TAHA Engineering Toolsby TAHA Knowledge Lab

HVAC & Building Services

Duct Size & Air Velocity Calculator

Air velocity in round or rectangular ducts, round duct size for a velocity, and rectangular-to-round equivalent diameter.

Inputs

Calculate from
Two duct cross-sections. Left: a rectangular duct with width a and height b. Right: a round duct with diameter D. Both show airflow going into the page.a — widthbDrectangularround
Duct cross-sections, airflow into the page. Velocity = airflow ÷ inside area. The equivalent round diameter De gives the same friction loss per metre as the rectangular duct at the same airflow — it is not the same area. Diagram not to scale.

Result

Air velocity
3.97887
Duct cross-section area
0.125664
Working
A = π × D² ÷ 4 = π × 0.4² ÷ 4 = 0.12566 m² V = Q ÷ A = 0.5 ÷ 0.12566 = 3.9789 m/s

The air moves at about 3.97887 m/s in this duct.

Educational estimate — check the assumptions below.

About this calculator

Ducts are sized so that the air velocity is high enough to keep the duct small and economical, but low enough to limit friction loss, fan power and noise. This calculator finds the velocity for a given airflow and duct size, the round duct diameter for a chosen velocity, and the equivalent round diameter of a rectangular duct — the round size with the same friction loss per metre at the same airflow, used to read friction charts that are drawn for round ducts.

Formula

Velocity in a duct

V = Q ÷ A    Around = π D² ÷ 4    Arect = a × b

Q = airflow (m³/s), A = inside cross-section area (m²), V = average air velocity (m/s). Inch-pound: fpm = cfm ÷ ft².

Round size for a velocity

A = Q ÷ V    D = √(4 A ÷ π)

The inside diameter of a round duct that carries airflow Q at average velocity V.

Rectangular → equivalent round

De = 1.30 × (a b)0.625 ÷ (a + b)0.25

Huebscher’s equation for the circular equivalent of a rectangular duct of sides a and b, giving equal friction loss per length at equal airflow (as given in the ASHRAE Handbook — Fundamentals, Duct Design chapter). Any consistent length unit can be used.

Worked example

  • Velocity: 0.5 m³/s in a 400 mm round duct → A = π × 0.4² ÷ 4 = 0.1257 m² → V = 0.5 ÷ 0.1257 = 3.98 m/s.
  • Inch-pound: 1000 cfm in a 12 in round duct → A = 0.785 ft² → 1273 fpm.
  • Round size: 1 m³/s at 5 m/s → A = 0.2 m² → D = √(4 × 0.2 ÷ π) = 505 mm; choose the nearest standard size and recheck.
  • Equivalent diameter: 300 mm × 300 mm → De = 1.30 × 90 0000.625 ÷ 6000.25 = 328 mm; 12 in × 12 in → 13.1 in.

Assumptions and limitations

  • Average velocity over the inside cross-section. Use inside dimensions; insulation or lining inside the duct reduces the area.
  • The equivalent diameter applies to friction loss only. It must not be used to calculate the velocity or area of the rectangular duct.
  • Friction loss, fittings, noise and fan pressure are not calculated here.
  • No velocity limits are built in. Suitable design velocities depend on the application and the design guide or standard used.

References

  • ASHRAE Handbook — Fundamentals, chapter “Duct Design” (circular equivalents of rectangular ducts, Huebscher equation).
  • Continuity equation: Q = V × A.