HVAC Formulas and Calculations Field Reference Guide for Technicians: CFM, BTU, Cv, GPM, ΔT, and More
Publié par Jason Tables
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Whether you work on large commercial HVAC air handlers, VAV boxes, and hydronic loops or you spend your days on residential split systems and furnaces, the same small set of HVAC formulas and calculations does most of the heavy lifting. With a clamp meter, a few temperature readings, some pressure measurements, and these equations for CFM, BTU, Cv, GPM, ΔT, superheat, and subcooling, you can check system capacity, verify airflow, and troubleshoot comfort and performance problems without guessing.
This field reference is written for working commercial HVAC technicians, but it is just as useful for residential techs who need a quick way to confirm their numbers in the field. It is meant to be an HVAC formula and calculation guide you dip into as needed, not something you read end to end. When you are on a job, you can jump straight to the HVAC formula that matches what you are trying to check, plug in the numbers you have, and compare the result to what the equipment or design calls for.
For each HVAC formula and calculation, you will see a brief explanation, the equation itself, and a simple field example that shows how a technician would use it on real equipment. If you are a field technician, installer, commissioning specialist, or controls technician, this is the kind of HVAC reference guide you will return to often. It is worth bookmarking this article on your phone so you can pull it up in a mechanical room or on a rooftop whenever you need to check a calculation.
Sensible Heat in Air
Sensible Heat in Water
Total Cooling Capacity from Airside Readings
Latent Cooling from Moisture Removal
Sensible Heat in Air
Sensible Heat in Water
Total Cooling Capacity from Airside Readings
Latent Cooling from Moisture Removal
Heat Transfer Formulas for HVAC Systems
Sensible Heat in Air
Sensible heat is the portion of the heating or cooling load that changes the air temperature without changing the air’s moisture content.
The standard sensible heat formula for air is:
Q = 1.08 × CFM × ΔT
Q is sensible heat in BTU per hour, CFM is airflow in cubic feet per minute, and ΔT is the temperature difference in degrees Fahrenheit between return air and supply air. In this formula, the 1.08 is a standard value for typical indoor air, so you can treat it as a fixed number.
Here is a quick example. You measure 1,200 CFM across an evaporator coil. Return air is 78°F, supply air is 58°F, so ΔT is 20°F.
Q = 1.08 × 1,200 × 20 = 25,920 BTU/hr
You can also rearrange this formula to solve for airflow when you know the sensible load and the temperature difference:
CFM = Q ÷ (1.08 × ΔT)
Sensible Heat in Water
In hydronic systems, the same idea applies, but now you are looking at heat that shows up as a change in water temperature through the loop or coil. This formula tells you how much heat is being added to or removed from the water circuit.
For hot or chilled water loops, the go to equation is:
Q = 500 × GPM × ΔT
Q is sensible heat in BTU per hour, GPM is water flow in gallons per minute, and ΔT is the water temperature difference in degrees Fahrenheit between supply and return. In other words, Q is the heating or cooling load the water circuit is carrying at that flow and temperature difference. In this formula, the 500 is a standard value for plain water in typical hydronic systems, so you can treat it as a fixed number when the fluid is water. If the loop uses a glycol mixture, the constant is slightly lower for common glycol percentages. For example, for a typical 30 percent propylene glycol mixture, many designers use a constant of about 485 instead of 500, but the basic relationship is the same.
Here is an example. A pump is moving 8 GPM through a heating coil. Supply water is 180°F and return water is 160°F, so ΔT is 20°F.
Q = 500 × 8 × 20 = 80,000 BTU/hr
You can solve this formula for GPM when you know the load Q and ΔT, or for ΔT when you know the load and flow. That makes it useful for checking whether a coil, boiler, or chiller is seeing the flow and temperature difference it needs to deliver its rated output. If you know the sensible load Q and the water temperature rise or drop, you can also solve directly for flow:
GPM = Q ÷ (500 × ΔT)
Total Cooling Capacity from Airside Readings
When you use the 1.08 × CFM × ΔT formula above, you are only looking at sensible cooling in the air, which is the part that shows up as a temperature drop. At the same time, the coil is also removing moisture from the air. That part is called latent cooling. The total cooling capacity of the coil is the sum of sensible and latent cooling.
