Reference · ASHRAE fundamentals
Duct sizing formulas
Everything the calculator solves, shown with units. Standard air 0.075 lb/ft³ at 68°F, altitude-corrected.
Velocity and area
V (FPM) = CFM ÷ A (ft²)
Round Ø (in) = 13.54 × √(CFM ÷ V)
Rect V = CFM ÷ ((a × b) ÷ 144)
Friction loss (Darcy–Weisbach)
FR (in.wg/100ft) = f × (100 ÷ D) × (V² ÷ 2g) × 12 × (ρ ÷ ρwater)
D in ft · V in ft/s · g = 32.2 ft/s² · ρwater = 62.4 lb/ft³
The friction factor f comes from Swamee–Jain (explicit Colebrook–White): f = 0.25 ÷ [log₁₀(ε/3.7D + 5.74/Re^0.9)]², with Re = ρ·V·D/μ and 64/Re below Re 2,300. Roughness ε: galvanized 0.0003 ft · aluminum 0.00015 · duct board / taut flex 0.003 · compressed flex 0.01. Density ρ scales with altitude (≈86% at 5,000 ft, ≈74% at 10,000 ft).
Round ↔ rectangular (Huebscher, 1948)
De = 1.30 × (a·b)^0.625 ÷ (a+b)^0.25 — same friction loss at the same CFM.
A rectangle always needs more cross-section than its equivalent circle (more wetted perimeter per area). Example: 12×8 in rect → De ≈ 10.7 in. Matching by raw area undersizes the rectangle by ~30% — the most common DIY error. Cap aspect ratio at 4:1 per SMACNA; 2:1 is the sweet spot.
Friction-rate budget (Manual D)
FR = (ASP × 100) ÷ TEL
ASP = TESP − filter − coil − registers/grilles · TEL = straight ft + fitting equivalent ft
CFM helpers
Equipment CFM ≈ tons × 400
Room CFM = (room load ÷ whole-house load) × equipment CFM
Metric equivalents (display)
L/s = CFM × 0.471947 · m/s = FPM × 0.00508 · Pa/m = in.wg/100ft × 8.1727
What this tool does not size by
Static-regain sizes each downstream section to recover velocity pressure as heat — a commercial method needing section-by-section fitting coefficients. The T-method optimizes lifetime duct + fan-energy cost from utility rates and operating hours. Both are legitimate engineering; neither belongs in a residential field tool, where equal-friction plus a velocity check is the safe, standard answer.