Engineering reference // HVAC

Drawing No. EH–TH–024 // Thermal Engineering & HVAC

HVAC Formula Sheet

A practical HVAC reference connecting envelope transmission, airflow, psychrometrics, moisture control, ventilation, fan power and equipment efficiency. Mass-based moist-air equations are emphasized because air density and psychrometric properties vary with pressure, temperature and humidity.

Fast reference, with engineering context

Use the equations directly for screening calculations, then open the linked EngineerHub tools for input handling and unit conversion. Formula applicability and major limitations are stated beside each relation.

Start with Envelope Formula summary

Reference conventions

q̇ = UAΔTEnvelope transmission

q̇ = ṁcₚΔTSensible air heat

q̇ = ṁdaΔhTotal moist-air heat

ACH = 3600Q/VAir changes per hour

Room sensible and latent heat balance

HVAC sizing combines transmission, internal/solar loads, ventilation/infiltration and supply-air psychrometrics. A single formula rarely represents the full building load.

01 // Envelope transmission heat

For steady transmission through an assembly represented by an overall U-factor, heat flow is proportional to area and temperature difference.

Core relation

q̇ = UA(T_in − T_out)

R″ = 1/U

Symbol	Meaning	SI units	US customary
q̇	Transmission heat rate	W	Btu/h
U	Overall assembly U-factor	W/(m²·K)	Btu/(h·ft²·°F)
A	Assembly area	m²	ft²
ΔT	Indoor-outdoor temperature difference	K	°F

Open Wall Heat Transfer Calculator Worked example ↓

Worked example — winter wall transmission

Given: U = 0.35 W/(m²·K), A = 120 m², indoor-outdoor ΔT = 25 K.

q̇ = 0.35×120×25 = 1050 W

Answer: q̇ = 1.05 kW.

US check: ≈3583 Btu/h.

This is transmission only; infiltration, ventilation, thermal bridges and internal/solar gains are separate.

For dynamic cooling loads, thermal storage and solar/radiant effects matter. ASHRAE heat-balance or RTS methods are more complete than steady UAΔT.

02 // Sensible heat carried by air

For a known dry-air mass flow, the sensible heat associated with a dry-bulb temperature change is approximated with moist-air specific heat.

Core relation

q̇_s ≈ ṁ_da c_p,ma ΔT

c_p,ma ≈ 1.006 + 1.86W kJ/(kg_da·K)

Symbol	Meaning	SI units	US customary
ṁda	Dry-air mass flow	kgda/s	lbda/h
cp,ma	Moist-air heat capacity per kg dry air	kJ/(kgda·K)	Btu/(lbda·°F)
W	Humidity ratio	kgw/kgda	lbw/lbda
ΔT	Dry-bulb temperature change	K	°F

Open HVAC BTU Calculator Worked example ↓

Worked example — cooling supply air sensibly

Given: ṁda = 1.5 kg/s, cp ≈ 1.006 kJ/(kg·K), ΔT = 12 K.

q̇s = 1.5×1.006×12 = 18.108 kW

Answer: q̇s ≈ 18.1 kW.

US check: ≈61,800 Btu/h.

For precision, use the actual moist-air state instead of a fixed volumetric ‘air factor’.

ASHRAE also publishes convenient standard-air volumetric factors, but mass-based calculation is more accurate when altitude or temperature differs significantly from standard conditions.

03 // Total moist-air heat

The total heating/cooling rate of an airstream follows directly from the moist-air enthalpy difference.

Core relation

q̇_t = ṁ_da(h₂ − h₁)

ṁ_da = V̇ / v

Symbol	Meaning	SI units	US customary
h	Moist-air enthalpy	kJ/kgda	Btu/lbda
ṁda	Dry-air mass flow	kgda/s	lbda/h
V̇	Moist-air volume flow	m³/s	cfm
v	Specific volume per dry air	m³/kgda	ft³/lbda
q̇t	Total heat rate	kW	Btu/h

Open HVAC BTU Calculator Worked example ↓

Worked example — cooling a moist-air stream

Given: ṁda = 1.5 kg/s; entering h₁ = 60 kJ/kgda; leaving h₂ = 42 kJ/kgda.

q̇removed = 1.5(60−42) = 27.0 kW

Answer: 27.0 kW of total cooling.

