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Heating Your Soaking Tub – Basic Science
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The most common way of figuring this next part out is with BTUs. A BTU is an abbreviation for British Thermal Unit, which is the amount of energy required to raise 1 pound of water 1 degree Fahrenheit at sea level. Since a gallon of water is 8.34 pounds, we have about 892.38 pounds of water in our tub, requiring about 900 BTUs to heat your tub 1 degree.
If the water coming out of your hose into the tub is 54 degrees, we need to raise the temperature about 50 degrees, so in total that would be about 45,000 BTUs to get your tub up to temp.