Fan Affinity Law Calculator - HVAC Calculator Toolbox

About this calculator This calculator applies the fan affinity laws to a fan whose speed has changed. Enter the baseline operating point, then enter any one final value — airflow, fan speed, static pressure, or brake horsepower — and the other three are calculated from it. Every one of the four values is governed by the same speed ratio, so any one of them is enough to fix the rest. The results show that ratio along with the change in power, which is where a speed reduction pays off: cutting speed to 80% drops airflow to 80% but power to roughly 51%. Use it when rebalancing a system, setting a VFD frequency, or estimating the energy saved by slowing a fan down.

Use when A fan is being sped up or slowed down and you need the resulting airflow, pressure, and power — rebalancing a system, setting a VFD, or estimating the energy saved by a speed reduction.

Formula CFM ∝ RPM · SP ∝ RPM² · BHP ∝ RPM³

Variables

Airflow Fan airflow in CFMFan Speed Fan wheel speed in RPMStatic Pressure Fan static pressure in inches water columnPower Brake horsepower at the operating point

Enter the baseline operating point, then type any one final value — the other three follow from the fan laws.

Baseline

Final

vs. Baseline

AirflowCFM

—

Fan SpeedRPM

—

Static Pressurein. w.c.

—

PowerBHP

—

Enter a baseline value and its matching final value to see the speed change.

What are the fan affinity laws?

The fan affinity laws describe how a fan’s performance changes with rotational speed, for a fixed fan operating in a fixed system. The first law states that airflow varies directly with speed: CFM₂ = CFM₁ × (RPM₂ ÷ RPM₁). The second law states that static pressure varies with the square of speed: SP₂ = SP₁ × (RPM₂ ÷ RPM₁)². The third law states that power varies with the cube of speed: BHP₂ = BHP₁ × (RPM₂ ÷ RPM₁)³. Because all three share the same speed ratio, knowing any single final value determines the other three — a final static pressure implies a speed ratio equal to the square root of the pressure ratio, and a final brake horsepower implies the cube root of the power ratio. The cube relationship in the third law is the reason variable speed drives save so much energy: reducing fan speed to 80% cuts airflow to 80% of the original but power to about 51%, and reducing to 50% speed cuts power to roughly 12.5%. These laws assume the system resistance curve does not change and that air density stays constant, so they apply to speed changes on an existing installation rather than to comparisons across different systems, different fan sizes, or significantly different air densities. Where density does change — a large elevation or temperature difference — a separate density correction is required, because static pressure and power both vary directly with air density while airflow does not.

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