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Discover LudwigThe phrase "a square mile" is correct and usable in written English.
It can be used when referring to an area measurement, particularly in geographical or real estate contexts.
Example: "The national park covers an area of over 10,000 acres, which is equivalent to approximately 15.6 square miles."
Alternatives: "one square mile" or "a mile squared".
Exact(60)
About a square mile.
SIZE -- Less than a square mile.
"There's 300 bars in a square mile.
Manchester has four such areas within a square mile.
The area covers a little over a square mile.
Wreckage strewn over half a square mile of water.
The neighborhood takes up less than half a square mile.
Over all, Fieldston covers 140 acres, or about a fifth of a square mile.
By this definition, it would cover about two-tenths of a square mile.
Another clue: there are between four and five hundred clinics and hospitals within a square mile.
On Saturday, Male, an island of less than a square mile, was calm.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com