HVAC Formulas - A Quick and Handy Guide for Common HVAC Calculation

The average person probably doesn't understand the level of precision required to do top-of-the-line HVAC work. To them, it may seem like a 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 good HVAC work, informing the decisions technicians make out in the field. Of course, not every HVAC technician knows these formulas by heart, and some may not fully understand how they work. Many common, widely available tools can assist in the completion of the calculations your employees regularly make in their day to day operations. Still, gaining a better understanding of the underlying formulas that drive those calculations can help increase the efficiency of your techs and contribute to their growth as HVAC specialists. To that end, we've compiled some of the most common HVAC formulas in use today. Formulas included in this guide:

• Electrical Formulas
• Work and Horsepower Formulas
• HVAC Formulas and Specific Terms
• Other Useful Formulas

Electrical 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 electrons
VA (rating of secondary transformer) = volts × amps

Ohm’s Law

This principle states that the current through a conductor between two points is directly proportional to the voltage across those points.

E = I × R
I = E / R
R = E / I

Wattage Formula

P = E × I

To measure by kilowatts: P = (E × I) / 1000

Three-Phase Motor Voltage Imbalance

Compressor overheating is often caused by a voltage imbalance between the motor terminals of an engine’s compressor. The basic formula here is:

Percent unbalance = (largest unbalance ÷ average volts) × 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) / 3 = an average of 220 V

Step Three: Determine the imbalance for each phase by comparing the difference between the voltage of each phase and the average voltage. When conducting this step, remember that the result must be a positive number. The calculations for the numbers we’re working with 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 in step three and divide it by the average volts found in step two. Multiply by 100 to create a percentage. Since the largest imbalance was 8 V and the average voltage was 220 V, the formula is:

Percent unbalance = (8 / 220) × 100 = 3.64%

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 the percentage imbalance we determined above, the formula looks like this:

Percent temperature rise = 2 × (3.64)² = 26.5%

As you can see, even a small imbalance in voltage can lead to a temperature rise of more than 26%. Train your technicians to watch for this issue when examining overheating compressors.

Work and Horsepower Formulas

Work = force × distance
Horsepower (HP) = 33,000 ft-lbf of work in one minute
HP = 745.7 watts
Metric HP = 735.5 watts
1 kW = 3,412 BTU/hr

HVAC Formulas and Specific Terms

Ton of Refrigeration

The amount of heat needed to melt one ton of ice at 32°F, equivalent to 12,000 BTU per hour.

Air Composition

Dry Air = 78% nitrogen + 21% oxygen + ~1% other gases (mostly argon)
Specific Density of Air = 1 / 13.33 (or .075 lbs. per cubic foot)
Raising one pound of standard air one degree Fahrenheit requires .24 BTUs

Heat / Humidity

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 °C) = observed temperature (in °C) - ((100 - relative humidity percentage) / 5)

The formula for determining dew point temperature may also be expressed as:

Td = T - ((100 - RH) / 5)

Remember that this formula is a very accurate approximation only when the relative humidity value is above 50%. A more precise (and more complicated) formula can be found here.

Determining Heat in Conditions Other Than Standard Air

Total Heat (BTU/hr) = 4.5 × cubic feet per minute (CFM) × Δh (std. air)
Sensible Heat (BTU/hr) = 1.1 × CFM × Δt (std. air)
Latent Heat (BTU/hr) = 0.69 × CFM × Δgr. (std. air)

Other Useful Formulas

Total Heat (BTU/hr) = 500 × gallons per minute (GPM) × Δt (water)
BTU/hr = 3.413 × watts = HP × 2,546 = Kg Cal × 3.97
1 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 × kilopascal (kPa)
GPM = 15.85 × liters per second
CFM = 2.119 × liters per second
W/ft² = 0.0929 × W/m²

Keep Your HVAC Technicians Sharp

While not meant to function as a comprehensive list, the formulas above will be of great assistance to your technicians in their typical, day-to-day work. Encourage your employees to print this out as a cheat sheet, or simply direct them to this resource to study in their downtime. If your team uses our HVAC software solution Smart Service, you can store some (or all) of the most important formulas or calculations in a custom form. This lets technicians easily reference the calculations from a mobile device, and you can store previous calculations for a given customer or piece of equipment so your company can reference them on a future service call (businesses that offer preventative maintenance contracts will find this especially useful). An informed technician is an efficient technician. As the skills and knowledge of your team grow, so too will the success of your HVAC business. Try a free demo to see how Smart Service fits into your shop!