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Calculate first hour delivery of water heater
Approximately: (tank capacity) x .70 + (recovery) = first hour delivery
 
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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 is "the calculated amount of hot water a fully heated water heater can deliver in the first hour period.
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First hour is based on 2 factors: (tank capacity) x .70 + (recovery) = first hour delivery
1) Initial storage tank capacity (gallonage of tank)
2) Recovery or the ability to heat water as it is being drawn (how fast the heater can heat the water). So a gas water heater rated for 40,000 BTU will heat water faster than 30,000 BTU, so the 40,000 BTU tank will have higher recovery, and thus higher first hour delivery. 

ENERGYGUIDE label sometimes shows first hour rating.
The number is approximation.
Part I: 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? 
As hot water is being used, cold water enters bottom of heater. 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.

Check your heater with Draw-down test:

Is the tank producing enough hot water to match size of tank?
"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."

Steps:  Turn off heater. Connect hose to drain. Run hose into 5 gallon bucket.
With a 50 gallon tank. Expect minimum 70% or 35 gallons of hot water before it starts to cool.  Run water fast before it cools.
If result shows correct amount of hot, then tank is functioning.
Part II: 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
Part III:  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 calculations:
Summertime: Assume 60° incoming temperature and thermostat set at 120° resulting in 60° rise in temperature.
 40 gallon, 30,000 BTU gas water heater
(40 x .7) + 61 = 89 gallons first hour delivery

Winter: Assume 40° incoming temperature and thermostat set at 120° resulting in 80° rise in temperature.
40 gallon, 30,000 BTU gas water heater
(40 x .7) + 46 = 74 gallons first hour delivery
More first hour calculations
40 gallon electric water heater with 4500 watt elements:
Summertime: Assume 60° incoming temperature and thermostat set at 120° resulting in 60° rise in temperature.
(40 gallon x .7) + 31 gallon recovery = 59 gallons

40 gallon electric water heater with 5500 watt elements:
(40 gallon x .7) + 38 gallon recovery = 66 gallons
40 gallon electric water heater with 4500 watt elements:
Winter: Assume 40° incoming temperature and thermostat set at 120° resulting in 80° rise in temperature
(40 gallon x .7) + 23 gallon recovery = 51 gallons

40 gallon electric water heater with 5500 watt elements:
(40 gallon x .7) + 28 recovery = 56 gallons
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