EngineeringFormulaFluid Mechanics
Duct Size Calculator
Size round or rectangular HVAC ducts from airflow and target velocity, or check velocity through an existing duct.
A duct size calculation starts with the continuity relationship between airflow, cross-sectional area, and average velocity. This calculator turns CFM and a target FPM into the required duct area, round diameter, square equivalent, and an optional rectangular size. It can also check the velocity through an existing round or rectangular duct so you can spot high-noise/high-friction situations before using a friction chart or full Manual D workflow.
Q · Duct airflow to size or check.
v · Design average duct velocity.
H · Optional known side for a rectangular duct suggestion.
This is a velocity-method sizing helper. It does not calculate friction loss, available static pressure, balancing dampers, flex-duct compression, fittings, or Manual D duct-system design.
Solution
Enter airflow and velocity or an existing duct size to calculate duct sizing results.
A = Q / v; d = √(4A / π)
Formula Sheet
- QAirflow
- vDuct Velocity
- ADuct Area
- dRound Diameter
- W, HRectangular Sides
- DeEquivalent Round Diameter
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| Q | Airflow | Volumetric airflow through the duct. | CFM, m³/h, L/s |
| v | Duct Velocity | Average air velocity through the duct cross-section. | ft/min, m/s |
| A | Duct Area | Internal cross-sectional duct area. | in², ft², m² |
| d | Round Diameter | Internal diameter of an equivalent round duct. | in, mm |
| W, H | Rectangular Sides | Internal width and height of a rectangular duct. | in, mm |
| De | Equivalent Round Diameter | Round diameter with comparable friction behavior for a rectangular duct. | in, mm |
How to Use This Calculator
- 01Use Size from CFM + FPM when you know the airflow and a target design velocity. The calculator returns required area, round diameter, square side, and optional rectangular side.
- 02Use Check Existing Duct when you know the duct size and airflow. Choose Round or Rectangular, then enter the inside dimensions.
- 03Enter internal duct dimensions, not outside dimensions including insulation or lining.
- 04For a rectangular suggestion, enter one fixed side in Required Size mode. The calculator divides required area by that side to give the other side.
- 05After choosing a practical duct size, use a static-pressure or friction-rate check to confirm the duct will not exceed the blower's available pressure budget.
- 06Review the velocity band as a rough comfort flag only. Final duct design still needs friction loss, fittings, available static pressure, and balancing.
How the Formula Works
The core relationship is A = Q/v. In imperial HVAC terms, Q is airflow in CFM, v is average velocity in ft/min, and A is duct area in ft². Multiplying A by 144 gives square inches for layout.
For a round duct, A = πd²/4, so d = √(4A/π). The calculator reports that round diameter in inches, plus a square side √A for quick comparison.
For a rectangular duct, velocity check uses A = W×H and v = Q/A. The equivalent round diameter uses the common HVAC equivalent-diameter equation De = 1.30(ab)^0.625/(a+b)^0.25 for comparing rectangular ducts to round duct friction charts.
Worked Example 01
400 CFM branch at 800 FPM
Known
- Airflow (Q): 400 CFM
- Target velocity (v): 800 ft/min
Formula
d = √(4A / π)
Substitution
A = 400/800 = 0.5 ft² = 72 in²; d = √(4×72/π)
Result
d ≈ 9.57 in, so a nominal 10 in round duct is the next practical size
The required area is 72 square inches. A round duct with the same area has an exact diameter of about 9.57 inches.
Worked Example 02
Rectangular option with one fixed side
Known
- Airflow (Q): 1200 CFM
- Target velocity (v): 800 ft/min
- Fixed side: 8 in
Formula
Other side = A / fixed side
Substitution
A = 1200/800 = 1.5 ft² = 216 in²; other side = 216/8
Result
Other side = 27 in
An 8 by 27 inch rectangular duct has the same 216 in² area needed to carry 1200 CFM at 800 FPM.
Worked Example 03
Velocity through a 14 inch round duct
Known
- Airflow (Q): 1200 CFM
- Diameter (d): 14 in
Formula
v = Q / A
Substitution
A = π×14²/4 = 153.94 in² = 1.069 ft²; v = 1200/1.069
Result
v ≈ 1122 ft/min
That velocity is relatively high for a quiet branch, so the duct may need friction/noise review before final selection.
Applications
- 01Sizing a supply or return branch from target CFM and FPM
- 02Checking whether an existing duct is running at an unusually high average velocity
- 03Finding a quick round duct diameter before checking friction loss
- 04Comparing rectangular duct options with equivalent round diameter and aspect ratio
Assumptions
- 01Uses average duct velocity, not peak local velocity.
- 02Duct dimensions are internal clear dimensions.
- 03Required-size mode is a velocity-method geometry estimate, not a pressure-loss calculation.
- 04Equivalent diameter is most useful for rectangular duct comparison against round-duct friction references.
Where This Model Stops
- 01Does not calculate friction loss, available static pressure, fitting losses, duct roughness, leakage, balancing, or blower performance.
- 02Does not round to every local stocked duct size or verify aspect-ratio, sheet-metal gauge, insulation, fire/smoke damper, or code clearance requirements.
- 03Does not replace ACCA Manual D, SMACNA design tables, or a project-specific HVAC design.
- 04Velocity bands are broad screening guidance only; acceptable velocity depends on noise, location, duct type, and pressure budget.
- 05Flex duct compression and bends can reduce effective airflow significantly and are not modeled here.
References
- [1]Duct Velocity
Engineering ToolBox
Reference for v = Q/A and round/rectangular duct velocity formulas in imperial and SI units.
- [2]Equivalent Diameter - Rectangular vs. Circular HVAC Ducts
Engineering ToolBox
Reference for equivalent round diameter and rectangular/round duct comparison.
Frequently Asked Questions
Is this the same as a Manual D duct design?
No. This is a velocity-method sizing and checking calculator. Manual D also considers friction rate, available static pressure, fittings, equivalent length, leakage, and balancing.
What target velocity should I use?
Residential branch ducts are often screened around 500-900 FPM, with lower velocities generally quieter and larger. Use project standards or Manual D for final values.
How is this different from the CFM Calculator?
The CFM Calculator solves airflow and ACH relationships. This page is focused on duct-size selection: required area, round diameter, rectangular side, equivalent diameter, and velocity screening.
Why does the rectangular result show equivalent round diameter?
Rectangular ducts with the same area can have different friction behavior. Equivalent round diameter helps compare a rectangular duct to round-duct friction charts.
Should I size by velocity or friction rate?
Velocity sizing is a quick geometry screen and helps control noise. Friction-rate sizing is needed for real duct design because it checks whether the blower has enough available static pressure for the full run and fittings.