Unknown quantity is an idiomatic phrase from mathematics. Though it originally referred to unspecified variables, it’s now used more broadly to mean a person or thing whose action or effect is unknown or unpredictable. For example, we might use unknown quantity to describe someone whose behavior is erratic, someone who has received a chance to do something for the first time, or someone we simply don’t know much about.
Of course, unknown quantity can still be used to describe an unspecified amount of something—for example, an unknown quantity of beer or an unknown quantity of money.
Examples
He is now the complete picture of a star player, and a striking contrast to the unknown quantity who entered spring training a year ago. [Toronto Star]
Carroll is an unknown quantity, and different historians have wildly different opinions on how to interpret his life. [quoted in The Atlantic]
Plumpton College was an unknown quantity to Krajewski until his daughter Charlotte, who inherited his passion for wine-making, chose to study there. [Guardian]
New Zealand can hardly claim Pakistan are an unknown quantity when they square up in a crunch World Cup game in Pallekele, near Kandy tonight. [New Zealand Herald]