Storage Water-Heater Sizing (First-Hour Rating)
Whether a storage water heater meets the household peak-hour demand.
Example
You enter
- Tank capacity (gal) 50
- Input rate (BTU/hr) 40000
- Recovery efficiency (%) 80
- Temperature rise (°F) 90
- Usable-storage fraction 0.7
- Peak-hour demand (gal) 80
You get
- Recovery 42.7 gph
- First-hour rating 77.7 gph
- Short by (GPH) 2.3163
Checked against published worked examples from: A. O. Smith Corporation.
Details, formula, and sources
ScopeThe first-hour rating (FHR) is the usable storage plus one hour of recovery, with recovery = input x efficiency / (8.33 x rise), checked against the peak-hour draw. The manufacturer's rated FHR on the EnergyGuide label governs the final selection; this is a sizing check, not the rating.
Formula or tablerecovery_gph = input_btuh x efficiency/100 / (8.33 x rise_F); first-hour rating FHR_gph = tank_gal x usable_fraction + recovery_gph; the verdict compares FHR to the peak-hour demand.
Source and editionFirst-principles recovery Q = 8.33 x gph x delta-T with the DOE/AHRI first-hour-rating definition (usable storage plus one hour of recovery), by name, not reproduced.
Free accessThe recovery relation is public physics; the DOE/AHRI first-hour-rating test value on the EnergyGuide label and the manufacturer govern the rating.
What governsEstimate. AHJ and licensed professional govern.
API field namestank_gal, input_btuh, efficiency_pct, rise_F, usable_fraction, peak_hour_gal, recovery_gph, fhr_gph, short_by_gph
- Constants the default 0.70 usable-storage fraction (before the stored water drops below the set point) is editable; the 8.33 lb/gal water constant is fixedfirst principles / DOE FHR method
- FHR definition first-hour rating = usable storage + one hour of recovery; match it to the peak-hour draw, not to tank gallons aloneDOE/AHRI first-hour-rating method
- Check, not rating this is a sizing check; the manufacturer's tested FHR on the yellow EnergyGuide label is the governing valuemanufacturer EnergyGuide label