HVAC & Refrigeration

Heating, cooling and air: sensible/latent loads, COP, EER, airflow, humidity and refrigeration tons

This HVAC & Refrigeration formula collection covers the key calculations used to size, analyze, and compare heating, cooling, ventilation, and refrigeration systems, including loads, airflow, humidity, COP, EER, and refrigeration tons. It’s useful for students, exam prep, and engineers or technicians in real-world design, service, and troubleshooting, where these formulas help turn comfort and efficiency goals into practical numbers.

Sensible Heat Load

Q = m c \Delta T

Heat needed to change air or water temperature without a phase change.

Latent Heat Load

NEWIntermediate

Q = m L

Heat absorbed or released when moisture condenses or evaporates — the hidden load air conditioners fight.

Coefficient of Performance (Cooling)

NEWIntermediate

COP = \frac{Q_c}{W}

Cooling delivered per unit of work input — higher is more efficient.

Energy Efficiency Ratio (EER)

EER = \frac{BTU/h}{W}

Cooling capacity in BTU/h per watt of power — a common AC rating.

Refrigeration Tons

TR = \frac{Q}{12000}

Cooling capacity in tons, where one ton removes 12,000 BTU/h.

Airflow (Sensible)

NEWIntermediate

CFM = \frac{Q}{1.08 \, \Delta T}

Air volume flow needed to carry a sensible heat load (imperial units).

Carnot COP (Refrigerator)

COP = \frac{T_c}{T_h - T_c}

Maximum possible cooling efficiency between two temperatures (in kelvin).

Heat Pump COP

COP = \frac{T_h}{T_h - T_c}

Ideal efficiency of a heat pump running in heating mode.

Humidity Ratio

w = 0.622 \frac{p_v}{p - p_v}

Mass of water vapour per unit mass of dry air.

Relative Humidity

RH = \frac{p_v}{p_{sat}} \times 100

Vapour pressure as a percentage of the saturation pressure.

Fan Power

NEWIntermediate

P = \frac{Q \, \Delta p}{\eta}

Power a fan needs to move air against a pressure drop.

Sensible Heat Ratio

NEWIntermediate

SHR = \frac{Q_s}{Q_{total}}

Fraction of the cooling load that is sensible rather than latent.

Thermal Resistance (R-value)

R = \frac{L}{k}

Insulating power of a material layer of given thickness.

Log Mean Temperature Difference

LMTD = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}

Effective average temperature gap driving heat across an exchanger.

Duct Air Velocity

V = \frac{Q}{A}

Speed of air in a duct from flow rate and cross-section.

Seasonal Energy Efficiency (SEER)

NEWIntermediate

SEER = \frac{\text{annual BTU}}{\text{annual Wh}}

Cooling output over a season divided by electrical energy used.

Heating Degree Days

NEWIntermediate

HDD = \sum (T_{base} - T_{avg})

Cumulative measure of how much and how long outdoor temperature sits below a base.