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How many kilowatts needed to heat water in water heater
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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 65F 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 1F

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 65F 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 1F
0.0024444 Kwh to raise 1 gallon of water 1F
0.146666  Kwh to raise 1 gallon of water 60F (60-120F)
5.866689  Kwh to raise 40 gallons of water 60F (60-120F)
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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water consumption bathtub
Take showers instead of bath.
Regular bath uses 13- 15 gallons hot water (20 gal water total)
Set water heater timer for 45-60 minutes for hot bath

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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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