Air Velocity Calculator
This calculator converts a volumetric airflow and a duct’s open cross-sectional area into average velocity. It is a transparent continuity-equation check for measurements that use cubic feet per second (ft³/s) and square feet (ft²); the result is feet per second (ft/s).
Both inputs must refer to the same section and operating condition. Enter the effective open area through which the measured flow passes, not merely the nominal outside dimensions of a grille or duct.
Formula
For steady volumetric flow, the continuity relationship is Q = A × v, where Q is volumetric flow rate, A is flow area, and v is average velocity. Rearranging gives:
v = Q ÷ A
The units cancel directly: (ft³/s) ÷ ft² = ft/s. Flow may be zero, producing zero velocity, but area must be greater than zero.
Worked example
For a measured flow of 500 ft³/s through an effective area of 50 ft²:
500 ft³/s ÷ 50 ft² = 10 ft/s
The result is the cross-sectional average. It does not mean every point in the duct is moving at exactly 10 ft/s.
What the result means
Average velocity is useful for a preliminary duct check, comparing operating points, or converting a verified flow measurement into a representative speed. If the area is halved while the same volumetric flow is maintained, the calculated average velocity doubles.
Real velocity profiles are affected by walls, bends, dampers, transitions, fans, obstructions, and measurement location. A point measurement at the centre of a duct is therefore not automatically equal to the area average used by this equation.
Accuracy and limitations
This page does not calculate the duct area from shape, correct standard flow to actual flow, or compensate for leakage. Confirm whether the source reports ACFM, SCFM, or another reference condition before converting a flow rate. Air density changes with temperature, pressure, and humidity; those changes matter when mass flow or flow at different conditions is being compared.
For compressible flow with large pressure or temperature changes, a single volumetric flow and area may not represent the whole system. HVAC commissioning also requires suitable instruments, straight measurement runs, traverse methods, and applicable standards. Do not use this arithmetic alone for smoke control, hazardous exhaust, clean-room certification, or life-safety acceptance.
Sources
- U.S. Department of Energy, Fluid Flow handbook — defines volumetric flow as cross-sectional area multiplied by average velocity.
- NIST Guide to the SI, Chapter 8 — authoritative guidance on quantities, units, and unit symbols.
Editorial record
Written and formula-checked by the SoupCalc Editorial Team. The unit cancellation, zero-flow case, invalid-area case, and displayed example were tested against the implementation.
Last reviewed: August 10, 2026.