Complete HVAC Formula Guide — Expanded sections, Worked examples.

Complete HVAC Formula Guide — expanded sections, worked examples.

Cooling and heating equations
R‑values and U‑values
Water system equations (hydronic)
Air change rate (ventilation)
Mixed air temperature (air mixing)
Ductwork equations and equivalent round size
Fan laws
Pump laws and NPSH
Condensate, humidification and humidifier heat gain
Expansion tanks (hydronic)
Air balance and economizer mass balance
Efficiencies, COP and EER
Cooling towers and heat exchangers (range/approach)
Moisture condensation on glass (surface temperature)
Electricity (power calculations)
Transient heating (loading docks / vestibules)
Refrigeration room ventilation (refrigerant leak control)
Flat‑oval duct formulas and equivalent diameter
Pipe expansion allowances (L, Z, U loops)
Steam and condensate (mass & pipe sizing)
Psychrometrics (humidity ratio, enthalpy)
Pools and domestic water heater sizing
Relief valve sizing and venting rules
Steel pipe geometry & unit conversions
Cooling tower water balances and cycles of concentration
Motor drive / belt drive formulas
Printable cheat sheet (compact)

1 Cooling and heating equations

Formulas

Sensible heat: Hs = 1.08 × CFM × ΔT (Btu/hr).
Latent heat (lb H2O/lb dry air): HL = 0.68 × CFM × ΔW (Btu/hr) or HL = 4840 × CFM × ΔW(grains).
Total heat: HT = Hs + HL = 4.5 × CFM × Δh (Btu/hr).
Conduction through envelope: H = U × A × ΔT (Btu/hr).
Sensible heat ratio: SHR = Hs / HT.

Definitions

CFM = airflow (ft³/min), ΔT = temperature difference (°F), ΔW = humidity ratio change (lb H2O/lb dry air) or grains/lb, Δh = enthalpy difference (Btu/lb).

Why this matters

Separate sensible and latent loads to size coils, choose coil face areas and ensure dehumidification capacity (SHR). The constants come from 60 × ρair × cp (approx 60×0.075×0.24 ≈ 1.08) and conversions for enthalpy/humidity.

Worked example

Room design: supply 1000 CFM, supply air 55°F, room 75°F → ΔT = 20°F. Hs = 1.08 × 1000 × 20 = 21,600 Btu/hr. If latent ΔW = 0.003 lb/lb → HL = 0.68 × 1000 × 0.003 = 2.04 Btu/hr (negligible here) → HT ≈ 21,602 Btu/hr.

ASHRAE refs

ASHRAE Handbook — Fundamentals: cooling/heating load methods and psychrometrics (see chapters on load calculations and psychrometrics).

2 R‑values and U‑values

Formulas

U = 1 / ΣR where ΣR is the sum of layer resistances (hr·ft²·°F/Btu).
R (for homogeneous layer) ≈ thickness / k (k = conductivity).

Definitions

U (Btu/hr·ft²·°F), R (hr·ft²·°F/Btu), include inside/outside film resistances and thermal bridging effects.

Why this matters

Envelope heat transfer uses H = U × A × ΔT. Accurate ΣR ensures correct conductive heat addition/subtraction from sensible loads.

Worked example

Wall assembly has ΣR = 10 hr·ft²·°F/Btu → U = 0.10. Area A = 200 ft², ΔT = 20°F → H = 0.10 × 200 × 20 = 400 Btu/hr.

ASHRAE refs

ASHRAE Handbook — Fundamentals: material properties and conductance tables.

3 Water system equations (hydronic)

Formulas

H = 500 × GPM × ΔT (Btu/hr).
For typical 12,000 Btu/hr per ton: GPM = (12,000 × Tons) / (500 × ΔT) → simplified rules: GPM_evap = (Tons × 24) / ΔT, GPM_cond = (Tons × 30) / ΔT (approx).

Why 500?

8.33 lb/gal × 60 min/hr × cp_water(1.0) ≈ 499.8 → rounded to 500.

Worked example

Chilled water system 10 tons, design ΔT = 10°F: GPM = (12,000×10) / (500×10) = 24 GPM (matches GPM_evap = 24×Tons/ΔT = 24×10/10 = 24).

ASHRAE refs

ASHRAE Handbook — HVAC Systems and Equipment / Fundamentals: hydronic system sizing tables and pump selection guidance.

4 Air change rate (ventilation)

Formulas

ACH = (CFM × 60) / Volume (hr⁻¹).
Conversely CFM = (ACH × Volume) / 60.

