What duct size do I need?
Type the airflow in CFM and choose a friction rate or a velocity. The duct calculator gives the round duct diameter, the air velocity, the friction rate, and the other side of an equivalent rectangular duct.
- Round duct diameter
- 10.21 in
Use a 10.21 in round duct (11 in rounded up): 703 ft/min at 0.08 in. w.c. per 100 ft.
- Next whole inchin
- 11
- Velocityft/min
- 703
- Friction ratein. w.c./100 ft
- 0.08
- Friction rate, Pa/mPa/m
- 0.654
- Reynolds number
- 61,531
Round duct diameter: 10.21 in. Use a 10.21 in round duct (11 in rounded up): 703 ft/min at 0.08 in. w.c. per 100 ft.
How to calculate
Duct calculator: the round duct size for an airflow in CFM by the equal-friction method or a target velocity, with the velocity, the friction rate and the equivalent rectangular duct.
Example with the default inputs (Airflow (CFM) 400, Size by Friction rate, Friction rate, in. w.c. per 100 ft 0.08): Use a 10.21 in round duct (11 in rounded up): 703 ft/min at 0.08 in. w.c. per 100 ft.
Method: Velocity method: D = √(4Q ÷ (πV)). Friction method: the D where f × ρ ÷ 2 × V² ÷ D equals the friction rate, with V = 4Q ÷ (πD²) and f from Colebrook–White. Rectangle: b with 1.30 (ab)^0.625 ÷ (a + b)^0.25 = D.
- Standard air at 20 °C: density 1.2041 kg/m³, kinematic viscosity 15.06 × 10⁻⁶ m²/s.
- Round galvanized steel duct, absolute roughness 0.15 mm. Flex duct is rougher and needs a larger size.
- Straight duct only: fittings add pressure drop, which the friction rate you choose has to allow for.
Worked examples
Each example is checked against the calculator on every build.
- Airflow (CFM) 400, Size by Friction rate, Friction rate, in. w.c. per 100 ft 0.08 gives Round duct diameter 10.21 in, Next whole inch 11.Source: Wikipedia, Darcy–Weisbach equation (Δp ÷ L = f × ρ ÷ 2 × V² ÷ D), https://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation, and Darcy friction factor formulae (Colebrook–White, f = 64 ÷ Re below Re 2,300), https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae (retrieved 2026-10-03); Wikipedia, Density of air (1.2041 kg/m³ at 20 °C, 101.325 kPa), https://en.wikipedia.org/wiki/Density_of_air; Engineering ToolBox, Air – Dynamic and Kinematic Viscosity (15.06 × 10⁻⁶ m²/s at 20 °C), https://www.engineeringtoolbox.com/air-absolute-kinematic-viscosity-d_601.html; Engineering ToolBox, Surface Roughness of Ventilation Ducts (galvanized steel 0.15 mm), https://www.engineeringtoolbox.com/surface-roughness-ventilation-ducts-d_209.html (retrieved 2026-10-03)
- Airflow (CFM) 100, Size by Friction rate, Friction rate, in. w.c. per 100 ft 0.08 gives Round duct diameter 6.09 in, Next whole inch 7.Source: Wikipedia, Darcy–Weisbach equation (Δp ÷ L = f × ρ ÷ 2 × V² ÷ D), https://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation, and Darcy friction factor formulae (Colebrook–White, f = 64 ÷ Re below Re 2,300), https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae (retrieved 2026-10-03); Wikipedia, Density of air (1.2041 kg/m³ at 20 °C, 101.325 kPa), https://en.wikipedia.org/wiki/Density_of_air; Engineering ToolBox, Air – Dynamic and Kinematic Viscosity (15.06 × 10⁻⁶ m²/s at 20 °C), https://www.engineeringtoolbox.com/air-absolute-kinematic-viscosity-d_601.html; Engineering ToolBox, Surface Roughness of Ventilation Ducts (galvanized steel 0.15 mm), https://www.engineeringtoolbox.com/surface-roughness-ventilation-ducts-d_209.html (retrieved 2026-10-03)
- Airflow (CFM) 400, Size by Velocity, Velocity, ft/min 700, Rectangular duct side 10 in gives Round duct diameter 10.24 in, Velocity, ft/min 700, Other rectangular side 8.78 in.Source: Wikipedia, Darcy–Weisbach equation (Δp ÷ L = f × ρ ÷ 2 × V² ÷ D), https://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation, and Darcy friction factor formulae (Colebrook–White, f = 64 ÷ Re below Re 2,300), https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae (retrieved 2026-10-03); Engineering ToolBox, Equivalent Diameter (Huebscher: de = 1.30 (a b)^0.625 ÷ (a + b)^0.25; 300 × 500 mm gives 420 mm), https://www.engineeringtoolbox.com/equivalent-diameter-d_205.html (retrieved 2026-10-03)
How it works
All maths runs in SI units. Airflow Q = CFM × 0.028316846592 ÷ 60 m³/s; 1 ft/min = 0.00508 m/s; 1 in. w.c. = 249.08891 Pa; 100 ft = 30.48 m.