To get both sensible and latent cooling in one calculation, you can use air enthalpy. You can think of enthalpy as a heat content number that already includes the effect of both air temperature and moisture. You can determine the enthalpy for the entering and leaving air using a psychrometric chart or an app, then use the difference between those two values in the airside total capacity formula below:
Q = 4.5 × CFM × Δh
Q is total capacity in BTU per hour, and Δh is the change in air enthalpy in BTU per pound of dry air across the coil.
Here is a quick example. The system moves 1,400 CFM. From a psychrometric app you find that entering air enthalpy is 30 BTU per pound and leaving air enthalpy is 22 BTU per pound, so Δh is 8.
Q = 4.5 × 1,400 × 8 = 50,400 BTU/hr
Comparing this result with the sensible result from 1.08 × CFM × ΔT tells you how much of the coil capacity is going into dehumidification versus temperature drop.
If you know total capacity and the enthalpy change, you can also solve for airflow:
CFM = Q ÷ (4.5 × Δh)
Latent Cooling from Moisture Removal
In the total capacity formula above, sensible and latent cooling are combined. When you want to look only at the moisture side of the load, you can use grains per pound in a latent cooling equation:
Q = 0.69 × CFM × ΔW
Q is latent heat in BTU per hour, CFM is airflow in cubic feet per minute, and ΔW is the change in humidity ratio in grains of moisture per pound of dry air across the coil.
Quick example. The system moves 1,200 CFM. From a psychrometric app you find that the return air humidity ratio is 90 grains per pound and the supply air humidity ratio is 70 grains per pound, so ΔW is 20.
Q = 0.69 × 1,200 × 20 = 16,560 BTU/hr
Comparing this result to the total capacity from 4.5 × CFM × Δh and the sensible capacity from 1.08 × CFM × ΔT shows how much of the coil output is going into dehumidification.
If you know the latent load and the change in humidity ratio, you can rearrange the formula to solve for airflow:
CFM = Q ÷ (0.69 × ΔW)
HVAC Airflow, Duct, and Fan Formulas
Air Changes per Hour
For ventilation and indoor air quality work, you will often need to determine air changes per hour. Air changes per hour, or ACH, tells you how many times the air volume in a room is replaced in one hour.
The formula is:
ACH = (CFM × 60) ÷ Volume
ACH is air changes per hour, CFM is the total supply or exhaust airflow serving the room in cubic feet per minute, and Volume is the room volume in cubic feet. The 60 factor converts minutes to hours so that ACH comes out in “per hour.”
For example, a room is 20 feet by 15 feet with a 9 foot ceiling. Volume is 20 × 15 × 9 = 2,700 cubic feet. The supply to the room is 300 CFM.
ACH = (300 × 60) ÷ 2,700 ≈ 6.7 air changes per hour
If you know the target ACH for a space, you can rearrange this formula to find the supply CFM needed to meet that air change rate:
CFM = (ACH × Volume) ÷ 60
Duct Airflow, Velocity, and Area
When you need to connect a duct velocity reading or a duct size to actual airflow, you can use the relationship between CFM, air velocity, and duct area. If you know any two of these, you can solve for the third.
CFM = Velocity × Area
CFM is airflow in cubic feet per minute, Velocity is air speed in feet per minute, and Area is duct cross sectional area in square feet.
Quick example. A rectangular duct is 18 inches by 12 inches. Area is (18 × 12) ÷ 144 = 1.5 square feet. If velocity is 800 feet per minute, then:
CFM = 800 × 1.5 = 1,200 CFM
This is useful when you have a velocity reading from a traverse and need to know if you are close to design airflow.
Velocity from Pitot Tube Readings
A Pitot tube is a small metal probe with pressure ports that faces into the airflow in a duct. You can connect it to a manometer and read the pressure created by the moving air at the tip. That reading is called velocity pressure, and it shows up on the gauge in inches of water column.
At standard air conditions, you can convert velocity pressure to air velocity with:
V = 4,005 × √Pᵥ
V is air velocity in feet per minute, and Pᵥ is velocity pressure in inches of water column. In this formula, the 4,005 is the standard constant that converts inches of water velocity pressure into feet per minute for standard air, so you can treat it as a fixed number.
Here is an example. Velocity pressure in a main supply duct is 0.20 inches of water.
