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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2Is “E = (mc)²” any particular equation? (Total relativistic energy?) If not, you're really best off avoiding those three letters and the ensuing confusion.– HugoCommented Jun 14, 2012 at 20:16
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28@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.Commented Jun 14, 2012 at 21:00
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2Just use units with c = 1 and so E equals m squared, without room for confusions. This could seem a joke, but isn't :-)– FrancescoCommented Jun 15, 2012 at 8:54
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5Wouldn't this be a better fit @ math.stackexchange.com ? But I might read that "E equals the square of mc"– TecBratCommented Jun 15, 2012 at 10:41
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2Often mathematical expressions are verbally described in quite a vague and ambiguous way - the specifics tend to be obvious from the context. In this case, with the usual meanings of these letters in special relativity, E=(mc)² is not dimensionally consistent and is therefore meaningless, so there shouldn't really be room for confusion. Having said that, in my experience the usual way of saying this kind of thing would be "m squared c squared", or maybe "m c all squared".– JamesCommented Jun 15, 2012 at 13:06
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25 Answers
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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34This is what I was taught to say in algebra. If you wanted to be extra diligent, E equals the product of MC, squared.– chosterCommented Jun 14, 2012 at 19:38
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5Well then how would you say
E = (MC² + X)²? Take that, math community. Commented Jun 14, 2012 at 20:14 -
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9I 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. Commented Jun 17, 2012 at 8:25
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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2What'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.– MacroCommented Jun 17, 2012 at 23:58
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3Hi 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.Commented Jun 18, 2012 at 0:55
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1Well, 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.Commented Jun 18, 2012 at 1:28
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1I 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.Commented Jun 18, 2012 at 1:52
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1Hi 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.Commented Jun 18, 2012 at 2:11
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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E equals open parentheses M C close parentheses square;) Commented Jun 15, 2012 at 16:31
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. Commented Jun 15, 2012 at 1:02
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2This 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". Commented Jun 22, 2012 at 2:05
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.
answered Jun 15, 2012 at 8:17
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3+1 : the best answer... the problem is with spoken language. Commented Jun 15, 2012 at 13:50
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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. Commented Jun 16, 2012 at 14:13
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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7Well 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".– chharveyCommented Jun 15, 2012 at 3:12
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1E = 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. Commented Jun 17, 2012 at 10:11
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5@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. Commented Jun 17, 2012 at 10:44
Apparently I'm the odd one out:
E equals paren M C close-paren squared
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5+1 I'd use "bracket" rather than "paren", but otherwise this is one of the approaches I'm familiar with. Commented Jun 15, 2012 at 7:19
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This is not an "English language usage" answer... you are just reading out the symbols. Commented Jun 17, 2012 at 5:08
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@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.– IzkataCommented Jun 17, 2012 at 14:07
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@ThePopMachine Besides, how exactly is "using English" not an "English language usage" answer?– IzkataCommented Jun 17, 2012 at 14:07
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@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". Commented Jun 17, 2012 at 14:24
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"
answered Jun 15, 2012 at 0:59
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2I 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 squaredandE = mc ... squaredwould just sound the same. As the formula is that famous, I wonder if anybody would getE = (mc)²from the last utterance.– EgonCommented Jun 15, 2012 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.Commented Jun 15, 2012 at 11:09
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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.– dj18Commented Jun 15, 2012 at 13:23
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2It'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. Commented Jun 15, 2012 at 14:28
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2I do this casually, but I usually add a (mostly automatic) gesture, that I think aids comprehension.– AesinCommented Jun 17, 2012 at 10:50
"E equals square of the product of M and C"
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1@CoderAtHeart "It's" square? For goodness sake, this is an English site. Can we please learn to use the possessive? Its square.– OrionCommented Oct 12, 2012 at 23:58
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1This is still ambiguous to me. It could be interpreted as either 'the product of $m$ and $c^2$' or 'the product of $m$ and $c$, squared.' (both have the same pronunciations),– MitchCommented Jul 19, 2022 at 12:54
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1Sid you must not edit your answer so drastically when it has this many votes. Moving squared to the end, after C, actually introduces the ambiguity the question seeks to avoid. If you want to alter your answer so drastically, you need to remove this one first in order that you can simply add another.– Andrew Leach ♦Commented Jul 19, 2022 at 14:53
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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I have actually seen this before, so sadly this is not the start of mathmiming. Commented Jun 17, 2012 at 19:38
Since, E=mc^2 is common everyone assumes the first version:
E=mc^2should be conveyed asE equals m, c-squared.E=(mc)^2is conveyed asE 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.– Wolf5370Commented Jun 16, 2012 at 16:53
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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.– IiridaynCommented Jul 16, 2012 at 22:27
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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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..– vinayanCommented Jun 17, 2012 at 4:04
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1"This is the notation used in schools and Universities usually" - no it's not, not in general. I've both learned and taught mathematics at universities, and never heard "whole squared". Maybe this is specifically Indian English? Commented Aug 24, 2019 at 10:11
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.
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).
E equals the squared product of m and c.
Read it as
E is Equal to MC the Whole Square
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my friends from India often say it as 'the whole square'. I'm from the US, we learn to say it as 'squared'. do they teach it in India as 'the whole square'? Commented Feb 28, 2016 at 18:09
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@s.matthew.english : when you say, MC squared we dont know whether it is (MC)2 or MC2 ., its different meaning., so we say whole squared.– loganCommented Mar 4, 2016 at 19:05
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.
The most unambiguous way to say this, if a little awkward, would be:
E equals the square of the product of M and C.
(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
It will be read as E equals to whole of mc square.
What about this.
E equals MC in brackets squared.
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.
answered Jul 13, 2013 at 18:08
I’d just say
E equals mc whole square/squared.
answered Aug 4, 2012 at 12:41
How about E equals m squared times c squared?
answered Jan 7, 2016 at 17:04
