The rules are always changing. You will see this abbreviation written both ways, with periods (U.S.), and without (US). Some prefer the first while others the second. Finally, the choice partly depends on whether U.S. is functioning as a noun or as an adjective.

In formal writing, spell out the two words as “United States" (as in "The United States Ambassador"). This is always appropriate. In informal writing, when the abbreviation is functioning as an adjective (as in “U.S. Senator”), there seems to be a slight preference among native speakers and editors for the abbreviation with periods (U.S.). In casual writing, when United States is functioning as a noun (as in, “We are traveling to the US”), it’s a matter of personal preference. You can either spell out United States or abbreviate it, with periods or without. In other words, all three of the examples below are correct, and you can choose the style that you like best. Just be consistent.

The United States has more pet dogs than any other country in the world.

The U.S. has more pet dogs than any other country in the world.

The US has more pet dogs than any other country in the world.

U. S. (U period space S period) is not an acceptable use.

"Because American and British styles differ," notes Amy Einsohn, "CBE [Scientific Style and Format: The CE Manual for Authors, Editors, and Publishers] recommends eliminating periods in most abbreviations as the most efficient way to create an international style"

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