V = 4,005 × √0.20 ≈ 4,005 × 0.447 ≈ 1,790 feet per minute
If the duct area is 1.2 square feet, then, using CFM = Velocity × Area, CFM ≈ 1,790 × 1.2 ≈ 2,150 CFM.
On a duct traverse, you would take several velocity pressure readings across the duct, average them to get a single Pᵥ, then plug that average value into this formula to get the average duct velocity and from there the CFM.
Fan Laws in Simple Form
When you change fan speed with a pulley adjustment or a VFD, airflow, static pressure, and horsepower all change together. The fan laws let you estimate how those three values will change when you change speed, so you can see roughly what will happen to airflow and motor load before you make the adjustment.
Start with a known operating point. A fan is delivering 2,000 CFM at 0.6 inches of total static. At that point the motor is drawing 1 horsepower and the fan speed is 900 RPM. You want to increase the airflow to 2,400 CFM.
Airflow law. Airflow is proportional to speed, so
CFM₂ = CFM₁ × (RPM₂ ÷ RPM₁)
You can also write this as a ratio:
CFM₂ ÷ CFM₁ = RPM₂ ÷ RPM₁
Here, the airflow ratio you want is 2,400 ÷ 2,000 = 1.2. That means the new RPM must be 1.2 times the old RPM.
RPM₂ = 900 × 1.2 = 1,080 RPM
Static pressure law. Static pressure rises faster than airflow. Once you know the airflow ratio, you square that number and multiply by the original static pressure to get the new static pressure.
The fan law is:
SP₂ = SP₁ × (CFM₂ ÷ CFM₁)²
Using the same 1.2 CFM ratio:
SP₂ = 0.6 × 1.2²
First 1.2² = 1.44, then
SP₂ ≈ 0.6 × 1.44 ≈ 0.86 inches of water
Horsepower law. Fan horsepower changes with the cube of the airflow ratio.
The fan law is:
HP₂ = HP₁ × (CFM₂ ÷ CFM₁)³
Again, using the 1.2 CFM ratio:
HP₂ = 1 × 1.2³
1.2³ ≈ 1.73, so the new brake horsepower would be about 1.73 hp.
So in this example, bumping the fan from 2,000 to 2,400 CFM raises speed from 900 to 1,080 RPM, static pressure from about 0.6 to about 0.86 inches, and motor load from about 1 to about 1.73 horsepower. That gives you a quick check on whether a pulley change or VFD speed increase is likely to overload the motor or push system pressure too high.
Quick HVAC BTU and Tonnage Conversions
Technicians constantly move between BTU per hour and tons. The conversion is:
1 ton of cooling = 12,000 BTU/hr
So BTU/hr divided by 12,000 gives tons, and tons multiplied by 12,000 gives BTU/hr.
Quick example. From Q = 1.08 × CFM × ΔT you find that a furnace is delivering 60,000 BTU/hr. That is the output. On the cooling side, if a split system is rated at 48,000 BTU/hr, it is a 4 ton unit.
HVAC Control Wiring Sizing and Voltage Selection
Actuators and control valves are usually rated in volt amperes rather than plain watts. The VA rating tells you how much apparent power the device draws. You can convert that into current with a simple relationship:
I = VA ÷ V
I is current in amperes, VA is the actuator’s volt ampere rating from the nameplate, and V is the supply voltage.
Once you know the current, you can look up the proper wire gauge and maximum run length in the manufacturer’s wiring tables or in the applicable electrical code. This is especially important on 24 volt control circuits. Long runs of small gauge wire create voltage drop along the run. When 24 V is run more than ~20 feet on wire that is too small, the voltage at the actuator can fall far enough that it will not produce its rated torque or may not even start.
In general, 24 V is appropriate for short control runs, for actuators located close to their transformer, and where low voltage control wiring is required by the design. For long runs to remote dampers or valves, or for large high torque actuators, it often makes more sense to use a higher supply voltage such as 120 V, or to add a local transformer so the 24 V run stays short. Use the current formula as a quick check, then rely on the manufacturer’s wiring diagrams and tables to pick a wire size and a maximum length that avoid excessive voltage drop.
HVAC Sensor Selection Basics
When you are installing or replacing sensors, a few quick guidelines help you choose the right parts so the control system reads accurately.
