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How many kilowatts needed to heat water in water heater

Electric water heater math

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

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.)

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
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
> 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

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
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

More formulas


[15 gallons hot for bath x 8.34 llb per gallon x 60 degree rise in temperature x .14 cets per kwh] divided by
]3413 BTU content of fuel x .96 efficiency rating of heater] =
= 32 cents cost of hot water per bath inside standard 15' x 30" x 60" Princeton bathtub
My rule of thumb for solar is 5x to 6x the panel rating during a really sunny day. 
1250 watts of PV should make about (1250watts x 5) = 6.250 Kwh

How much water is heated using PV solar water heater

Read more about solar water heating
Ultra low watt density
Ultra low watt density

What does watt rating mean

Wattage is just a rating that does not measure heating power.

Wattage over time, or watt-hours or Kilowatt-hours (Kwh) is measure of heating power.
If you have 1250 watts for 1/2 hour, then you have 625 watt-hours or .625 Kwh.
If you have 1250 watts for 2 hours of the day, and 750 watts for 3 hours, then you have 4.75 Kwh... which should raise 40 gallons of water from 75 to 120

Select and understand water heater elements

3-phase water heaters
9000 watt water heater
Temperature for killing bacteria

Same 4500 watt element @ 240 volts and @ 120 volts
Wattage drops when voltage is reduced
See water heater label showing difference between 208V - 240V

Resistive loads such as light bulbs and elements burn less hot when voltage is reduced.
Examples: ordinary household dimmer for incandescent bulbs, or power brown-out when household voltage is reduced and light bulbs dim.
Same is true for water heater elements.
Lower wattage heats less water per hour See chart
Convert water heater from 240 volts to 120 volts
Select and understand water heater elements

More resources

See Family chart for setting  water heater timer
Shallow ground water temperature map
How much electricity to heat water
How to increase amount of hot water
Off peak water heater strategies
9 ways to save with water heater
How to maintain water heater
How to adjust water heater temperature
Change water temperature using timer
Change water heater temperature using zwave
Gas water heater timer/ change temperature using timer
Add another thermostat to water heater
Temperature needed to kill bacteria
Water heater timers/ gas and electric
Future of water heater?
Project: DIY solar water heater
Review: DIY solar water heater
Review: Should you buy solar water heater system
Install meter on electric water heater
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

Shower uses 6 - 8 gallons of hot water (10 gal water total)
Set water heater timer for 20-30 minutes for hot shower

How much hot water for bath or shower
Compare water heater timers
Off peak water heater options

Bathtubs and shower stalls at Amazon
Shower stalls at Amazon
Home energy savings books at Amazon
oversized bathtub

What size water heater for oversize bathtub?

Large bathtub / whirlpool tub

Recommend 80 gallon first hour delivery
Electric: minimum 60-to-80 gallon size just for that one tub
Gas: minimum 50 gallon size just for that one tub

Electric heat pump water heaters generally cannot produce enough hot water.

Tankless promise unlimited hot water, but temperature of water is 120 F and water in tub may be cool by time tub fills. Cost of maintenance and repairs never pay back. All costs are energy.

80 gallon electric water heater ended in April 2015
over 50 gallon electrci must be hybrid
residential energy chart hot water consumption
Fuse on power pole Price of water

No water/ no electricity/

Read about electric generation/ What is 3-phase electricity

Gas and electric water heaters Industrial electric at Amazon

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Intermatic control centers Intermatic control centers:
+ manuals and parts

Including Z-wave
box timers Compare box timers

Compare ways to control Gas and Electric heaters
programmable timer Compare programmable timers

Control water heater with programmable wall timer
Countdown timers Compare countdown timers

Control water heater with countdown timer
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