# How to read “A = (πr)²” so as not to mistake it for “A = πr²” [duplicate]

None of the 26 answers given here, or the 5 answers given here mentions any similarity between the pronunciation of E = mc² and A = πr², yet I still remain confusioned as to what distinguishes the reading of E = (mc)² and A = (πr)² with the reading of the first two.

• Could you spell out your confusion explicitly? This question ("How to read...") is answered by the first question you link to. What is not clear about "the quantity πr squared" or "πr all squared"? Oct 17, 2014 at 7:59
• In a lecture, 'air quotes' and a sizeable gap between 'pi-r' and 'squared' could be used. But this is not a question really suited to this site, as it is far from mainstream English. Oct 17, 2014 at 8:30
• It's not that it's not on topic, but I agree that the number one answer on the first link is the answer to this question. Oct 17, 2014 at 11:10
• Also it seems that the quantity prepended is used in AmE and all squared appended is used in BrE. Oct 17, 2014 at 11:15
• "The square of the product of pi and r." Oct 17, 2014 at 11:53

To read A=(πr)2 to a class, items in parentheses tend be categorized as the quantity with contents terminated by a pause in speech.

Parentheses - read as “the quantity”
3(x + 2) is read as “three times the quantity ‘x’ plus two”
(y – 5) ÷ 6 is read as “ the quantity ‘y’ minus five (pause) divided by six”

Which is to be interpreted for the question as:

A equals the quantity pi 'r' (pause) squared

Edit to add: "Is it pi 'r' or is it pi times r?"

Expressions containing variables (any letter may be used as a variable):
“‘V’ equals four thirds pi ‘r’ cubed”

I think it should be noted that vocalization of a math(s) expression is likely to be accompanied by a written version of what's being said: either on the board and/or for students to transcribe. In the case of the AmE the quantity, this signals the beginning of a parenthetical expression (i.e., write or read an opening parenthesis) where the pause signals the end (close parenthesis). It may be trivial to retroactively assign parentheses as the expression is complete (all squared), so this distinction is not as problematic as it may seem, especially since it can be argued that "all" is an unambiguous demarcation point between the parenthetical expression and the accompanying exponent, versus a pause in speech.

Reviewing the body of the question:

.. the pronunciation of E = mc² and A = πr², yet I still remain confusioned as to what distinguishes the reading of E = (mc)² and A = (πr)²

Taking the latter first:

E equals the quantity of mc (pause) squared

A equals the quantity of pi r (pause) squared.

Contrast this with:

E equals m c squared,

or

A equals pi r squared

(no pause, and without the quantity) one understands that the exponent only applies to the preceding variable/operand. If one asks how the written version distinguishes the coverage of exponent to its applicable operand (e.g., why the exponent applies to the entire expression in parentheses), that is indeed a math(s) question.

Further edit:
There appears to be some confusion that the quantity is dependent on the content within parentheses being a sum or difference rather than being agnostic to the contents. It can be argued that a quantity can contain any expression but while it has been generally associated with add/subtract, it's the parentheses that determines whether the quantity is being used or not.

Additional usage examples of the quantity:
mathforum post

http://www.mastermathmentor.com/mmm/ReadingMath.ashx (How to read to the blind and dislexic). Replaces the pause with "end quantity".

Yes, while the expressions tend to be sum/difference, every discussion talks about the parentheses being addressed, not the content, and at no time is there any distinction being made about the expression within parentheses changing the attribute describing parentheses.

Further, quantity itself does not distinguish the expression configuration as does sum, difference, or product. The free dictionary does not indicate anything about how an expression is defined for the definition of quantity.

• I know this is AmE standardized for math teachers. In BrE for maths teachers, it's likely standardized as "all squared" appended. Oct 17, 2014 at 11:20
• Thank you very much for the link, I have been looking for something like that for a long time. Oct 17, 2014 at 12:09
• Oct 17, 2014 at 13:29
• Using quantity in either E = mc² or A = πr² is incorrect as PI is a constant and m is a measured value of mass, neither of which are unknown quantities of anything (although m could be an unknown value). Quantity should refer to an unknown number of things x, or the addition of two numbers 2+3, or generalized as the count or total of something. In this case it would be more accurate to say A equals the product of PI and r, squared. Oct 17, 2014 at 16:56
• If you notice, every place in that link that the quantity is used it is in reference to some variable added to some value (or sometimes subtraction). This is because quantity specifically refers to a total count (typically addition, but it can also be subtraction). Using the term quantity anywhere else in math is incorrect. In the examples, the quantity does not reference the parenthesis themselves but rather it references everything inside them and if there are any operations other than addition and subtraction then quantity is patently wrong. Oct 20, 2014 at 13:33

Most of the mathematicians I know would pronounce these as:

A = πr²
A equals pi r squared

A = (πr)²
A equals pi r all squared

There is no fixed rule, so this really comes under the category of primarily opinion based.

• As a maths guy, +1
– M.M
Oct 17, 2014 at 10:45
• It is not opinion. It is standardized for teaching. It may be regional, but if one asks one's math(s) teacher the answer, there is only one answer she will state. Oct 17, 2014 at 11:18
• If it's regional, and the region isn't specified in the question, it isn't usefully standardized. Besides, I don't see the question limiting the scope to teaching. Oct 17, 2014 at 14:00
• @Useless ok, then it's opinion for everyone else except for specific people who use the terminology on a daily basis. Oct 17, 2014 at 18:19

A = (πr)² can be read as "πr all squared", and is another way of writing π²r² which is also the same as π² x r² (pi squared times r squared). In other words, the original formula [A = (πr)²] is just a different, and sometimes shorter way of writing the equivalent formulas. It doesn't save much time in this particular example, but it would if you wrote A = (a + b)² instead of the equivalent A = a² + 2ab + b²

It is common that A equals PI R squared is understood to be A = πr². If someone wanted to say something more like B = π(r²) then they might say B equals PI, times R squared.

The typical way it is pronounced will be by using timing and inflection to attempt to let the listener know what you mean. Some teachers, in order to alleviate any confusion, might sometimes actually say paren(s) or parenthesis. I have only witnessed this a small number of times and it was done in a classroom environment when the instructor could see that many students were taking notes without looking up very much. Mostly, the actual speaking of any parenthesis is done with more complicated formulas then the ones noted here.

• What's the difference between pi r squared and pi times r squared? The question relies on the spoken difference between pi r squared and (pi r)^2 Oct 17, 2014 at 18:45
• Pi, times r squared more explicitly states that it does not mean (pi r)^2. Although I don't imagine there is any way to completely eliminate any misunderstanding Oct 17, 2014 at 20:10
• But what are you trying to answer? The question is about how to speak the difference between A=(xy)^2 and A=xy^2. All you said was A=xy^2 or A=x times y squared. Oct 17, 2014 at 20:30
• precisely, there are two options in the original question and I gave an example of how to more clearly state one of those options; which by its nature provides a difference between the two. Oct 17, 2014 at 21:44

A = πr² (A equals pi r squared)

A = (πr)²(A equals whole square of pi multiplied by r) That's another way to define parentheses in mathematics.

• "A equals whole square of pi multiplied by r" could be misinterpreted as A=π²r if one is not expecting this use of whole. Oct 17, 2014 at 10:52