Instructions: In the yellow boxes, you can enter the variables you want to work with.

"Mixed Temp" is the desired desired shower head temperature when taking  a shower.
"Cold Supply Temp" refers to the temperature of your incoming cold water supply.
"Tank Temp." refers to the t-stat setting on the water heater.
"Draw Down" is typically about 70% on a storage tank water heater. If you understand the concept of "draw down" and need to change it, you're welcome to do so, otherwise, don't worry about it.
"Minutes" refers to the duration of the shower. 
"GPM" refers to the flow rate of the shower head.
"Minimum WH Size in Gallons" refers to the tank size required to deliver the shower.  NOTE: This calculator does not consider the recovery rate of the burner even though it slightly affects the first shower from a tank. 

Example: Let's say your shower head flows at 5 gallons per minute. If your water temperatures are similar to the data we've inclucded then you will need at least a 53 gallon tank (which doesn't exist so you would have to take a shorter shower or get the next size larger tank.

But if you changed to a more water efficient shower head, you could get by with a smaller sized water heater.  The size difference is like having a more fuel efficient car.

NOTE: This calculator is NOT intended to replace the qualified engineering advice  of a plumbing design professional.  It is free to use but you are responsible for making sure you get the results you desire.