For differential pressure sensors, pick a span that places the normal operating pressure in the middle half of the range rather than right at the bottom or at the top. For example, if a duct normally runs between 0.3 and 0.7 inches of water, a sensor with a range of 0 to 1 inch of water gives you good resolution and headroom. If you choose a range that is much higher than the actual pressures you expect, the readings will be less useful for control.
For temperature sensors, the key is matching the resistance curve that the controller expects. Many modern HVAC control systems use 10 k ohm negative temperature coefficient thermistors for room and duct sensing, while others use platinum sensors such as Pt1000. When you replace a sensor, match the resistance type and curve printed on the existing probe or on the controller documentation, not just the physical style of the sensor.
For CO₂ and other gas monitoring, make sure the range matches the application. For indoor air quality and demand controlled ventilation, CO₂ sensors are typically set up for a range that covers outdoor air levels and common indoor setpoints, for example 0 to 2,000 or 0 to 5,000 parts per million. For refrigerant or other safety gas monitors, the required range and alarm levels come from the gas type and the safety code you are working under. Use the design documents and manufacturer recommendations as your primary guidance, and use these rules of thumb as a quick check that the selected sensor and range make sense for the job.
HVAC Valve Sizing With CV
Control valves are often sized using the Cv rating, which is defined as how many gallons per minute of water will flow through the valve at a 1 psi pressure drop with the valve fully open. For water at typical HVAC conditions, the most commonly used sizing relationship is:
Cv = GPM ÷ √ΔP
Cv is the valve flow coefficient, GPM is the design flow in gallons per minute, and ΔP is the pressure drop across the valve in pounds per square inch when it is wide open.
You can rearrange this formula depending on what you know. If you know the desired Cv and the pressure drop you can tolerate, you can solve for flow:
GPM = Cv × √ΔP
If you know the design flow and the valve Cv, you can solve for the expected pressure drop:
ΔP = (GPM ÷ Cv)²
In practice, you usually start with the required flow and a target pressure drop across the valve, then solve for the Cv you need and select the closest standard valve size that gives you that Cv rating. This quick set of equations lets you check whether a proposed replacement valve is close enough to the original for the system to behave properly.
Refrigeration Formulas: Superheat and Subcooling
Superheat and subcooling are two of the most useful checks in refrigeration and air conditioning. Both are simple temperature differences that tell you whether the evaporator is boiling off all the liquid refrigerant and whether the condenser is delivering a full column of liquid refrigerant to the metering device.
Superheat is how far the suction vapor temperature is above its saturation temperature at the measured suction pressure.
Superheat = measured suction line temperature − saturation temperature at suction pressure
Subcooling is how far the liquid temperature is below its saturation temperature at the measured liquid line pressure.
Subcooling = saturation temperature at liquid line pressure − measured liquid line temperature
You read saturation temperatures from a pressure temperature chart or a digital manifold for the refrigerant you are working with.
Quick example for superheat. On an R 410A system, the suction pressure corresponds to 40°F saturation, and the suction line at the evaporator outlet is 55°F.
Superheat = 55 − 40 = 15°F
Quick example for subcooling. The liquid line pressure corresponds to 115°F saturation, and the liquid line temperature is 100°F.
Subcooling = 115 − 100 = 15°F
Taken together, these two numbers tell you a great deal about charge level, how well the metering device is feeding the coil, and how the evaporator and condenser are performing.
How to Use This HVAC Formula Glossary in the Field
On real service and startup calls, you use these formulas as quick checks. You do not need all of them on every job. You pick the one that connects what you can measure to what you want to know, plug in a few readings, and see whether the result makes sense for the equipment and the conditions you are looking at.
For example, you might use 1.08 × CFM × ΔT or 500 × GPM × ΔT to see if a coil is moving roughly the right BTU/hr, use the Pitot and duct formulas to verify airflow in a main, or use superheat, subcooling, and tonnage calculations to see whether a split system is charged and performing the way it should. The idea is always the same. Measure what you can, run a simple calculation, and compare the answer to what you know the system should be doing.
With a little practice, these formulas become part of your normal troubleshooting. The math stays simple, and the payoff is that you can walk into a mechanical room or attic, take a few readings, and quickly tell whether the system is delivering close to its rated capacity.