Duct Pressure Drop Calculator (Rectangular & Round)

Estimate Pressure Loss in a Duct

Duct Pressure Drop Formula

Formula

\[ \Delta p = f \cdot \frac{L}{D_h} \cdot \frac{\rho v^2}{2} + \Sigma K \cdot \frac{\rho v^2}{2}, \qquad v = \frac{Q}{A}, \qquad D_h = \frac{2WH}{W+H} \]

Where:

\(\Delta p\) — total pressure drop (Pa)
\(f\) — Darcy friction factor (dimensionless)
\(L\) — duct length (m)
\(D_h\) — hydraulic diameter (m); for a circular duct it equals the diameter, for a rectangular duct it is \(2WH/(W+H)\)
\(\rho\) — air density (kg/m³)
\(v\) — air velocity (m/s)
\(Q\) — airflow (m³/s)
\(A\) — cross-section area (m²)
\(\Sigma K\) — sum of fitting loss coefficients

The formula is the Darcy–Weisbach equation: the first term is the friction lost along the straight duct run, the second term adds the dynamic losses from fittings such as bends, tees and grilles. Both terms are driven by the velocity pressure \(\rho v^2/2\), which is why smaller ducts produce disproportionately higher losses.

Duct Pressure Drop – Calculation Example

Example: a rectangular galvanized steel duct 400 mm wide × 200 mm high, 10 m long, carrying 1000 m³/h of air (ρ = 1.2 kg/m³, f = 0.02), with fittings totalling ΣK = 1.

\[ A = 0.4 \times 0.2 = 0.08\ \text{m}^2, \qquad Q = \frac{1000}{3600} = 0.2778\ \text{m}^3/\s \]

\[ v = \frac{0.2778}{0.08} = 3.47\ \text{m/s}, \qquad D_h = \frac{2 \times 0.4 \times 0.2}{0.4 + 0.2} = 0.267\ \text{m} \]

\[ \frac{\rho v^2}{2} = \frac{1.2 \times 3.47^2}{2} = 7.23\ \text{Pa} \]

\[ \Delta p_{\text{friction}} = 0.02 \times \frac{10}{0.267} \times 7.23 = 5.43\ \text{Pa}, \qquad \Delta p_{\text{fittings}} = 1 \times 7.23 = 7.23\ \text{Pa} \]

Result: total pressure drop = 5.43 + 7.23 = 12.66 Pa ≈ 1.29 mm H₂O ≈ 0.051 in. w.g., at an air velocity of 3.47 m/s.

How to Use the Calculator

Select the Duct shape — Rectangular or Circular. The width, height and diameter fields switch automatically.
For a rectangular duct, enter the Duct width (W) and Duct height (H) with their units (mm or in). For a circular duct, enter the Duct diameter (D).
Enter the Duct length (L) in metres or feet — the straight-run length only.
Enter the Airflow (Q) in m³/h or CFM.
Check the Air density (ρ); the default 1.2 kg/m³ corresponds to air at about 20 °C. Adjust for hot, cold or high-altitude air.
Set the Friction factor (f). A value of 0.015–0.025 is typical for galvanized steel ductwork.
Enter the Fitting loss coefficient (ΣK) — the sum of the K-values of all bends, tees, dampers and grilles in the section. Use 0 for a straight duct with no fittings.

The results show the air velocity, the friction loss along the straight duct, the fitting loss, and the total pressure drop in Pa, mm H₂O and inches of water gauge.

What Is Duct Pressure Drop?

As air moves through a duct, it loses energy to friction against the duct walls and to turbulence at every change of direction, junction or restriction. This lost energy appears as a drop in static pressure along the duct, and the fan must make it up to keep the air flowing. Duct pressure drop — also called duct pressure loss or friction loss — is therefore one of the key numbers in sizing ventilation systems: too much pressure drop means an oversized, noisy, energy-hungry fan, while underestimating it means poor airflow at the grilles.

The Darcy–Weisbach equation used here splits the loss into two parts. The friction term grows with the length-to-hydraulic-diameter ratio: a long, narrow duct loses far more pressure than a short, wide one carrying the same airflow. The fitting term accounts for local losses, each fitting contributing a multiple of the velocity pressure according to its K-value. Since both terms scale with \(v^2\), halving the duct cross-section roughly quadruples the pressure drop at a given airflow — the single most common cause of underperforming systems.

The hydraulic diameter is what makes a rectangular duct comparable to a round one. A flat, wide duct has a smaller hydraulic diameter than its area suggests, so it suffers higher friction per metre than a square or circular duct of the same cross-section. That is why round ducts are usually the most efficient shape when space allows.

To judge whether your result is reasonable, check the air velocity: comfort ventilation typically runs at 3–5 m/s in main ducts and below 2 m/s near occupied spaces, while industrial systems may reach 10 m/s or more. Pressure drops of about 1 Pa per metre of duct are a common design target for low-energy systems.

