Formulas
The formulas our calculators use, grouped by topic. Each has a note on when to use it and a link to the matching calculator.
Airflow and traverse
Velocity from velocity pressure
V = 4005 × √VP
Use with a pitot tube reading in in. w.c. at standard air. 1.00 in. gives 4005 FPM.
Airflow
CFM = V × A
Use with the average velocity and the duct area in square feet.
Duct area
Rectangular: A = L × W ÷ 144 · Round: A = π × D² ÷ 4 ÷ 144
Use with inside dimensions in inches (take off the lining) to get square feet.
Equal-area traverse points
Line of N points at (2i + 1) ÷ (2N) of the side · Round, distance from wall = D × (1 − √((2k − 1) ÷ N)) ÷ 2
Use to find where to put the probe marks. Log-Tchebycheff rectangular points use the TSI-106 fractions.
Outside air
Design %OA
%OA = design OA ÷ design supply CFM
Use to see the %OA the design calls for.
%OA by temperature
%OA = (RAT − MAT) ÷ (RAT − OAT)
Use with return, mixed, and outdoor air temperatures when the spread is at least a few degrees.
OA CFM and mixed air target
OA CFM = %OA × supply CFM · MAT = OAT × %OA + RAT × %RA
Use to find the OA CFM, or the mixed air temperature to aim for.
Setting OA by static pressure
Target RA = actual SA − design OA · Target RA SP = (target RA ÷ actual SA)² × RA SP · Actual RA = √(SP2 ÷ SP1) × RA CFM1 · Actual OA = actual SA − actual RA
Use when the return air static pressure method is the way to set the minimum OA.
RVA and grilles
Field Ak and percent open
Ak = CFM ÷ FPM · % open = Ak ÷ grille size
Use with a known CFM and the average RVA FPM on one grille.
CFM from RVA
CFM = Ak × FPM
Use with a grille's Ak and the RVA reading.
Ak from a unit traverse (several grilles)
Factor = (CFM ÷ average FPM) ÷ total area · Ak = factor × area
Use when a traverse gives the total CFM and RVA readings are taken on up to 12 grilles.
Percent of design
% of design = reading CFM ÷ design CFM
Use for prelim and final readings on each grille. The key grille is the one with the lowest prelim percent.
Fans and sheaves
Desired RPM
Ratio = design ÷ actual CFM · Desired RPM = actual fan RPM × ratio
CFM changes in proportion to RPM.
Amp limit
Amp limit = ∛(FLA ÷ measured amps) · %Change = the smaller of the ratio and the amp limit
Amps change with the cube of the speed, so use this before speeding a fan up.
New motor sheave PD
Motor PD = %Change × actual fan RPM × fan PD ÷ motor RPM
Use to size a new motor sheave. Use mid range on a variable sheave.
New fan sheave PD
Fan PD = motor PD × motor RPM ÷ (actual fan RPM × %Change)
Use to size a new fan sheave.
Belt length
L = 1.57 × (D + d) + 2 × CD + (D − d)² ÷ (4 × CD)
D is the larger PD and d the smaller. Not for drives with an idler.
Coils
Coil area
Area (sq ft) = L × W ÷ 144
Use with the coil face dimensions in inches, or the area from the submittals.
Airflow from Velocity Grid readings
Area used = gross area × 0.84 · CFM1 = average FPM × area used
Use only with a Velocity Grid. 0.84 is the Velocity Grid coil factor.
Correct for the static pressure change
Final CFM = √(static before test ÷ static during test) × CFM1
Use because the static pressure changes with the filters out and the doors open.
Target discharge static
Target SP = static before test × (design CFM ÷ final CFM)²
Use to find the discharge static the unit should read at design airflow (static changes with the square of the CFM).
Kitchen hoods
CFM per filter from face velocity
CFM = average FPM × conversion factor (Greenheck / Accurex) · CFM = free area × average FPM × K (CaptiveAire)
Use with the filter-face readings the manufacturer calls for (Velocity Grid or rotating vane). The factor depends on the make, filter type, filter size and instrument; sum each filter's CFM for the hood.
CFM from a hood test port
CFM = K × √ΔP
Use on hoods with a published K-factor per section (Halton KVL/KVM by KSA filter count).
CFM from design SP (square-root ratio)
Actual CFM = design CFM × √(measured SP ÷ design SP)
Use with the design CFM and SP on the hood label or submittal; run the exhaust and the capture jet separately.
Make-up air plenum
ASP: CFM = W (in) × L (in) × FPM × 0.62 ÷ 144 (14/18 in.), × 0.95 (10 in.) · PSP: CFM = FPM × (W ÷ 12) × L (ft) × K
Use with Velocity Grid readings along the plenum length. Compare the make-up total to the measured exhaust for the balance.
Water and glycol
Feet of head from PSI
ft = PSI × 2.31 (water) · ft = PSI × 2.31 ÷ SG (other fluids)
Glycol factors at 50°F, % by mass (ASHRAE): ethylene 30% 2.20, 35% 2.18, 40% 2.16, 45% 2.15, 50% 2.13; propylene 30% 2.25, 35% 2.24, 40% 2.23, 45% 2.22, 50% 2.21. For other temps use the Specific Gravity calculator.
Evaporator flow
GPM = tons × 24 ÷ (EWT − LWT) · Tons = GPM × ΔT ÷ 24
Rule of thumb 2.4 GPM/ton.
Condenser flow
GPM = tons × 30 ÷ (LWT − EWT) · Tons = GPM × ΔT ÷ 30
Rule of thumb 3.0 GPM/ton.