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Calculate first hour delivery of water heater
Approximately: (tank capacity) x .70 + (recovery) = first hour delivery
What is first hour delivery?
First hour delivery is amount of hot water a fully heated water heater can deliver in the first hour period. 
Start with a water heater that is fully heated (has recovered to its thermostat setting) and someone begins to use hot water such as a shower or bath. 
It does not mean the hot water will last for one full hour.

First Hour Rating
"The calculated amount of hot water a fully heated water heater can deliver in the first hour period. The output of a water heater is normally given in gallons per hour at a 100F temperature rise.  It is the quantity of water that the heater will deliver at 140F, when the cold start temperature is 40F." Footnote: typical bath-shower is 104-110F and not dangerously high 140F. Resources: Average temperature shallow groundwater   How to calculate cost of running gas water heater
First hour is based on initial storage (gallonage of tank) plus the ability to heat water as it is being drawn (recovery). 

Federally mandated ENERGYGUIDE label on residential water heater shows first hour rating for the product.
First part of formula: Tank capacity x .70
"Residential water heater can deliver 70% of tank capacity at the thermostat setting minus 20 degrees.  What does this mean?  If the thermostat is set on 120 degrees, the unit should deliver 70% of tank volume at a temperature between 100 degrees and 120 degrees."
What does 70% of tank capacity mean?  It means 70% of the gallon capacity listed on the rating plate.  For example 30 gallon x .7 = 21 gallons as seen on chart.
Why 70% of the tank capacity? 
Cold water enters heater as the hot water is being used. The cold water mixes with hot water in the tank, causing the water inside tank to cool, just like adding cold water to a hot cup of tea.
As hot water is used, the dip tube, attached to the cold water inlet on water heater, delivers cold to the bottom of the tank.  The pressure of incoming cold
water pushes hot water out of the tank. Once cold water has mixed with the hot water, the water turns warm, then tepid, then cold.
Once cold reaches 30% of tank capacity, the available hot is 70% and the water will quickly become cold.
Second part of formula: Recovery
Offsetting loss of heat, the water heater thermostat responds to cold water and turns on the burner or element. The tank is heating the water even while hot water is being used. This means the tank is recovering.
Water heater recovery must be factored with the 70% rule to determine first hour delivery. To determine the 'ballpark' first hour delivery use the following formula:
(tank capacity) x .70 + (recovery) = first hour delivery
Resource:How to calculate recovery

Larger image
Calculate first hour:
(tank capacity) x .70 + (recovery) = first hour delivery

Use chart on left for recovery.  Check the rating plate of your water heater for the input in watts (electrical) or BTUs (gas). Resource:How to calculate recovery

Example first hour calculation:
40 gallon, 40,000 BTU gas water heater
40 x .7 + 36 = 64 gallons first hour delivery

Footnote: degree F rise is difference between incoming cold water temperature and water heater thermostat setting.
Example calculation 80 gallon electric water heater with 4500 and 5500 watt elements:
(80 gallon x .7) + 31 gallon recovery = 87 gallons
(80 gallon x .7) + 37.8 recovery = 93.9 gallons
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