Why this matters

Convert between required air changes and ventilation supply flow. Use ASHRAE 62.1 occupant and area rates for required ventilation.

Worked example

Room volume 12,000 ft³, target 1.5 ACH → CFM = (1.5 × 12,000) / 60 = 300 CFM.

ASHRAE refs

ASHRAE Standard 62.1 — Ventilation for Acceptable Indoor Air Quality (ventilation rate procedures).

5 Mixed air temperature

Formula

T_MA = (T_RA × CFM_RA + T_OA × CFM_OA) / CFM_SA where CFM_SA = CFM_RA + CFM_OA.

Why this matters

Entering mixed air temperature sets coil entering condition for capacity and approach calculations. When humidity is significant, use enthalpy mixing (enthalpy weighted) instead of simple temperature mixing.

Worked example

Return 1800 CFM at 75°F, outside 200 CFM at 95°F → T_MA = (75×1800 + 95×200) / 2000 = (135000 + 19000)/2000 = 154000/2000 = 77°F.

ASHRAE refs

ASHRAE Handbook — Fundamentals: air mixing and ventilation impact on coil selection.

6 Ductwork equations and equivalent round size

Key relations

TP = SP + VP (total pressure = static + velocity pressure).
Velocity pressure VP (in. wg) ≈ V² / 4005 when V in fpm.
Velocity: V (fpm) = Q / Area_ft² = Q / ((W × H) / 144) where W,H in in.
Rectangular → equivalent round (DEQ) approximate empirical: DEQ ≈ 1.3 × (A×B)^0.625 / (A + B)^0.25 (PDF gives a similar relation).

Why this matters

Use friction charts (in. wg/100 ft) referenced to equivalent round diameter and chosen friction rate to size ducts; ensure acceptable velocities (mains vs branches).

Worked example

Branch flow Q = 800 CFM; rectangular duct W=10 in, H=6 in → area ft² = (10×6)/144 = 0.4167 ft² → V = 800 / 0.4167 ≈ 1920 fpm → VP = 1920²/4005 ≈ 921 in.wg? (check units: VP in in.wg ≈ V²/4005 → 1920²/4005 ≈ 921/4005? Actually compute: 1920²=3,686,400; /4005 ≈ 920.6 (in.wg) — this large value indicates high velocity; design target velocities are much lower, so increase duct area). Use friction charts for final sizing.

ASHRAE refs

ASHRAE Handbook — Fundamentals and HVAC Systems: duct design chapters and recommended friction rates.

7 Fan laws

Affinity laws

Flow ∝ RPM: CFM2 / CFM1 = RPM2 / RPM1.
Pressure ∝ (RPM)²: SP2 / SP1 = (RPM2 / RPM1)².
Power ∝ (RPM)³: BHP2 / BHP1 = (RPM2 / RPM1)³.

Power conversion (units)

BHP ≈ (CFM × SP × sp.gr.) / (6356 × FanEff) (PDF gives a constant form; verify unit system before using).

Worked example

Fan baseline: 10,000 CFM at 1000 RPM; at 800 RPM new CFM = 10,000 × 800/1000 = 8,000 CFM; SP scale = (0.8)² = 0.64 → new SP = 0.64 × SP1; BHP scales by (0.8)³ = 0.512.

ASHRAE refs

ASHRAE Handbook — HVAC Systems and Equipment: fan selection, system curves and VFD operation.

8 Pump laws and NPSH

Affinity laws

GPM ∝ RPM: GPM2 / GPM1 = RPM2 / RPM1.
Head ∝ (RPM)²: HD2 / HD1 = (RPM2 / RPM1)².
Power ∝ (RPM)³: BHP2 / BHP1 = (RPM2 / RPM1)³.

Pump power

BHP = (GPM × HD × SG) / (3960 × PumpEff) (3960 constant uses GPM, ft head).

NPSH available

NPSHavail = HA + Hs − HF − Hvp; must exceed NPSHreq (pump manufacturer) to avoid cavitation.

Worked example

Pump: required GPM 100, head 60 ft, SG=1, pump eff 0.7 → BHP ≈ (100×60×1) / (3960×0.7) ≈ 2.17 BHP.

ASHRAE refs

ASHRAE Handbook — HVAC Systems and Equipment and pump selection chapters; consult pump curves and manufacturer NPSH data.

9 Condensate, humidification, humidifier sensible heat

Condensate

GPM_condensate ≈ (CFM × ΔW) / (SpV × 8.33) (use grains or lb/lb consistent units; PDF shows grain forms with ×7000 conversion).

