Boiler formulas are useful tools for anyone who operates or installs boilers. In this article we will provide some useful boiler formulas, along with a few other calculations you can use with your system.
All formulas on this page are typical in nature and will change with actual site conditions, equipment capabilities, efficiencies, etc.. These are offered as a general means of estimating requirements or conditions without all necessary values known. Assuming a boiler ‘Fuel to Steam’ efficiency of 80%.
Useful Gas/Oil Boiler Formulas:
KW x 0.10 = BHP
34.5 x Boiler Horsepower (BHP) = LB/STM/HR (from and at 212°F)
0.069 x Boiler Horsepower (BHP) = GPM (evaporation rate)
33,479 x Boiler Horsepower (BHP) = BTUH (nominal gross output) (divide x.8 to get input)
0.3 x Boiler Horsepower (BHP) = GPH No.2 Fuel Oil
0.28 x Boiler Horsepower (BHP) = GPH No.5/6 Fuel Oil
42 x Boiler Horsepower (BHP) = CFH Nat. Gas
139 x Boiler Horsepower (BHP) = SQ/FT EDR
9.809 x Boiler Horsepower (BHP) = KW
LB/STM/HR x 0.002 = GPM
LB/STM/HR x 1000 = BTU/HR (nominal gross output)
Gallon of Water @ 70°F x 8.34 = LB of water
2.31 x PSIG = FT of water
6.9 x PSIG = kPa
27.71 x PSIG = in w.c.
1.73 x Ounce = in w.c.
1 lb of Steam = 970.2 Btu
1 Sq ft EDR (steam) = 240 Btu per hour
Btu/hr Hot Water Boiler Output Calculation
1.Calculate the water flow through the hot water boiler in lbs. /hr.
Example: 800 gpm is the flow through boiler
800 gpm * 60 min/hr. = 48,000 gph
48,000 gph * 8.31 lbs. /gal = 398,880 lbs. /hr.
2. Calculate the Δ T of water flow through the hot water boiler in F.
Example: 160°F entering and 180°F leaving – 180°F – 160°F = 20°F
3. Calculate Btu/hr. output of boiler. (one pound of water by one degree Fahrenheit)
Example: 398,880 lbs. /hr. * Δ 20°F = 7,977,600 Btu/hr.
Output of boiler will need to be greater than 7,977,600 Btu/hr.
Shortcut Version of Same Formula: (8.31 x 60) ≈ 500 x GPM x ΔT = Btu/Hr
1 Cu Ft Water = 7.48 gallons of water or 62.4 lbs
Typical Fuel Values
1 CU/FT Natural Gas @ 60°F = 1,000 BTU/CU/FT
1 Therm = 100,000 BTU’s (100 CU/FT natural gas)
1 Dekatherm = 1,000,000 BTU’s (1,000 CU/FT natural gas)
1 GAL of LPG (propane liquid) @ 60°F = 91,600 BTU/GAL
1 CU/FT of LPG vapor (propane gas – raw) @ 60°F = 2,500 BTU/CU/FT (typical @ 1.53 SG)
NOTE: LPG may be blended with air to approximate the operational characteristics of Natural Gas. It may have a nominal BTU content of 1,300 to 1,500 BTU/CU/FT (determine by application).
1 GAL No.2 Fuel Oil = 140,000 BTU/GAL
1 GAL No. 5/6 Fuel Oil = 150,000 BTU/GAL
Hot Water Boiler Sizing:
British thermal unit (BTU) = the amount of energy needed to cool or heat one pound of water by one degree Fahrenheit in one hour.
One (1) gallon of water weighs 8.31 lbs. /gallon
In an article written by Forbes Marshall, they provide a formula to find the direct efficiency of a boiler. The formula is as follows:
η=(Energy output)/(Energy input) X 100
In order to calculate boiler efficiency, we divide the total energy output by total energy input, multiplied by hundred.
This formula further breaks down to:
E= [Q (H-h)/q*GCV]*100
Q= Quantity of steam generated (kg/hr)
H= Enthalpy of steam (Kcal/kg)
h= Enthalpy of water (kcal/kg)
GCV= Gross calorific value of the fuel.