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    Air distribution / duct sizing

    Duct sizing calculator

    Duct sizing is a trade: a smaller duct saves space but raises velocity and fan energy. This calculator finds the circular diameter for a target velocity, computes the Darcy friction factor and the pressure gradient per metre, and shows how steeply the gradient rises as you push the velocity up.

    Flow1.00 m³/sVelocity5.0 m/sRoughness0.15 mm
    Duct diameter
    505 mm
    At 5.0 m/s
    Pressure drop
    0.54 Pa/m
    16 Pa over 30 m
    Velocity pressure
    15.0 Pa
    0.5 ρ v²
    Friction factor
    0.0182
    Darcy, Swamee-Jain approximation
    Duct selection
    Diameter, area and pressure gradient at the chosen velocity.
    505 mm
    Duct selection
    TermValue
    Airflow1.000 m³/s (3600 m³/h)
    Velocity5.0 m/s
    Cross-section0.2000 m²
    Diameter505 mm
    Pressure gradient0.54 Pa/m
    Total over run16 Pa

    Round duct. Rectangular equivalents use the same area with a hydraulic-diameter correction.

    Inspect the model
    Choose a quick result view, a scaled comparison, or the complete diagnostic set.
    Pressure gradient against velocity
    Higher velocity means a smaller duct but a much steeper pressure gradient.
    Pressure gradient against velocity0.0001.092.183.264.355.442233445566778899101011111212Pa/m
    Canonical equations
    The exact relationships implemented by this engine.

    A = Q / v · Flow divided by velocity.

    D = √(4A/π) · Circular equivalent.

    Δp = f (L/D) (ρv²/2) · Darcy–Weisbach; f from Swamee-Jain.

    engineering methodology

    A clear path from inputs to results.

    Duct sizing is a trade: a smaller duct saves space but raises velocity and fan energy. This calculator finds the circular diameter for a target velocity, computes the Darcy friction factor and the pressure gradient per metre, and shows how steeply the gradient rises as you push the velocity up.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Enter the airflow.
    2. Set the target velocity.
    3. Enter the run length and duct roughness.
    4. Read the diameter and the pressure drop.

    The formula

    D=4Q/(πv),Δp=fLDρv22D = \sqrt{4Q/(\pi v)}, \qquad \Delta p = f \frac{L}{D} \frac{\rho v^2}{2}

    Reference: Darcy–Weisbach with the Swamee-Jain approximation to Colebrook–White.

    Worked example

    1 m³/s at 5 m/s

    Inputs
    • Airflow 1 m³/s.
    • Velocity 5 m/s.
    • Roughness 0.15 mm.
    Calculation path
    1. 1

      Area: 1 / 5 = 0.2 m².

    2. 2

      Diameter: √(4 × 0.2/π) = 0.505 m, or 505 mm.

    3. 3

      Velocity pressure: 0.5 × 1.2 × 25 = 15 Pa.

    4. 4

      Friction factor about 0.016, giving roughly 1.2 Pa/m.

    Result

    505 mm duct · about 1.2 Pa/m.

    Interpreting the result

    Doubling the velocity halves the area but roughly quadruples the pressure gradient, so fan power climbs with the cube of velocity. Most low-velocity systems stay at 4–6 m/s in mains for that reason.

    Assumptions & limitations

    • Straight circular duct.
    • Standard air at 1.2 kg/m³.
    • No fittings, dampers or terminal losses.
    • Rigid duct; flexible duct has a higher roughness.

    Frequently asked questions

    What velocity should I use?

    4–6 m/s in mains, 2–3 m/s in branches near occupied space for noise.

    Does this include fitting losses?

    No. Add local loss coefficients for elbows, tees and terminals.

    How do I convert to rectangular?

    Match the cross-sectional area, then correct the hydraulic diameter.

    Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.