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Formula for heating water inside tank: Gallon Per Hour (Electric) = (KW x 3413) divided by (temp. rise x 8.25) or (KW x 414) divided by (temp rise.) Let's say you have 5500 watt elements. let's say incoming water temperature is 65°F and you want to heat tank to 105°, or 40° rise in temperature. 5500 watt or 5.5Kw elements x 3413 = 18771.5 40 degree temperature rise x 8.25 = 330 So in this specific situation, the element would heat 56.88 gallons per hour If you have 4500 watt elements and incoming water temperature is 55°, and you want to heat to 120°, then the temperature rise is 65° 4.5 KW x 3413 = 15358.5 65 degree temperature rise x 8.25 = 536 So one element would heat 28 gallons per hour This number is for EACH element, but does NOT consider heat loss from tank, room temperature, or thickness of insulation etc. Remember, with residential simultaneous tank, only ONE element is ON at one time. Upper element is ON, or lower element is ON, or BOTH elements are off. At no time are both elements on. 
Kilowatt
hours of electricity needed to heat water ... the math formula: 1.) Basic formula > it takes .0002931 Kwh to raise 1 pound of water 1°F 2.) Basic number >A gallon of water weighs 8.34 lbs (pounds) 3.) "A BTU is amount of heat needed to raise 1 pound of liquid water by 1° from 60° to 61° F at constant pressure of one atmosphere. Other definitions of BTU exist which are based on different water temperatures and cause the results to vary by .5%." (For analysis of water heaters, .5% is ignored. Variation in atmospheric pressure is also ignored. Water heater 'science' is an approximation since calcium carbonate in tank will vary electrical efficiency and tank capacity.) Formula for heating water inside tank: Gallon Per Hour (Electric) = (KW x 3413) divided by (temp. rise x 8.25) or (KW x 414) divided by (temp rise.) Let's say you have 5500 watt elements. let's say incoming water temperature is 65°F and you want to heat tank to 105°, or 40° rise in temperature. 5500 watt or 5.5Kw elements x 3413 = 18771.5 40 degree temperature rise x 8.25 = 330 So in this specific situation, the element would heat 56.88 gallons per hour This number is for EACH element, but does NOT consider heat loss from tank, room temperature, or thickness of insulation etc. Remember, with residential simultaneous tank, only ONE element is ON at one time. Upper element is ON, or lower element is ON, or BOTH elements are off. At no time are both elements on. 4.) BTU formula > 1 BTU = 2.931 x 10–4 Kwh (kilowatt hours). BTU = 2.931 x .0001 = .0002931 Kwh Therefore it takes .000293 Kwh to raise 1 pound of water 1° F 5.) 30 Gallons of water x 8.34 = 250.2 lbs 40 Gallons of water x 8.34 = 333.6 lbs Calculation using 40 Gallon water heater: > Ordinary 40 gallon water heater in attic. Temperature in attic = 50° F. Temperature of water in tank = 50° F. > Water in tank weighs 333.6 lbs. > How much electricity is needed to raise temperature of full tank to 120° F. > 120° minus 50° = 70° > so the temperature needs to go up 70° > Multiply 333.6 x 70 x .0002931 = 6.84 Kwh Calculation using 30 Gallon water heater: > Same problem as above > Water in tank weighs 220.2 lbs > Multiply 250.2 x 70 x .0002931 = 5.13 Kwh 
0.0002931 Kwh to raise 1 pound of
water 1°F 0.0024444 Kwh to raise 1 gallon of water 1°F 0.146666 Kwh to raise 1 gallon of water 60°F (60120°F) 5.866689 Kwh to raise 40 gallons of water 60°F (60120°F) 1 Kw = 3413 BTU 2.42 watt required to raise 1 gallon water 1 degree 1 Kwh will raise 6.8 gallon water 60 degrees F 8.33 BTU will raise 1 gallon of water 1 degree at 100% efficiency 11 BTU required to raise 1 gallon of water 1 degree at 75% efficiency (gas) 1 cubic foot natural gas = 1000 BTU 1 therm 100,000 BTU or 100 cubic feet 1 cubic foor propane = 2500 BTU 1 gallon propane = 91,250 BTU 
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Take showers instead of bath. 
Regular
bath uses 13 15
gallons hot water (20 gal water total) Set water heater timer for 4560 minutes for hot bath Shower uses 6  8 gallons of hot water (10 gal water total) Set water heater timer for 2030 minutes for hot shower Resources: How much hot water for bath or shower Compare water heater timers Off peak water heater options Buy: Bathtubs and shower stalls at Amazon Shower stalls at Amazon Home energy savings books at Amazon 
Cost for 1 bath 15 gallons hot for bath x 8.34 llb per gallon x 60 degree rise in temperature x .14 cets per kwh = 1050 3413 BTU content of fuel x .95 efficiency rating of heater = 3139 1050 divided by 3193 = 33¢ cost of hot water per bath inside standard 15' x 30" x 60" Princeton bathtub. 9 gallon shower cost 19.8¢ 

Temperature of water 
Cost if you use 40 Gallon per day  Cost if you use 30 Gallon per day 
Raise from 32° to 120°  8.60 Kwh x 14¢ = $1.20  6.45 Kwh x 14¢ = 90¢ 
Raise from 50° to 120°  6.84 Kwh x 14¢ = 96¢  5.13 Kwh x 14¢ = 72¢ 
Raise from 70° to 120°>  4.88 Kwh x 14¢ = 68¢  3.66 Kwh x 14¢ = 51¢ 
Raise from 85° to 120°  3.42 Kwh x 14¢ = 48¢  2.56 Kwh x 14¢ = 36¢ 
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