Find the place on your tires that comes closest to rubbing anything on your bike. How much distance is that? Usually seat tubes, chain stays and the underside of the fork crown are problem points. If you have caliper rim brakes then check that too for how much clearance there is to it's mount point in the center.

If the difference in the tire size from what you want to get and currently have is less than the place you measured that has the least clearance to the tire, then you might be good. But different model tires measure slightly different from their stated nominal size. Also, you should leave a certain amount of space for times when your tires might pick up mud or other debris. I once went briefly through some gumbo mud we have here and quickly came to a stop on the other side because the mud jammed the tire. And I think that bike probably had a ¼ inch clearance as I wasn't running over size tires on it.

Tires change in height by about the same as they change in width. At least it's close enough. If you are needing to know to the last couple millimeters, then you probably aren't leaving nearly enough room for safety.