HVAC Formulas – A Quick and Handy Guide
Your average customer likely isn’t aware of the level of precision in top-of-the-line HVAC work. To them, it may seem like your technician merely puts up some ductwork or replaces a broken part in their air conditioner. In reality, however, you know that very specific formulas govern the work they do, informing the decisions they make out in the field. You also realize that not all your employees know those formulas by heart, or may not fully understand how they actually work. There are, of course, tools available that can assist in the completion of the calculations your employees regularly make in their day to day operations. Gaining a better understanding of the formulas that drive those calculations, however, can help increase the efficiency of your technicians and contribute to their growth as HVAC specialists.
Formulas in this guide:
- Electrical Formulas
- Work and Horsepower Formulas
- HVAC Formulas and Specific Terms
- Other Useful Formulas
Below, we’ve included some of the electrical formulas most common to HVAC work along with some brief explanations of the related terms.
Common HVAC Electrical Terms
E = voltage, or emf
I = amperage, or current
R = resistance, or load
P = power
U factor (the overall heat transfer coefficient) = 1/R
Farad = one amp stored under one volt of pressure
MFD (microfarad) = 1 Farad/1,000,000
Coulomb (charge transported by a constant current of one ampere in one second) = 6.242 × 1018
VA (rating of secondary transformer) = volts x amps
This principle states that the current through a conductor between two points is directly proportional to the voltage across those points.
E = I x R
I = R / E
R = E/I
P = E x I
To measure by kilowatts: P = (E x I)/1000
Three-Phrase Motor Voltage Imbalance
Compressor overheating can often be caused by a voltage imbalance between the motor terminals of an engine’s compressor. The basic formula is as follows:
Percent unbalance = (largest unbalance divided by average volts) x 100
Let’s run a quick example to go through the steps of how to collect the necessary data to run this formula.
Step One – Measure the line voltage between the phases of the compressor’s motor terminals.
In this example, the voltage readings for the lines between the phases are…
Line 1 to Line 2 = 218 V
Line 2 to Line 3 = 228 V
Line 3 to Line 1 = 214 V
Step Two – Determine the average of the readings.
Given the numbers above, the formula in this case would be…
218 + 228 + 214 = 660/3 = an average of 220 volts
Step Three – Determine the imbalance for each phase by comparing the difference between the voltage of each phase to the average voltage.
When conducting this step, remember that the result must be a positive number. The calculations for the numbers we’re working are…
Line 1 to Line 2 = 220 – 218 = 2 V
Line 2 to Line 3 = 228 – 220 = 8 V
Line 3 to Line 1 = 220 – 214 = 6 V
Step Four – Take the largest imbalance found by step three and divide it by the average volts found in step two. Multiply by 100 to create a percentage.
Since the largest imbalance we found was 8 volts and the average voltage was 220, the formula is as follows…
Percent unbalance = (8/220) x 100
Percent unbalance = (0.03636363636) x 100
Percent unbalance = 3.636363636%
Step Five – Square the unbalance percentage and multiply it by two to determine the percentage increase in winding temperature.
This step allows your technician to determine the actual impact of this imbalance on the temperature of the motor. With our above-determined percentage imbalance, the formula looks like this…
Percent temperature rise = 2 x (3.636363636)²
Percent temperature rise = 2 x (13.2231404932)
Percent temperature rise = 26.4462809864
As you can see, a small imbalance in voltage can lead to an increase in temperature of over 26%. Ensure that your technicians look out for this issue when examining overheating compressors.
Work and Horsepower Formulas
Work = force x distance
Horsepower (HP) = 33,000 ft-lbf of work in one minute
HP = 745.7 watts
Metric HP = 735.5 watts
Kilowatt (KW) = 3413 British Thermal Units (BTU)
HVAC Formulas and Specific Terms
Ton of Refrigeration
The amount of heat needed to melt one ton of ice at 32 degrees Fahrenheit, equivalent to 12,000 BTU per hour.
Dry Air = 78% nitrogen + 21% oxygen + 1% various other gases
Specific Density of Air = 1 / 13.33 (or .75 lbs. per cubic foot)
Raising one pound of standard air one degree Fahrenheit requires .24 BTUs
Relative Humidity = moisture present / total moisture air can hold
Specific Humidity = mass of water vapor / total mass of moist air parcel
Dew Point Temperature (in degrees Celsius) = observed temperature (in degrees Celsius) – ((100 – relative humidity percentage) / 5)
The formula for determining dew point temperature may also be expressed as…
Td = T – ((100 – RH) / 5)
It is also worth mentioning that this formula is merely a very accurate approximation to be used only when the relative humidity value is above 50%. A more precise (and complicated) formula can be found here.
Determining Heat in Conditions Other Than Standard Air
Total Heat (BTU/hr.) = 4.5 x cubic feet per minute (CFM) x Δh (std. air)
Sensible Heat (BTU/hr) = 1.1 x CFM x Δt (std. air)
Latent Heat (BTU/hr) = 0.69 x CFM x Δgr. (std. air)
Other Useful Formulas
Total Heat (BTU/hr) = 500 x gallons per minute (GPM) x Δt (water)
BTU/hr = 3.413 x watts = HP x 2546 = Kg Cal x 3.97
Lb. = 453.6 grams
Pounds per Square Inch (PSI) = ft. water / 2.31 = inch of mercury(HG) / 2.03 = inch of water / 27.7 = 0.145 x kilopascal (kPa)
GPM = 15.85 x liters per second
CFM = 2.119 x liters per second
Wattage per Square Foot = .0926 x wattage / mass²
Keep Your HVAC Technicians Sharp
While not meant to function as a comprehensive list, the above selection of formulas should be of great assistance to your technicians in their typical day-to-day work. You can encourage your employees to print this out to use as a cheat sheet, or merely direct them to this resource to study in their downtime. If your team is utilizing an HVAC software solution, consider storing important formulas or calculations in a custom form. This way, technicians can reference the calculations again on future jobs and your company can provide continuity of service. An informed technician is an efficient technician. As their skills and knowledge grow, so too will the success of your HVAC business.