You didn't do anything wrong. Your procedure for using the gear calculator was spot on, but you flip-flopped (pun intended) the numbers when you typed your post.

While I understand gear inches, and find them helpful when comparing different bikes and/or tire sizes, but if all I want to know is whether a different chainring or cog will be easier/harder to push I use gear ratio instead. Divide the number of teeth on the chainring by the number of teeth on the cog. Bigger number = harder to push, smaller number = easier to push.