Drawing No. EH–TH–013 // Thermal Engineering & HVAC
Fan Laws Calculator
Reviewed August 2026
Apply the fan affinity laws to predict how flow, pressure and shaft power change when fan speed changes, for the same system and impeller.
What problem does this solve?
For a fixed duct/system and unchanged impeller diameter, a fan's flow, pressure and power all scale predictably with rotational speed: flow scales linearly, pressure scales with the square of speed, and power scales with the cube. This is the physical basis for variable-speed drive energy savings — even a modest speed reduction cuts power dramatically.
Inputs
Known operating point (speed N₁)
Results at new speed
Background
For the same fan and impeller diameter at dynamically similar corresponding points: Q2/Q1 = N2/N1 (flow scales linearly with speed); ΔP2/ΔP1 = (N2/N1)² (pressure scales with speed squared); W2/W1 = (N2/N1)³ (power scales with speed cubed). These are the same relationships used across EngineerHub's Thermal & HVAC formula sheet.
Because power scales with the cube of speed, even a modest speed reduction gives a large power saving — running a fan at 80% speed theoretically needs only 0.8³ ≈ 51% of full-speed power, delivering 80% of the flow. This cubic relationship is the entire economic case for variable-frequency drives on fan and pump systems that spend most of their time at part load.
Frequently asked questions
Practical questions about inputs, assumptions and interpretation.
The same three exponents (1, 2, 3) apply to impeller diameter changes at fixed speed too, but that comparison additionally assumes similar flow geometry (dynamically similar operating points) and is less accurate over large diameter changes than for speed changes on the same impeller, which is the more common and more reliable application.
The ideal affinity-law ratios compare dynamically similar points on the same fan. In a real installation, changing speed moves both the fan curve and the intersection with the system curve, while fan efficiency can also change. The equations are therefore a first-order scaling tool; use the manufacturer’s fan curves when the exact operating point or motor loading matters.
Yes — analogous similarity relationships are widely used for centrifugal pumps as well. Their most reliable use is comparing corresponding points for geometrically similar operation; the actual system operating point still depends on the pump curve and the system curve.