If those are measurements in inches, the old standby 212 EVO won't fit. Can you give us the make/model of the case? You have to subtract the height that the MB stands off the backplate, plus the distance from the back of the case to where the backplate is, plus the distance the socket holds the CPU off the MB. So as you can see, it isn't as easy as just knowing the width of the box.
Also, what processor are you trying to cool? The socket it uses will make a difference which cooler will work. Overclocking or just a stock cooler replacement? Plenty of airflow/fans?