Assumptions, Limitations and Practical Tips

The calculation assumes incompressible, steady airflow with uniform properties along the duct — valid for normal ventilation pressures (a few hundred pascals).
The friction factor is a fixed input, not computed from the surface roughness and Reynolds number. For most galvanized steel ducts, 0.02 is a safe value; flexible ducts can be significantly worse and may need f = 0.03 or higher. To check the flow regime, calculate the Reynolds number for your duct.
Each fitting must be counted once in ΣK. Typical K-values: 90° smooth bend 0.2–0.3, sharp 90° elbow 0.8–1.2, branch tee 0.5–1.5, grille or diffuser 1–3, sudden expansion 0.5–1. Check manufacturer data where accuracy matters.
The tool computes one duct section with constant dimensions and airflow. Real systems have tapered ducts and branches; split the network into sections, calculate each one, and sum the losses along the critical path (usually the longest or most resistive run).
Leakage, crushed flexible sections, dirty filters and fan entry/exit losses are not included. A design margin of 10–20 % on the calculated total is common practice.
The same Darcy–Weisbach method applies to liquids in pipes — see the Pipe Pressure Drop calculator — and once you know the total pressure loss and airflow, you can size the fan with the Pump Power calculator.

Frequently Asked Questions

How do I convert pressure drop between Pa, mm H₂O and in. w.g.?

1 mm H₂O (millimetre of water gauge) equals about 9.81 Pa, and 1 inch of water gauge equals 249.1 Pa or 25.4 mm H₂O. To convert pascals, divide by 9.81 for mm H₂O or by 249.1 for in. w.g. For example, 100 Pa ≈ 10.2 mm H₂O ≈ 0.40 in. w.g. HVAC datasheets often mix units, so always check which one the fan curve uses before comparing with your result.

How do I calculate the Darcy friction factor instead of guessing it?

First find the Reynolds number: \( Re = \rho v D_h / \mu \), where \( \mu \approx 1.8\times10^{-5} \) Pa·s for air. If \( Re < 2300 \), flow is laminar and \( f = 64/Re \). For turbulent flow in a rough duct, solve the Colebrook equation \( 1/\sqrt{f} = -2\log_{10}(\varepsilon/3.7D_h + 2.51/Re\sqrt{f}) \) iteratively. For typical ventilation velocities in galvanized steel (roughness ≈ 0.15 mm is too high — use 0.00015 m), f lands near 0.015–0.025, which is why the fixed default works well.

What is the equal-friction method for designing ducts?

It is the most common duct-sizing approach: you choose a target pressure loss per metre (typically 0.8–1.2 Pa/m for low-noise systems, up to 2–3 Pa/m for industrial ones) and then size every duct section so it hits that value. Use this calculator in reverse: try different widths and heights until the friction loss divided by the length matches your target. Branches and fittings are then added on top, which is why the total is always higher than length × target.

How does a rectangular duct compare to an equivalent round duct?

A rectangle with an aspect ratio above 2:1 has a smaller hydraulic diameter than a round duct of the same area, so it loses noticeably more pressure. To find the equivalent round duct with equal friction and airflow, use the ASHRAE approximation \( D_e = 1.30\,(WH)^{0.625}/(W+H)^{0.25} \). For example, a 400×200 mm duct behaves roughly like a 273 mm round duct. Squeezing the aspect ratio toward square (or round) is one of the cheapest ways to cut pressure drop.

Why is my flexible duct losing so much more pressure?

Flex duct has deeply corrugated walls, and every sag or bend adds roughness. Fully extended, well-supported flex needs a friction factor of roughly 0.03–0.05; compressed to 80 % of its length, losses can double or triple. Never rely on the galvanized-steel value of 0.02 for flex. Also avoid sharp bends at the flex-to-plenum connection — a tight bend there can alone add the equivalent of ΣK = 1 or more.

How do I use the result to pick a fan?

Add up the pressure drop of every section along the most resistive duct run — the longest path with the most fittings — plus any filters, dampers, coils and grilles, then add a 10–20 % margin. Match that total static pressure and the required airflow on the fan's performance curve: the fan must deliver the airflow at that pressure, not at free delivery. Undersizing the pressure rating is the most common cause of a system that moves only half its design air.

What is the difference between static, velocity and total pressure?

Velocity pressure is \( \rho v^2/2 \) — the kinetic energy of the moving air. Static pressure is the stored energy pushing on the duct walls; it's what the fan must spend to overcome friction and fitting losses, and it falls along the duct as that energy is dissipated. Total pressure is their sum \( p_t = p_s + \rho v^2/2 \) and always decreases in the flow direction, since both friction and turbulence consume total energy. This calculator gives the static (and total) pressure loss the fan must make up.

Duct Pressure Drop