US check: ≈92,100 Btu/h.

Use a consistent psychrometric enthalpy reference within one unit system.

Cooling below dew point also removes condensate. A complete coil energy balance may include the enthalpy of drained condensate.

04 // Humidity ratio from vapor pressure

At a known total pressure, humidity ratio follows from water-vapor partial pressure.

Core relation

W = 0.621945 p_w/(p − p_w)

p_w ≈ φ p_ws(T_db)

Symbol	Meaning	SI units	US customary
W	Humidity ratio	kgw/kgda	lbw/lbda
pw	Water-vapor partial pressure	Pa or kPa	psia
p	Total absolute pressure	Pa or kPa	psia
φ	Relative humidity	fraction or %	fraction or %
pws	Saturation vapor pressure at dry bulb	Pa or kPa	psia

Open Wet-Bulb Calculator Worked example ↓

Worked example — 25°C and 50% RH at sea-level pressure

Given: Tdb = 25°C, RH = 50%, pws ≈ 3.1692 kPa, p = 101.325 kPa.

pw = 0.5×3.1692 = 1.5846 kPa

W = 0.621945×1.5846/(101.325−1.5846) = 0.009881 kg/kg

Answer: W ≈ 9.88 g/kg dry air.

Use local station pressure for altitude-sensitive psychrometrics.

Relative humidity alone does not identify moisture content; the same RH at different temperatures corresponds to different humidity ratio and dew point.

05 // Cooling and dehumidification moisture removal

The water removed from an airstream follows directly from the humidity-ratio reduction.

Core relation

ṁ_w = ṁ_da(W₁ − W₂)

q̇_{latent,approx} ≈ ṁ_w h_fg

Symbol	Meaning	SI units	US customary
ṁw	Condensate / moisture-removal rate	kg/s	lb/h
ṁda	Dry-air mass flow	kg/s	lb/h
W₁,W₂	Entering/leaving humidity ratio	kg/kgda	lb/lbda
hfg	Approx. vaporization enthalpy	kJ/kg	Btu/lb

Open Dew Point Calculator Worked example ↓

Worked example — dehumidifying an airstream

Given: ṁda = 1.5 kg/s, W₁ = 0.012, W₂ = 0.008 kg/kgda.

ṁw = 1.5(0.012−0.008) = 0.006 kg/s

ṁw = 21.6 kg/h

Approx. latent rate using 2500 kJ/kg = 15 kW

Answer: 21.6 kg/h of condensate; approximate latent component 15 kW.

Use the full moist-air/condensate enthalpy balance for accurate coil duty.

The 2500 kJ/kg latent approximation is convenient but not a substitute for a psychrometric energy balance when coil leaving conditions and condensate temperature matter.

06 // Air changes per hour

ACH normalizes ventilation or infiltration flow to the room volume.

Core relation

ACH = 3600 V̇ / V_room

V̇ = ACH·V_room/3600

Symbol	Meaning	SI units	US customary
ACH	Air changes per hour	h⁻¹	h⁻¹
V̇	Volumetric airflow	m³/s	cfm
Vroom	Room volume	m³	ft³

Open Ventilation & ACH Calculator Worked example ↓

Worked example — ventilating a 250 m³ room

Given: V̇ = 0.25 m³/s and room volume = 250 m³.

ACH = 3600×0.25/250 = 3.6 h⁻¹

Answer: ACH = 3.6 air changes/h.

US check: 0.25 m³/s ≈ 530 cfm.

ACH is a volumetric turnover metric; it does not directly measure contaminant-removal effectiveness.

Outdoor-air requirements may be based on occupancy, floor area, contaminant generation or code-prescribed minimums rather than ACH alone.

07 // Fan / air-moving power

Ideal air power is pressure rise times volumetric flow; divide by fan/system efficiency for shaft or electrical input as appropriate.

