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Related to count up: stopwatch
To tally the total amount of something. Count up all the people in this room so we know how many trays of hors d'oeuvres to bring out.
count someone or something up
to count things or people to see how many there are. Let's count them up and see how many we have. I counted all the guests up, and there are too many to seat. Please count up all these books and tell me how many there are.