Fan Calculator — Fan Affinity Laws (Speed, Flow, Power)
Use the fan affinity laws to calculate how changing fan speed affects flow rate, static pressure, and shaft power — essential for sizing variable-frequency drives and estimating energy savings.
m³/h
Па
kW
RPM
RPM
Power scales as the cube of speed ratio: W₂ = W₁ × (N₂/N₁)³
- 1
Speed ratio N₂ ÷ N₁
1 800 ÷ 1 500 = 1,2 - 2
Ratio cubed
1,2³ = 1,728Shaft power scales as the cube of the speed ratio — the cube law. - 3
New shaft power
2,5 × 1,728 = 4,320
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Fan affinity laws: flow ∝ speed, pressure ∝ speed², power ∝ speed³. Enter initial flow, pressure, power, and both speeds. A 10% speed reduction cuts power by about 27%; a 20% cut saves about 49%. The cubic law makes VFDs on fans one of the most impactful energy-saving measures in HVAC.
Формула
How this is calculated
The fan affinity (similarity) laws describe how a centrifugal or axial fan's performance scales when its rotational speed changes, assuming the same impeller diameter and air density. The three relationships are: volumetric flow rate scales linearly with speed (Q ∝ N); static pressure scales with the square of speed (P ∝ N²); and shaft power scales with the cube of speed (W ∝ N³). These laws follow directly from dimensional analysis of the Navier–Stokes equations.
The cubic power law has a powerful engineering consequence: reducing a fan from 100% to 80% speed cuts power consumption to 0.8³ = 51.2% of the original — nearly half the energy — while delivering 80% of the flow. This is why variable-frequency drives (VFDs) on fans and pumps are one of the most cost-effective energy-saving measures in HVAC systems.
The laws are exact for geometrically similar fans operating at the same efficiency point and with incompressible flow (density-change effects become material above roughly Mach 0.3, or fan pressures above about 5 kPa). In practice, motor efficiency and mechanical losses also change with speed, so actual power savings are usually somewhat less than the cubic law predicts. Use manufacturer performance curves for final design.
Поширені запитання
Mechanical power equals pressure times flow rate (W = P × Q). Since pressure scales as speed² and flow scales as speed, their product scales as speed³. This cube relationship makes even small speed reductions very effective at saving energy.
The speed ratio is 1200/1500 = 0.80. Power scales as 0.80³ = 0.512, so the fan uses about 51% of its original power — a saving of roughly 49%. Flow drops to 80% and pressure to 64% of original.
Yes. The same affinity laws (flow ∝ N, head ∝ N², power ∝ N³) apply to centrifugal pumps for the same reasons — they are known as the pump affinity laws and are used in the same way for variable-speed pump drives.
Також відомий як
TG we-Calculate Editorial Team. (2026). Fan Calculator — Fan Affinity Laws (Speed, Flow, Power) [Online calculator]. TG we-Calculate. https://we-calculate.com/uk/calculator/fan-calculator
TG we-Calculate Editorial Team. "Fan Calculator — Fan Affinity Laws (Speed, Flow, Power)." TG we-Calculate. 2026. https://we-calculate.com/uk/calculator/fan-calculator.
TG we-Calculate Editorial Team, "Fan Calculator — Fan Affinity Laws (Speed, Flow, Power)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/uk/calculator/fan-calculator
@misc{wecalculate_fan_calculator, title = {Fan Calculator — Fan Affinity Laws (Speed, Flow, Power)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/uk/calculator/fan-calculator}}, year = {2026}, note = {TG we-Calculate} }
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