"A day has twenty-four hours."

Translation: Ein Tag hat vierundzwanzig Stunden.

[JimCobb1]

Is there some kind of rule as to when to use "uhr" vs. "stunden"?

[az_p]

Uhr means "clock" and can be used to mean "o'clock" as well as a shortened version of Armbanduhr ("wristwatch"). Stunde means "hour".

Jetzt ist es vier Uhr = "Now it is four o'clock"
Gefällt dir meine neue Uhr? = "Do you like my new watch?"
Die Fahrt dauert drei Stunden = "The trip takes three hours"
Die Bahn kommt in einer halben Stunde = "The train comes in half an hour"