CFM Formula for HVAC Systems: Every Equation You Need
The Core CFM Formula
The fundamental relationship in HVAC duct sizing is:
Q = A × V
Where:
- Q = airflow in CFM (Cubic Feet per Minute)
- A = cross sectional area of the duct in square feet
- V = air velocity in FPM (Feet per Minute)
This single formula connects duct size, airflow, and velocity. If you know any two, you can solve for the third.
Duct Area Formulas
Round Duct
A = π × (D/2)²
Where D is the diameter in feet (divide inches by 12).
Simplified: A = π × D² / 4
Rectangular Duct
A = W × H
Where W and H are width and height in feet.
Round Equivalent for Rectangular
De = 1.3 × (a × b)^0.625 / (a + b)^0.25
Where a and b are rectangular sides in inches.
CFM from Duct Size and Velocity
If you know the duct size and want to find the airflow capacity:
CFM = A × V
Example: 10 inch round duct at 700 FPM
- Convert 10 inches to feet: 10/12 = 0.833 ft
- Area: π × (0.833/2)² = π × 0.1736 = 0.545 sq ft
- CFM = 0.545 × 700 = 382 CFM
Duct Size from CFM and Velocity
If you know the required CFM and want to find the duct diameter:
D (inches) = √(4 × CFM / (π × V)) × 12
Example: 200 CFM at 700 FPM
- D = √(4 × 200 / (π × 700)) × 12
- D = √(800 / 2199) × 12
- D = √0.364 × 12
- D = 0.603 × 12
- D = 7.2 inches → round up to 8 inch duct
Velocity from CFM and Duct Size
If you know CFM and duct size, calculate velocity to check noise levels:
V = CFM / A
Example: 300 CFM through a 10 inch duct
- Area = π × (10/24)² = 0.545 sq ft
- V = 300 / 0.545 = 550 FPM ✅ (well within quiet range)
BTU to CFM Conversion
CFM = BTU / (1.08 × ΔT)
Where:
- BTU = heating or cooling load in BTU/hr
- ΔT = temperature difference between supply and return air
- 1.08 = constant (density × specific heat × conversion)
| Application | ΔT | Simplified Formula |
|---|---|---|
| Cooling | 20°F | CFM = BTU / 21.6 |
| Gas furnace heating | 60°F | CFM = BTU / 64.8 |
| Heat pump heating | 30°F | CFM = BTU / 32.4 |
Tonnage to CFM
CFM = Tons × 400
| Tonnage | CFM |
|---|---|
| 1 ton | 400 CFM |
| 1.5 tons | 600 CFM |
| 2 tons | 800 CFM |
| 3 tons | 1,200 CFM |
| 4 tons | 1,600 CFM |
| 5 tons | 2,000 CFM |
CFM per Square Foot Rule
CFM = Floor Area (sq ft) × 1
This simple rule works for standard residential spaces with 8 foot ceilings and average insulation.
Pressure Loss Formula
ΔP = f × (TEL / 100)
Where:
- ΔP = pressure drop in inches of water gauge (in/wg)
- f = friction rate (in/wg per 100 ft)
- TEL = Total Effective Length in feet
Available Friction Rate
f = (ASP / TEL) × 100
Where:
- f = available friction rate
- ASP = Available Static Pressure for ductwork (in/wg)
- TEL = longest duct run’s Total Effective Length
Quick Reference: All Formulas
| What You Need | Formula |
|---|---|
| CFM from duct size | CFM = A × V |
| Duct diameter from CFM | D = √(4 × CFM / (π × V)) × 12 |
| Velocity from CFM | V = CFM / A |
| Round duct area | A = π × (D/2)² |
| CFM from BTU | CFM = BTU / (1.08 × ΔT) |
| CFM from tonnage | CFM = Tons × 400 |
| Pressure loss | ΔP = f × (TEL / 100) |
| Friction rate | f = (ASP / TEL) × 100 |
| Rect to round | De = 1.3 × (a×b)^0.625 / (a+b)^0.25 |
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