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I was just asked the question, is there a difference between 12 square inches and 12 inches squared. At first I assumed that 12 inches squared mean a square with sides of 12 inches. In this case the answer would be no. 12 inches squared would be 144 square inches. I've been searching the web for quite a long time for what is meant by 12 inches squared. I can't find anything. Is there some formal use for the phrase "inches squared"?

Jordan
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  • Yes, 12 inches squared is 144 square inches; 12 square inches could be a square Sqrt(12) along the sides. –  Sep 16 '14 at 15:12
  • I would contend that they are the same, with the caveat that the phrasing "12 inches, squared", emphasis on the comma, implies what @mistermarko suggests. I see the terminology used interchangeably, often depending on the speaker's native language. – Emily Sep 16 '14 at 15:21
  • Yeah, it kind of hit me that 12 inches squared means 12 inches × 12 inches. The term in my industry is used in as jargon. I should have known that 12 inches squared literally meant 12 inches squared. Couldn't see the forest for the trees. Thanks. – Jordan Sep 16 '14 at 15:21
  • @Arkamis, yeah, these people are confusing as hell! Don't get me started on what they mean by 100 thousandths. Hint, it's not 0.0001. – Jordan Sep 16 '14 at 15:23
  • I will also note that the interpretation that "12 inches squared" means "a square 12 inches on a side" only really makes sense in any context in which you actually expect a square -- such as manufacturing or something. It doesn't make any difference if you are talking about pressure, for instance: "fill the tire to 30 pounds per inches squared" is unambiguous, as the meaning is clear and you don't need to find any nice happy squares in your tire. – Emily Sep 16 '14 at 15:26
  • I'm aware of that. I am a programmer, and my business domain is a manufacturer of wood cutting products, so when they say "12 inches squared" or even "12 inches square" they mean a square of wood. I wasn't sure whether they mean by that a square of wood 12 inches by 12 inches or a square with an area of 12 square inches. As no one that uses that term knows much about math, they couldn't give me a straight answer. Thanks again. – Jordan Sep 16 '14 at 18:18

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In a context in which you actually expect a square -- such as manufacturing -- one can naturally interpret "12 inches square[d]" as "a square 12 inches on a side". This would be the area of $144$ square inches.

In other context, "inches squared" may be used synonymously with "square inches". This may also depend on the speaker's native language.

Based on comments by Arkamis

Community
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Dr. Math from the Math Forum gives a pretty good explanation here:

It's written as $12 m^2$ (that is, with an exponent of 2), but is better read as "12 square meters" than as "12 meters squared."

The reason for this is as you say, that the latter sounds as if it means $(12 m)^2$, the square of 12 meters, rather than $12 (m^2)$, as it really is, 12 times one meter squared.

The fact is, however, that you will find both forms used; I think it is generally agreed that "12 square meters" is better, in order to avoid that problem, but both are "correct." That is, the problem is not that "12 meters squared" MEANS the area of a 12-meter square, but that it can be taken either way, and is thus ambiguous. We simply want to avoid the ambiguity.

johnnyodonnell
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  • Also important to note, m here is not a variable. It is a unit. The ² is part of the unit not the degree of an unknown. It's not like ƒ(m) = 12m². This isn't algebra per se. – Jordan Jan 15 '19 at 20:08
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This topic represents an interesting overlap of mathematics and grammar.

In order to remove ambiguity, if you want “12 inches squared” to equate to the area of a 12” x 12” square, “12 inches” becomes a compound adjective and needs to be hyphenated. Hyphens link words together to remove ambiguity, performing the same function as parentheses in an equation.

If “12 inches squared” refers to a 4” x 3” rectangle, then you would need to hyphenate inches squared, linking those words together to form a compound noun.

However, nobody uses hyphens when writing these mathematical terms, so the only logical way to remove ambiguity is to agree that “12 inches squared” is a square with 12-inch sides, while “12 square inches” is an area that equals twelve 1” x 1” squares. That’s how I have always used these terms.

Mathematics is no place for ambiguity, so a convention needs to be agreed upon. Instead of using inches squared and square inches interchangeably, which obviously creates confusion, area should be measured in square inches (or other units) and abbreviated “sq. in.”

Richard Sanderson
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Inches squared is right. Square inches is wrong

Xavier
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  • It depends on the context. A 3" by 4" rectangle would be 12 square inches in area. A 12" by 12" rectangle would be 12 inches squared. Completely different areas so they refer to completely different things, but they are both valid. – Jordan Feb 08 '17 at 16:23
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I always understood the “squared” part of __inches squared was pertaining to the inch itself, not the quantity of inches. An inch squared is a 1” x 1” square, not a linear one dimensional inch. That’s why 12 inches squared is 12 square inches, whether 6x2, 3x4, or 12x1.

Taken literally, 12 inches squared would simply be a linear 144” and in no way refer to area. Then it would be written 12^2 inches, not 12”^2.

Dimsy
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