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When describing a ratio, should ratio between or ratio of be used? Example:

The ratio between floor area of smallest rectangle to the enclosed contour area of a polygon is tested with a defined threshold.

The ratio of smallest rectangle's floor area to the enclosed contour area of a polygon is tested with a defined threshold.

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The correct usage would be with of-to instead of between-to. Instead of between-to, you should use between-and but even after that, the more correct usage will be of-to.

The ratio between floor area of smallest rectangle and the enclosed contour area of a polygon is tested with a defined threshold.

Also, from the text on Wikipedia about the notation and terminology of ratios

The ratio of numbers A and B can be expressed as:

  1. The ratio of A to B
  2. A is to B
  3. A:B
  4. A fraction (rational number) that is the quotient of A divided by B
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    It's worth noting that #4 is a formal definition. You'd see that written in a textbook, or hear that in that in a classroom, but that's not how people talk in everyday conversation. The between-and construct you mention is less formal, but maybe more apt for less formal speech: The ratio between girls and boys in the drama club is about 4 to 1. – J.R. Mar 21 '13 at 9:47
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    And there again, we use the to for representing ratios. @J.R. AFAR, I was explicitly taught(in school time) to use to when referring to ratios. – hjpotter92 Mar 21 '13 at 9:57
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    Yes, the ratio itself uses to, but the form The ratio between A and B is X to Y is not uncommon. Also, when you said you were taught to use "to", now I'm curious – was that in math class, or in English class? (It's not uncommon for something to be common conversationally, but considered erroneous mathematically, such as, "There are an infinite number of them." My math teacher would say, "There are infinitely many of them," and aver those are not the same thing, but my English teacher might ask, "Don't those mean the same?"). – J.R. Mar 21 '13 at 10:23
  • @J.R. It was more like my father told me. =) Times like this, and I'm proud that I had my parents as a teacher :P – hjpotter92 Mar 21 '13 at 10:40
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Generally I would use the pairs between / and and of / to, as shown below:

BMI is the ratio of someone's weight to their height.

BMI is the ratio between someone's weight and their height.

Both have the same meaning, and are otherwise interchangable.

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