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'unit of measure' is a correct and usable phrase in written English.
You can use it when referring to a system or standard used to measure something, such as length, volume, weight, or time. For example: "The recipe calls for 2 cups of sugar, which is a common unit of measure in cooking."
Dictionary
unit of measure
noun
Any standardized, reproducible unit that can be used to measure any physical property.
synonyms
Exact(59)
The unit of measure will be noted as square unites (square miles, square yards, etc).
First, focus on the right unit of measure.
(A vis is a unit of measure equal to 1.6 kilos, or about 3 pounds).
Each individual must discover their own "unit of measure", he says.
It is striking that the unit of measure he used was days.
Smoot, the shortest of the group, was chosen as the unit of measure.
"If the Obama were a unit of measure...".. A student's account of the president's visit.
Encyclopædia Britannica, Inc. Numerical values can be assigned to angles by selecting a unit of measure.
A unit of measure; one millionth (10-9) of a meter.
More importantly, the historical foreign aid numbers are small by any reasonable unit of measure.
Similar(1)
Its unit of measure the degree Rankine (°R)—equals the Fahrenheit degree, as the kelvin equals one Celsius degree.
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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