Humidification mass

LB steam/hr = (CFM × grains_req × 60) / 7000 = CFM × pounds_req × 60.

Humidifier sensible heat (PDF rule)

Hs = (0.244 × Q × ΔT) + (L × 380) where Q = lb steam/hr, ΔT = steam temp – supply air temp, L = manifold length (empirical term in PDF).

Worked example

2000 CFM, need to raise humidity by 40 grains → lb/hr = (2000 × 40 × 60)/7000 ≈ 685.7 lb/hr steam; convert to gallons condensate as needed.

ASHRAE refs

ASHRAE Handbook — Fundamentals: psychrometrics, humidification; manufacturer datasheets for steam injectors.

10 Expansion tanks

Concepts & variables

Use water specific volumes at fill and operating temps (V1, V2), system water volume Vs, pressures P1 (fill) and P2 (operating), and thermal expansion AT = T2 − T1 to size tank volume VT. PDF gives closed/diaphragm/open tank relations and system volume estimates (rule: ~12 gal/ton chilled, 35 gal/BHP).

Worked example (concept)

For a hydronic system Vs = 200 gal, ΔT = 40°F, lookup V1 and V2 from property tables → compute required tank using manufacturer equation (PDF suggests use of V1/V2 based relations). Use vendor calculator for accuracy.

ASHRAE refs

ASHRAE Fundamentals: properties of water and piping system expansions.

11 Air balance

Mass (CFM) relations

SA = RA + OA = RA + EA + RFA (supply must equal sum of return, exhaust, relief).
Economizer mode: OA = SA; RA = 0; ensure relief/discharge capacity to prevent overpressure.

Worked example

SA = 10,000 CFM, EA = 800 CFM, minimum OA required 1,200 CFM → RA = SA − OA = 8,800 CFM; RFA = OA − EA = 400 CFM relief required if EA < OA.

ASHRAE refs

ASHRAE 62.1 and ASHRAE Handbook: ventilation and air distribution guidance.

12 Efficiencies, COP and EER

Formulas

COP = Btu output / Btu input (dimensionless).
EER = Btu output / Watts input (EER = COP × 3.413 when converting units).
Overall thermal efficiency and combustion efficiency use gross input/output and stack loss definitions.

Worked example

A chiller producing 36,000 Btu/hr using 10,000 W → EER = 36,000 / 10,000 = 3.6; COP ≈ 3.6 / 3.413 ≈ 1.055 (low for chillers — indicates check units/conditions).

ASHRAE refs

ASHRAE Standard 90.1; Manufacturer performance ratings and handbook chapters.

13 Cooling towers and heat exchangers

Formulas

Range = EWT − LWT; Approach (tower) = LWT − ambient wet‑bulb (AWB).

Why this matters

Approach determines how close LWT can get to WB; smaller approach requires more cells or larger heat transfer area.

Worked example

Tower EWT = 95°F, LWT = 85°F → Range = 10°F. AWB = 75°F → Approach = 85 − 75 = 10°F.

ASHRAE refs

ASHRAE Handbook — HVAC Systems and Equipment: cooling towers and heat rejection chapters.

14 Moisture condensation on glass

Concept

Glass inner surface temperature depends on inside/outside temps, Uglass and film resistances. If Tglass < room dew point condensation occurs.

Worked example

If Tglass computed at 55°F and room dew point 57°F → condensation.

ASHRAE refs

ASHRAE Fundamentals: surface condensation and glazing thermal behavior.

15 Electricity

Formulas

kW = (V × A × PF) / 1000 for single-phase (three‑phase use √3 factor).
kVA² = kW² + kVAR² (vector relation), use PF to size transformers and conductors.

Worked example

3‑phase motor, V = 400 V, I = 50 A, PF = 0.9 → kW = √3 × 400 × 50 × 0.9 / 1000 ≈ 31.18 kW.

ASHRAE refs

ASHRAE and electrical design handbooks: motor starting and service sizing (also NEC/IE rules).

16 Loading docks / short‑duration heating

Method

Calculate volume (ft³). 2. Choose warm‑up time (min). 3. CFM = Volume / Time. 4. Use sensible heat Hs = 1.08 × CFM × ΔT to size heaters.

Worked example

Dock volume 20,000 ft³, want reheat in 10 min → CFM = 20,000 / 10 = 2,000 CFM; ΔT = 50°F → Hs = 1.08 × 2000 × 50 = 108,000 Btu/hr.

