In contrast to what you say, you can read out loud mathematical formulas easily - a long formula is just longer, not harder, to read, proportional to its length - independent whether you read it loud or silent. –  user unknown Jun 16 '12 at 14:13
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Due to the distributive property of exponentiation over multiplication, you could read this as "E equals M squared C squared", also written E = m²c².

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notably used in the more correct e2 = p2c2 + m2c4 –  jk. Jun 14 '12 at 19:52
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Well if you're going to take that route then you might as well say, "The square root of E is the absolute value of mc". –  chharvey Jun 15 '12 at 3:12
    
short and unambiguous –  chim Jun 15 '12 at 11:02
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E = m²c² is not the same formula as E = (mc)². Though equivalent as far as pure mathematics go, they are not at all equivalent in practice. For example, if m is very small, computing m² may cause floating underflow (result = 0) in a computer or in a calculator, which (mc)² might get evaluated without problems. The content of a mathematical expression should not be changed just to make the expression more pronounceable. –  Jukka K. Korpela Jun 17 '12 at 10:11
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@JukkaK.Korpela: The written form of a formula rarely has anything to do with the best way to actually carry out a calculation using lossy fixed precision floating point numbers. Any skilled numerical analyst will consider (mc)² and m²c² to mean exactly the same thing, and implement the calculation appropriately. –  Greg Hewgill Jun 17 '12 at 10:44
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Apparently I'm the odd one out:

E equals paren M C close-paren squared
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+1 I'd use "bracket" rather than "paren", but otherwise this is one of the approaches I'm familiar with. –  Peter Taylor Jun 15 '12 at 7:19
    
This is not an "English language usage" answer... you are just reading out the symbols. –  ThePopMachine Jun 17 '12 at 5:08
    
@ThePopMachine See hkBattousai's answer for why this is probably the best: There is no standard, and no upper bound on complexity. You shouldn't be saying mathematical equations aloud, but saying each symbol will at least remove ambiguity. –  Izkata Jun 17 '12 at 14:07
    
@ThePopMachine Besides, how exactly is "using English" not an "English language usage" answer? –  Izkata Jun 17 '12 at 14:07
    
@Izkata: That doesn't use English grammar, it uses mathematical grammar. If I take a Chinese sentence and directly translate each word to English, is that "English language usage"? I'm not saying this isn't a valid way to do it -- but it is using English vocabulary and mathematical grammar. Surely sometimes it makes sense to do this. But it is really just reading symbols aloud. This is more like quoting. The equation is "E equals paren M C close-paren squared". Fine. But what you said isn't really an "English sentence". –  ThePopMachine Jun 17 '12 at 14:24
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"E equals square of the product of M and C"

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Product of M and C = MC. It's square = (MC)^2 –  SidCool Jun 14 '12 at 22:04
    
Did you edit your answer or did I misread it? –  anon Jun 14 '12 at 22:08
    
Most correct answer for reading E=(MC)^2 in my opinion. Some describing MC as a quantity doesn't really qualify the operation that you perform to get the quantity. Product does. –  Rig Jun 15 '12 at 14:28
    
@anon I didn't edit the answer :) –  SidCool Jun 19 '12 at 18:04
    
@CoderAtHeart "It's" square? For goodness sake, this is an English site. Can we please learn to use the possessive? Its square. –  Orion Oct 12 '12 at 23:58
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I had a stats professor who drilled into my head the formula for variance:

E[x^2] - E[x]^2

by saying:

"E xsquared minus E x  ...   squared"

With a longer pause every time he said it. It may not work in all circumstances, but I found it to be a clear (and memorable) way of saying the formula aloud. So, for your question,I think it would be valid (at least to mathematically inclined listeners) to say:

"E equals m c    ...   squared"
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I feel that only works if you are paying extra attention to the squaring (or the distinction between both forms). In the variance, once you've seen the formula, you know the squares are somewhat tricky to put at the right places. If you don't know that, E = mc squared and E = mc ... squared would just sound the same. As the formula is that famous, I wonder if anybody would get E = (mc)² from the last utterance. –  Egon Jun 15 '12 at 6:02
    
You're right, this won't work in all circumstances. This technique works fine when a teacher points to a board (where everyone can see the equation), or when the equation is already well-known to the listeners (If I say a²+b² = c², most people realize I don't mean (a²+b)² = c², because the formula is familiar). Outside of those two cases, though, a pause is not a very reliable way to differentiate between parentheses and, say, indigestion. :^) In this example, even with the pause, I'd probably misinterpret what you said – I'm already familiar with E=mc², so I'd likely miss the pause. –  J.R. Jun 15 '12 at 11:09
    
