Duct sizing calculator
Enter the airflow and one of friction rate (equal-friction method), velocity or diameter to get the round duct diameter, a rectangular size, velocity and velocity pressure at once. The equations with numbers filled in are under Calculation steps; constants and sources are under Basis further down.
Basis
Friction loss in a round duct comes from the Darcy-Weisbach equation with the Colebrook friction factor. When sizing by friction rate, the diameter that gives that R is searched for; a rectangular duct is matched by its circular equivalent, which has the same friction loss at the same airflow.
| Item | Equation | Notes · basis |
|---|---|---|
| Friction loss (Darcy-Weisbach) | R = Δp/L = (f / D) · ρV²/2 | R in Pa/m, D in m, ρ in kg/m³, V in m/s. The Darcy equation of the ASHRAE Duct Design chapter |
| Friction factor (Colebrook) | 1/√f = −2 log₁₀( ε/(3.7 D) + 2.51/(Re √f) ) | Re ≥ 2300. f appears on both sides, so it is iterated (from the Haaland estimate to a relative change of 10⁻¹²). The 2300 to 4000 transition range also uses it, which errs on the high side |
| Friction factor (laminar) | f = 64 / Re | Re < 2300 (Hagen-Poiseuille); flagged as laminar in the result |
| Reynolds number, velocity pressure | Re = V·D / ν, Pv = ρV²/2 | V = Q / A, A = πD²/4 |
| Air density | ρ = p / (R_da · T) | Dry air, p = 101.325 kPa, R_da = 287.042 J/(kg·K) (ASHRAE 2017 chapter 1, the same constant as the psychrometric calculator). 1.204 kg/m³ at 20 °C |
| Viscosity (Sutherland) | μ = μ₀ (T/T₀)^1.5 · (T₀ + S)/(T + S), ν = μ/ρ | Air: μ₀ = 1.716 × 10⁻⁵ Pa·s, T₀ = 273.15 K, S = 110.4 K (White). At 20 °C ν = 1.506 × 10⁻⁵ m²/s, within 1 % of common property tables |
| Rectangular equivalent (Huebscher) | De = 1.30 (a·b)^0.625 / (a + b)^0.25 | The round diameter with equal friction loss for the same airflow and length (ASHRAE Duct Design chapter). Example: 400 × 200 mm gives 305 mm. The actual velocity in the rectangular duct is Q/(a·b) |
| Standard sizes | D, a, b → ⌈x / 50⌉ × 50 mm | The round diameter and both rectangular sides are rounded up to 50 mm (only the free side when one side is fixed). The equivalent diameter only grows when a side grows, so it ends up at or above the calculated value and the friction loss does not exceed the input. Velocity and loss are then recalculated. Check the manufacturer's size list |
| Rectangular limits | 1 ≤ a/b ≤ 8, short side ≥ 50 mm | Above 4 : 1 a warning is shown (more perimeter for the same area means more friction and material). Above 8 : 1, or with a short side under 50 mm, the calculator does not compute |
Material roughness ε
Roughness category values from Table 1 of the ASHRAE Handbook Fundamentals (SI) Duct Design chapter (Smooth 0.03, Medium smooth 0.05, Average 0.09, Medium rough 0.9, Rough 3.0 mm). Each material is one the same table places in that category. The same material varies with joint spacing and workmanship, so enter other values with Custom roughness.
| Material | ε (mm) | ASHRAE category |
|---|---|---|
| Galvanized steel | 0.09 | Average |
| Smooth (drawn tubing, PVC pipe) | 0.03 | Smooth |
| Commercial steel | 0.05 | Medium smooth |
| Fibrous glass duct | 0.9 | Medium rough |
| Flexible duct (fully extended) | 3.0 | Rough |
Air properties (dry air, 101.325 kPa)
| Temperature °C | Density ρ kg/m³ | Viscosity μ Pa·s | Kinematic viscosity ν m²/s |
|---|---|---|---|
| −20 | 1.3944 | 1.615 × 10⁻⁵ | 1.158 × 10⁻⁵ |
| 0 | 1.2923 | 1.716 × 10⁻⁵ | 1.328 × 10⁻⁵ |
| 20 | 1.2042 | 1.813 × 10⁻⁵ | 1.506 × 10⁻⁵ |
| 40 | 1.1272 | 1.907 × 10⁻⁵ | 1.692 × 10⁻⁵ |
| 60 | 1.0596 | 1.999 × 10⁻⁵ | 1.886 × 10⁻⁵ |
Choosing velocity and friction rate
Korean HVAC textbooks divide ducts into low-velocity ducts (15 m/s or less) and high-velocity ducts above that. The calculator warns when the round or rectangular velocity is above 15 m/s.
The equal-friction method sizes every section with the friction rate chosen for the main duct (commonly 0.1 mmAq/m, about 1 Pa/m). Change only the airflow for each section.
Worked example
Airflow 10,000 m³/h, friction rate 1.0 Pa/m, galvanized steel (ε 0.09 mm), air at 20 °C: Q = 2.778 m³/s, D = 649.9 mm, V = 8.37 m/s, Re = 361,000, f = 0.0154. Rounded up to 650 mm.
As a 2 : 1 rectangle the same duct is 853 × 427 mm, or 900 × 450 mm with both sides rounded up to 50 mm (equivalent 686 mm, actual velocity 6.86 m/s, friction 0.77 Pa/m).
Sources
- ASHRAE Handbook, Fundamentals (SI), Duct Design chapter: Darcy and Colebrook equations, Table 1 roughness, Huebscher circular equivalent
- Colebrook, C. F. (1939), Turbulent flow in pipes, Journal of the Institution of Civil Engineers 11
- Huebscher, R. G. (1948), Friction equivalents for round, square and rectangular ducts, ASHVE Transactions 54
- Haaland, S. E. (1983), Simple and explicit formulas for the friction factor in turbulent pipe flow, Journal of Fluids Engineering 105 (starting value and check)
- White, F. M., Viscous Fluid Flow: Sutherland constants for air
Last updated 2026-10-07.