Core relation

P = Δp V̇ / η

P_air = Δp V̇

Symbol	Meaning	SI units	US customary
P	Input power represented by η	W	hp
Δp	Fan total/static pressure rise, consistently defined	Pa	in. w.g. or lbf/ft²
V̇	Airflow	m³/s	cfm
η	Fan/drive efficiency used in equation	fraction	fraction

Open Ventilation & ACH Calculator Worked example ↓

Worked example — fan moving 2.5 m³/s

Given: V̇ = 2.5 m³/s, pressure rise = 600 Pa, overall efficiency = 0.65.

P = 600×2.5/0.65 = 2308 W

Answer: P ≈ 2.31 kW.

US check: ≈3.09 hp.

Be explicit whether η is fan-only, fan+drive, or wire-to-air efficiency.

Actual system operating point is set by the intersection of the fan curve and system-resistance curve. Filters and dampers change pressure demand.

08 // COP and EER

Coefficient of performance compares useful heating/cooling output to input power. EER is a common I-P cooling-efficiency expression.

Core relation

COP = Q̇_useful/P_input

EER [Btu/(Wh)] ≈ 3.41214 × COP

Symbol	Meaning	SI units	US customary
COP	Coefficient of performance	dimensionless	dimensionless
Q̇useful	Heating or cooling output	W	Btu/h
Pinput	Electrical input	W	W
EER	Energy efficiency ratio	—	Btu/(Wh)

Open Heat Pump Sizing Tool Worked example ↓

Worked example — heat pump at one operating point

Given: Useful heat output = 12 kW; electrical input = 3 kW.

COP = 12/3 = 4.0

EER-equivalent = 3.41214×4 = 13.65 Btu/(Wh)

Answer: COP = 4.0; equivalent EER ≈ 13.65.

Do not compare COP/EER values measured at different rating conditions as though they were identical.

Seasonal metrics (SEER, SCOP, HSPF and regional variants) include part-load and climate assumptions and are not simple point COPs.

09 // Quick formula summary

Compact print reference. Use the detailed sections above for definitions and limitations.

Topic	Equation	Purpose	Tool
Envelope	q̇=UAΔT	Transmission	Wall heat transfer
Sensible air	q̇=ṁcₚΔT	Dry-bulb load	HVAC BTU
Total moist air	q̇=ṁdaΔh	Sensible + latent	HVAC BTU
Humidity ratio	W=0.621945pw/(p−pw)	Moisture state	Wet bulb
Moisture removal	ṁw=ṁdaΔW	Condensate	Dew point
ACH	ACH=3600Q/V	Ventilation turnover	Ventilation
Fan power	P=ΔpQ/η	Air-moving power	Ventilation
COP	COP=Qout/Pin	Equipment efficiency	Heat pump

10 // Assumptions & limitations

Fundamental equations are only useful when their assumptions match the actual problem.

11 // Technical references

ASHRAE 2025 is the primary source basis. The sheet uses mass-based equations where practical and labels common approximations as approximations.

HVAC Formula Sheet

Fast reference, with engineering context

Reference conventions

Room sensible and latent heat balance

01 // Envelope transmission heat

This is transmission only; infiltration, ventilation, thermal bridges and internal/solar gains are separate.

02 // Sensible heat carried by air

For precision, use the actual moist-air state instead of a fixed volumetric ‘air factor’.

03 // Total moist-air heat

Use a consistent psychrometric enthalpy reference within one unit system.

04 // Humidity ratio from vapor pressure

Use local station pressure for altitude-sensitive psychrometrics.

05 // Cooling and dehumidification moisture removal

Use the full moist-air/condensate enthalpy balance for accurate coil duty.

06 // Air changes per hour

ACH is a volumetric turnover metric; it does not directly measure contaminant-removal effectiveness.

07 // Fan / air-moving power

Be explicit whether η is fan-only, fan+drive, or wire-to-air efficiency.

08 // COP and EER

Do not compare COP/EER values measured at different rating conditions as though they were identical.

09 // Quick formula summary

10 // Assumptions & limitations

11 // Technical references

12 // Related EngineerHub tools

Related resources