While this might not work for well-known equations where people anyways hear what they expect to hear, not necessarily what the speaker said, think of a more general case, such as differentiating between xy² and (xy)². –  dj18 Jun 15 '12 at 13:23
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It's also true that one usually knows (at some degree) the topic at hand and while following the reasoning, one is (should) be able to place correctly the brackets. I never had troubles to understand or to be understood (at a professional level, let's say university or phd). This could obviously be different at a lower level (primary education), where teachers should use extra care to avoid confusing the students. –  Francesco Jun 15 '12 at 14:28
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I do this casually, but I usually add a (mostly automatic) gesture, that I think aids comprehension. –  Aesin Jun 17 '12 at 10:50
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E equals the square of the product of m and c

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If your audience can physically see you, you could use a hand gesture while speaking:

"E equals" [use both hands to draw parentheses in the air] "mc" [finish gesture, slight pause] "squared".

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Is this the start of a whole field of math-mime artists? –  mgb Jun 15 '12 at 14:46
    
I have actually seen this before, so sadly this is not the start of mathmiming. –  Muhammad Alkarouri Jun 17 '12 at 19:38
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Since, E=mc^2 is common everyone assumes the first version:

  • E=mc^2 should be conveyed as E equals m, c-squared.
  • E=(mc)^2 is conveyed as E equals m,c whole squared.

It really comes down to the pause. Consider this, x+y/z and (x+y)/z.

When you say x plus (pause) y over z it means x+y/z. But, x plus y (pause) over z implies (x+y)/z

Edit: frankly I don't understand the use of quantity. But, that's just me.

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I still think "all" is the easiest way to express it verbally - x plus y all over z [(x+y)/z]. I agree use of terms such as quantity (or even product) can cause that glazed look and is meaninglessd to non mathmaticians. –  Wolf5370 Jun 16 '12 at 16:53
    
I would pronounce x+y/z more like "x plus y-over z" - shortening the pause between "y" and "over" instead of adding one between "plus" and "y". I generally pronounce closing parenthesis in maths with a pause, but not the opening parenthesis. It seems to be unambiguous enough for common use, but perhaps not rigorous. –  michaelc Jul 16 '12 at 22:27
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E equals mc whole squared.

This is the notation used in schools and Universities usually.

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+1,this is what is taught for us in India..No confusions and pretty simple.. –  vinayan Jun 17 '12 at 4:04
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E = mc² is pronounced as E equals M, C-squared. With slightly different rhythm, E = (mc)² can be pronounced as E equals (MC)-squared.

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should be "E equals MC, squared." –  chharvey Jun 15 '12 at 3:14
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Generally, I'd differentiate between (xy)² and xy² by saying for each:

(xy)² - "x y squared"

xy² - "x times y squared"

However, if you're concerned with the specific case of E = mc² this won't work since the accepted pronunciation of the familiar equation doesn't follow these rules.

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E equals the squared product of m and c.

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Read it as

E is Equal to MC the Whole Square

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Reorder by decreasing exponent and pronounce that way:

E equals c squared m

E equals c squared m squared

If only Einstein had thought to write it that way originally, sigh.

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(E)nergy is equal(=) (Mass of the Object(m) multiplied by the Speed Of Light(c)) Squared(²)

One would obey the order of operations and perform the multiplication inside the () parenthesis, then square the result.

The pronunciation would be said as Energy is calculated by multiplying the speed of light by the mass of the object and squaring the result

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That's how the equation might be explained, but it's certainly not how the equation would be pronounced or read. –  J.R. Jun 15 '12 at 11:02
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Actually it's the speed of light in a vacuum, but lets not split hairs :D –  Wolf5370 Jun 16 '12 at 17:01
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It will be read as E equals to whole of mc square.

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E = (mc)² should be spoken as:

E equals the squared product of MC

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I think "all" is still the easiest way to express that equation "e equals m,c all squared". This is meaningful to non mathmaticians too (unlike quantity or perhaps even product). Pauses are unsafe (especially on the phone etc). Order changes can work but can also confuse (e.g. "e = the square of mc").

For example - the famous quadratic factorisation equation (-b+/=SQR(b^2 - 4ac))/2a "minus b, plus or minus, the square root of b squared minus four a c, all over two a"

The real answer is, it depends on your audience - use the language graded to the least proficient listener (that you expect to understand - not the baby or dog).

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The most unambiguous way to say this, if a little awkward, would be:

E equals the square of the product of M and C.

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What about this.

E equals MC in brackets squared.

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I’d just say

E equals mc whole square/squared.

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The "open/close" parentheses sounds good. One simplistic option when pronouncing the statement would be to say M-C very quickly as if they were one.

I'd speak in pseudo-polish notation:

E is equal to the square of the product of M and C.

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