Duct sizing calculator
Equal-friction sizing for round and rectangular ductwork, solving Colebrook–White to convergence rather than reading a wheel drawn for one material.
The friction chart's own basis. The default for most UK ductwork.
Round duct
340 mm
Exact diameter required
Velocity
5.50 m/s
At that diameter
Reynolds
1.24e+5
Turbulent
Friction factor
0.0187
Colebrook, iterated
Rectangular equivalents
Sizes whose circular equivalent meets or exceeds 340 mm, in 50 mm increments, capped at 4:1. Closest match first.
| Size (w × h) | Aspect ratio | Circular equivalent | Oversize |
|---|---|---|---|
| 400 × 250 mm | 1.6:1 | 343 mm | +0.9% |
| 550 × 200 mm | 2.8:1 | 352 mm | +3.4% |
| 350 × 300 mm | 1.2:1 | 354 mm | +4.0% |
| 350 × 350 mm | 1.0:1 | 383 mm | +12.5% |
| 400 × 400 mm | 1.0:1 | 437 mm | +28.5% |
| 450 × 450 mm | 1.0:1 | 492 mm | +44.6% |
Preliminary sizing for schematic design. Not construction information: it takes no account of fittings, balancing, acoustics, the available ceiling void, or the fan pressure the index run actually needs.
Method and sources
Equations used
Δp/L = f · ρV² ÷ (2 D_h)Darcy–Weisbach. ASHRAE Handbook—Fundamentals duct-design chapter, Eq. (19).
1/√f = −2 log₁₀[ ε/(3.7 D_h) + 2.51/(Re √f) ]Colebrook, Eq. (20). Implicit in f, so iterated to convergence; Swamee–Jain provides the starting estimate only.
Re = D_h V ÷ (1000 ν)Eq. (22). Below Re 2000 the flow is laminar and f = 64/Re instead, independent of roughness.
D_e = 1.30 (ab)^0.625 ÷ (a+b)^0.250Huebscher (1948), Eq. (25) — circular equivalent of a rectangular duct for equal flow, resistance and length. Not the hydraulic diameter; the two are not interchangeable.
Constants assumed
| Symbol | Value | Source |
|---|---|---|
| ρ (standard air) | 1.204 kg/m³ | ASHRAE Handbook—Fundamentals, duct-design chapter |
| ν (standard air) | 1.506 × 10⁻⁵ m²/s | Implied by the chapter's own Re = 66.4·D_h·V shortcut for standard air |
| μ (standard air) | 1.813 × 10⁻⁵ Pa·s | ρ × ν, derived from the two rows above |
| ε galvanised steel | 0.09 mm | ASHRAE Table 1 — also the basis of the published friction chart |
| ε smooth (aluminium, PVC, carbon steel) | 0.03 mm | ASHRAE Table 1 |
| ε flexible, fabric and wire | 3.0 mm category | ASHRAE Table 1 |
Sources
- •ASHRAE Handbook—Fundamentals, duct-design chapter — Darcy–Weisbach, Colebrook, Reynolds number, the Huebscher circular equivalent, Table 1 roughness factors and the standard-air basis.
- •Colebrook (1938–39) and Huebscher (1948), as cited by that chapter.
- •Note an inconsistency within the source itself: Table 1 gives flexible metallic duct as 1.2–2.1 mm fully extended, while the chapter's body text says 0.1–2.1 mm. Table 1 is used here.
What this calculator deliberately does not do
Stainless steel is not offered as a material.
ASHRAE Table 1 does not list it and no substitute published table was obtained. Rather than assign a plausible-looking roughness, it is left out. Stainless is generally smoother than galvanised, so the 0.03 mm smooth figure would be a defensible sensitivity check — but that is a judgement for you to make, not a number this tool should assert.
The 4:1 aspect ratio cap is ours, not ASHRAE's.
The phrase "aspect ratio" does not appear in the chapter these equations come from. The cap reflects cost and fan-energy penalties that rise with perimeter, and it is applied as our convention with the reasoning stated rather than attributed to a standard.
Fitting losses are not included.
Bends, transitions, takeoffs and dampers frequently dominate the index run, and their loss coefficients depend on the specific geometry. This sizes straight duct only.
Preliminary sizing for schematic design, not construction documentation. It takes no account of fittings, balancing, acoustics, available void depth, fire dampers or the fan pressure the index run actually requires.