ASHRAE refs

ASHRAE handbook sections on space heating and specialized spaces.

17 Refrigeration equipment room ventilation

Rules (quick)

Enclosed equipment rooms: CFM = 100 × √G (G = largest system refrigerant mass, lb).
Partially enclosed: free opening area FA = √G (ft²).

Why

Provide dilute ventilation for potential refrigerant leak. Always verify to ASHRAE 15 and local code.

Worked example

Largest refrigerant charge G = 100 lb → CFM ≈ 100 × √100 = 100 × 10 = 1000 CFM.

ASHRAE refs

ASHRAE Standard 15 — Safety Standard for Refrigeration Systems.

18 Flat‑oval ductwork

Key relations

Compute cross‑sectional area A, perimeter P (given formulas) and then DEQ (equivalent round) by empirical DEQ formula in PDF, then use friction charts for DEQ.

Worked example

Compute A and P from major/minor axes, then use DEQ formula to find equivalent round for friction lookup.

ASHRAE refs

ASHRAE Fundamentals: duct shapes and equivalent diameters, friction charts.

19 Pipe expansion

Formulas (rules of thumb)

L‑bend leg length L ≈ 6.225 × V × A × D (PDF shows VAD grouping; treat VAD as expansion A) and similar L = 4 × VAD for Z bends and L = 6.225 × VAD for U loops; forces estimated as F ≈ (200–500 lb/pipe dia in²) × D (in) per PDF tables.

Why

Provide offsets/loop/leg length to absorb thermal expansion; check anchor forces.

Worked example

For a pipe with A = expansion inches, D = pipe OD and thermal expansion value, compute L using the formula and consult piping standards.

ASHRAE/ASME refs

Follow ASME B31.1/B31.3 and piping stress analysis standards for final calculations (PDF rules are engineering rules of thumb).

20 Steam and condensate

Mass & energy

lb steam/hr ≈ BTU/hr ÷ (latent heat per lb) — PDF uses approximation 1 lb steam ≈ 960 Btu (approx) and relations for condensate approximations (GPM water × ΔT factors).

Steam pipe sizing

PDF gives empirical relations linking W (lb/hr), ΔP, ID and velocity; use ASME/steam tables and manufacturer charts for accurate piping and trap sizing.

Worked example

Heating load 120,000 Btu/hr → steam required ≈ 120,000 / 960 ≈ 125 lb/hr (approx).

ASHRAE refs

ASHRAE Handbook — Fundamentals and ASME steam tables for detailed steam properties and piping sizing.

21 Psychrometrics

Key formulas

Humidity ratio: W = 0.622 × (Pw / (P − Pw)) where Pw = partial pressure of water vapor, P = total pressure.
RH = (W_actual / W_sat) × 100% or via Pw / P_sat relations.
Enthalpy & heat: Hs = m × cp × ΔT; HL = m × Lv × ΔW; HT = m × Δh.
PDF shows polynomial forms for W from Tdb/Twb (quick empirical forms) — use with caution; prefer psychrometric charts or libraries.

Worked example

For 75°F dry‑bulb and 60% RH: get Pw from tables or psychrometric function, compute W and enthalpy; use library for numbers.

ASHRAE refs

ASHRAE Handbook — Fundamentals: psychrometric properties, charts and equations.

22 Swimming pools and domestic water heater sizing

Pools

Pool volume (gal) = L × W × avg depth × 7.5.
Heater capacity: H_pool = H_heatup + H_surface_loss; H_heatup = (Gals × 8.34 × ΔT) / heat‑up time (hr); H_surface_loss = 5.5 Btu/hr·ft²·°F × ΔTwater‑air × pool area (adjust by wind factor).

Domestic water heaters

H_output = GPH × 8.34 × ΔT (Btu/hr); input = output / efficiency; convert kW via 3413 Btu/kW.

Worked example

Pool 30×15 ft, depth 5 ft → gal = 30×15×5×7.5 = 16,875 gal. To raise 20°F in 24 hr: H_heatup = (16875×8.34×20)/24 ≈ 117,188 Btu/hr.

ASHRAE refs

Use local codes, manufacturer sizing tables and ASHRAE guidance for domestic hot water systems and pool heat loss (ASHRAE Fundamentals).

23 Relief valve sizing and vent line length

Concepts

PDF provides empirical vent‑length formula and multiple relief valve area formulas depending on fluid (liquid, pilot, steam, gas) with correction factors K, KB, Kv, KN, KSH, Z, etc. These are safety critical and require full code (ASME/API) method and manufacturer verification.

