Flow Rate Calculator (Q = V × A)

Compute volumetric airflow from velocity and duct cross-section. Round, rectangular, or direct area — results in m³/s, m³/h and cfm.

How airflow Q = V × A works

The continuity equation Q = V × A is the foundation of ventilation engineering. Q is the volumetric flow rate (m³/s), V is the mean air velocity across the section (m/s), and A is the cross-sectional area (m²). The equation expresses conservation of mass: the same volume of air that passes through a large slow section must pass through a small fast section downstream.

A common mistake is to confuse a point velocity reading with the mean velocity of the section. A single pitot-tube or anemometer reading at the centre of a duct is typically 10–20% higher than the true mean because of the boundary layer near the walls. Industrial hygiene practice (ASHRAE 111, ACGIH IV Manual) requires a multi-point traverse — measuring velocity at a grid of equal-area sub-zones and averaging — to obtain a reliable Q.

Once you have a reliable mean velocity and the section geometry, this calculator does the rest: it converts your units to SI internally, computes the area from geometry, and outputs Q in three units simultaneously. The detailed calculation panel shows the exact substitution so you can verify each step.

Round vs rectangular ducts

Round ducts have the best area-to-perimeter ratio: for a given flow rate they require the lowest air velocity, produce the least friction loss, and are cheapest per unit of flow capacity. They are the default choice in industrial ventilation design whenever structural constraints allow.

Rectangular ducts are used when headroom is limited, or to follow architectural elements. Their hydraulic diameter Dₕ = 2wh / (w + h) is the equivalent circular diameter that would produce the same friction loss per unit length. The calculator displays Dₕ automatically when you select rectangular mode, because it is needed for duct sizing charts and pressure-drop calculations.

The direct-area mode is useful when you already know the section area from drawings or when measuring an irregular or flexible duct cross-section. Enter the area in any of the four available units (m², cm², ft², in²) and pair it with the measured mean velocity.

Frequently Asked Questions

What's a 'good' duct velocity for industrial ventilation?
It depends on the application. ACGIH IV Manual recommends 7–12 m/s (1400–2400 fpm) for general branch ducts carrying room air, 10–15 m/s (2000–3000 fpm) for main supply trunks, and 15–20 m/s (3000–4000 fpm) for industrial exhaust systems handling non-particulate contaminants. For particulate transport (dusts, fibres), minimum transport velocities of 15–25 m/s (3000–5000 fpm) are required to keep particles suspended. Too low a velocity causes particle fallout and duct plugging; too high increases fan energy and noise.
Why does my measured velocity vary across the duct?
Air velocity in a duct is not uniform — it forms a velocity profile. Near the walls, friction creates a boundary layer where velocity drops toward zero. At the centre, velocity peaks. The shape of the profile depends on the Reynolds number (turbulent vs laminar flow), upstream bends and fittings, and duct aspect ratio. This is why a single centre-point reading overestimates mean velocity. The ASHRAE 111 / ACGIH multi-point traverse method divides the duct cross-section into equal-area zones and averages the reading in each zone to obtain the true mean velocity for use in Q = V × A.
What's the hydraulic diameter for?
The hydraulic diameter Dₕ = 2wh / (w + h) lets you treat a rectangular duct as if it were a circular duct of equivalent friction behaviour. Duct sizing charts (Darcy-Weisbach friction factor charts, ASHRAE duct design charts) are typically drawn for circular ducts. To use them for a rectangular duct, you substitute Dₕ for the circular diameter. It is also used to calculate the Reynolds number, which determines whether flow is laminar (Re < 2300) or turbulent (Re > 4000) — a critical input for heat transfer and pressure-drop models. For square ducts (w = h), Dₕ simplifies to w.
Can I use this for liquids too?
Yes — Q = V × A is a general continuity equation valid for any incompressible fluid in steady flow. The formulas are identical for water, solvents, or other liquids in pipes and channels. The only caveat is that duct velocity rules of thumb quoted above (7–20 m/s) are specific to air. For liquids in pipes, typical design velocities are much lower: 0.5–2 m/s for water in supply lines, 2–4 m/s in pressurised industrial piping. Use this calculator freely for liquid flow — just interpret the output units accordingly (m³/s and m³/h are valid for any fluid).

You might also need

See all tools →

Complementary tools based on what you're doing