Air and duct. Density ρ = 1.2041 kg/m³ and kinematic viscosity ν = 15.06 × 10⁻⁶ m²/s (air at 20 °C); roughness ε = 0.15 mm (galvanized steel).
Velocity method. D = √(4Q ÷ (π × V)), with V the velocity you type.
Friction method. For a diameter D: velocity V = 4Q ÷ (πD²); Reynolds number Re = V × D ÷ ν; friction factor f = 64 ÷ Re when Re < 2,300, otherwise the Colebrook–White equation 1/√f = −2 log₁₀(ε ÷ (3.7D) + 2.51 ÷ (Re √f)), solved by 100 fixed-point steps from f = 0.02; pressure drop per metre = f × ρ ÷ 2 × V² ÷ D (Darcy–Weisbach). The calculator finds the D from 1 mm to 10 m where that drop equals the friction rate you type (converted to Pa/m), by 200 bisection steps on the geometric mean of the bounds.
Results at that D. Velocity in ft/min; friction rate in in. w.c. per 100 ft and in Pa/m; Reynolds number; and the diameter rounded up to the next whole inch.
Rectangular duct. If you type a side a, the other side b solves 1.30 (a × b)^0.625 ÷ (a + b)^0.25 = D (Huebscher), by bisection from 1 nm to 1,000 km.
Rules
- Airflow 1 to 1,000,000 CFM; friction rate 0.001 to 10 in. w.c. per 100 ft; velocity 10 to 20,000 ft/min; rectangle side 0.01 to 5 m.
- If the diameter would fall outside 1 mm to 10 m, there is no answer: "No round duct from 1 mm to 10 m carries this airflow at this rate."
Output format
Diameters show in inches (US) or millimetres (Metric) to 2 decimals; velocity and Reynolds number to whole numbers; friction rate to 4 decimals and Pa/m to 3. The maths is in floating point (roots, logarithms and iteration), rounded half up for display.
Worked examples by hand
400 CFM at 700 ft/min, with a 10 in rectangle side. Area = 400 ÷ 700 = 0.5714 ft². D = √(4 × 0.5714 ÷ π) = 0.8530 ft = 10.24 in. The other side b solves 1.30 × (10 b)^0.625 ÷ (10 + b)^0.25 = 10.24: b = 8.78 in (check: 1.30 × 87.77^0.625 ÷ 18.78^0.25 = 10.24).
400 CFM at 0.08 in. w.c. per 100 ft. Target 0.08 × 249.08891 ÷ 30.48 = 0.6538 Pa/m. Try D = 0.2594 m (10.21 in): V = 4 × 0.18878 ÷ (π × 0.2594²) = 3.572 m/s (703 ft/min); Re = 3.572 × 0.2594 ÷ 15.06 × 10⁻⁶ = 61,530; Colebrook gives f = 0.02207; drop = 0.02207 × 1.2041 ÷ 2 × 3.572² ÷ 0.2594 = 0.654 Pa/m, the target. So D = 10.21 in, 11 in rounded up.
100 CFM at 0.08. The same search gives D = 0.15464 m = 6.09 in.
Equivalent rectangle. Huebscher’s 300 × 500 mm duct: 1.30 × 150,000^0.625 ÷ 800^0.25 = 419.98 mm, the 420 mm Engineering ToolBox gives.
Other questions people ask
How do I size a duct for CFM?
Pick a friction rate, such as 0.08 in. w.c. per 100 ft, and find the round diameter whose pressure drop at that airflow matches it. 400 CFM at 0.08 needs a 10.2 in duct, so a 10 or 11 in duct by your judgement of the system.
What friction rate should I use?
Home systems are often sized at 0.08 to 0.1 in. w.c. per 100 ft. The right value comes from the fan’s available pressure less the losses of the coil, filter, grilles and fittings, spread over the longest duct run.
How does the velocity method work?
Divide the airflow by the velocity you want to get the duct area, then find the diameter: D = √(4 × area ÷ π). 400 CFM at 700 ft/min needs 0.571 ft², a 10.24 in duct.
What is an equivalent rectangular duct?
A rectangle with the same friction and airflow as the round duct. The Huebscher formula, de = 1.30 (ab)^0.625 ÷ (a + b)^0.25, gives it; type one side and the calculator finds the other.
How many CFM does a 6 in duct carry?
About 100 CFM at 0.08 in. w.c. per 100 ft: the calculator gives 6.09 in for 100 CFM at that rate.
Does this work for flex duct?
The roughness used is galvanized steel. Flexible duct is rougher and sags, so it needs a larger size for the same airflow.