Not to be pedantic, but the correct way to write the term would be person-month, or man-month. The distinction is that person/month implies units of people per month. This is inaccurate.
A person-month is a unit of work that's calculated by multiplying the number of persons by the number of months they work. So a team with three developers working on a task for two months has expended 6 person-months of labor. A person-month is equivalent to hours of labor (160 hours is a common value), but work is often expressed in person-month units because it’s easier to get a feel for how many people might be needed to finish a body of work in a fixed time, or conversely how long it might take a fixed group of people to finish a task.
However, the term man-month been broadly criticized when used as a predictive metric, most famously by The Mythical Man-Month, which makes a strong argument that man-months are not fungible in this naïve manner. That said, it’s still a useful unit of work.
In calculus terms, a person month is calculated by taking the integral of staffing as a function of time between two dates.
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