Worked example (note)

Do not rely solely on rule‑of‑thumb — use ASME/API relief sizing procedures and vendor software.

ASHRAE/ASME refs

Use ASME Section I/VIII, API 520/521 for relief valve sizing and piping — PDF gives starting equations and gas properties.

24 Steel pipe geometry & weight per foot

Formulas

Area A = 0.785 × ID² (in²).
Water weight per foot Ww ≈ 0.3405 × ID² (lb/ft) (empirical shown).
Metal area AM = 0.785 × (OD² − ID²) etc.

Worked example

Pipe ID = 2 in → A = 0.785 × 4 = 3.14 in²; water weight per ft ~0.3405 × 4 = 1.362 lb/ft (verify with standards).

ASHRAE refs

Use standard pipe schedules and manufacturer tables for weights and dimensions.

25 Units and English/Metric conversions

Common conversions shown (CFM↔CMM, GPM↔LPM, Btu↔kJ, ft↔m, lb↔kg, grains↔lb) — keep units consistent in calculations; PDF includes metric equivalents and conversion factors.

26 Cooling tower water balance

Formulas

Cycles of concentration C = (E + D + B) / (D + B) where E = evaporation, D = drift, B = blowdown. PDF approximations: E ≈ GPM_cond × R × 0.0008, D ≈ GPM_cond × 0.0002 (empirical).

Worked example

Use condenser GPM and range R to estimate E and D, then compute required blowdown to keep cycles of concentration within water chemistry limits.

ASHRAE refs

ASHRAE Handbook — HVAC Systems and Equipment and water treatment guidance.

27 Motor drive / belt formulas

Formulas

Pulley speed equality: D_fp × RPM_fp = D_mp × RPM_mp; belt length BL formula shown in PDF (empirical geometry).

Worked example

To change fan speed by pulley ratio, apply D×RPM equality to compute new RPM and torque/power impacts.

ASHRAE refs

Fan and motor drive chapters in ASHRAE handbook; manufacturer belt catalogs for belt length/selection.

(Compact set of core formulas — paste into a one‑page printable file)

Hs = 1.08 × CFM × ΔT (Btu/hr)
HL = 0.68 × CFM × ΔW (Btu/hr)
HT = Hs + HL = 4.5 × CFM × Δh
H(envelope) = U × A × ΔT
H_water = 500 × GPM × ΔT
GPM ≈ (12,000 × Tons) / (500 × ΔT) (i.e., GPM = 24×Tons/ΔT)
ACH = (CFM × 60) / Volume
T_MA = (T_RA × CFM_RA + T_OA × CFM_OA) / CFM_SA
VP = V² / 4005 (V in fpm; VP in in.wg)
DEQ ≈ empirical rectangular→round formula (PDF)
Fan laws: Q∝N, ΔP∝N², Power∝N³
Pump BHP = (GPM × HD × SG) / (3960 × Eff)
NPSHavail = HA + Hs − HF − Hvp
lb steam/hr ≈ Btu/hr ÷ latent heat (≈960 Btu/lb approx in pdf)
W = 0.622 × Pw / (P − Pw) (humidity ratio)
Pool: gal = L×W×avg depth×7.5; H_heatup = (gals×8.34×ΔT)/hrs.

ASHRAE Standards and Handbook references (table)

Below are quick ASHRAE references tied to the sections above. Use the ASHRAE Handbook volumes and standards for authoritative procedures and sample chapters.

ASHRAE Handbook — Fundamentals: psychrometrics, heat gain/loss calculations, envelope conduction, duct design, piping & steam properties, water properties (relevant chapters: Load Calculations; Psychrometrics; Duct Design; Properties of Air and Water).
ASHRAE Handbook — HVAC Systems and Equipment: fans, pumps, cooling towers, heat exchangers, hydronics (system selection and performance).
ASHRAE Standard 62.1 — Ventilation for Acceptable Indoor Air Quality: ventilation rates and procedures (ventilation & IAQ sections referenced).
ASHRAE Standard 90.1 — Energy Standard for Buildings Except Low‑Rise Residential Buildings: equipment efficiency and envelope thresholds (efficiency section references).
ASHRAE Standard 15 — Safety Standard for Refrigeration Systems: refrigerant room ventilation and safety for refrigeration equipment (refrigeration room rules).

(For blog links, link to ashrae.org pages for the above Handbooks and Standards — use your organizational access to the ASHRAE library. The PDF you provided contains many of the same formulas and notes used above.)

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