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In the context of length, a unit is a measure of distance, whereas a square unit is a measure of area.
A unit circle is not normally called 2 pi. Because the radius length measure of the unit circle is 1 unit, then the circumference of a unit circle is 2*pi, and its area is pi.
That means that if you have a measurement in one unit, you convert it to another unit. For example, if a measurement is given in millimeters, you may need to convert it to meters.
centimeters
a unit of measure equal to half of a pint