Fan Affinity Laws Calculator

Reviewed by the CalculatorHub team, edited by James Graham. Based on AMCA Publication 201 and ASHRAE Fundamentals. Last verified 14 June 2026.

The fan affinity laws allow you to predict the new performance of a fan when its speed changes (variable speed drive) or when the impeller diameter changes. Enter the known operating point (flow, pressure, power, and speed), then enter the new speed or new diameter ratio to calculate the new performance. The laws assume the fan operates at geometrically similar conditions and at the same efficiency point.

Original Flow Rate, Q1 (m3/s) Volumetric flow rate at original operating point

Original Static Pressure, P1 (Pa) Fan static pressure rise at original operating point

Original Power, W1 (kW) Shaft power at original operating point

Original Speed, N1 (RPM) Original fan rotational speed

New Speed, N2 (RPM) New fan speed after speed change (e.g. via VSD)

New Flow Rate, Q2 (m3/s)

-- m3/s

New Static Pressure, P2 (Pa)

-- Pa

New Power, W2 (kW)

-- kW

Power Saving (%)

-- %

Fan affinity laws (speed change)

Q₂ = Q₁ × (N₂/N₁)
P₂ = P₁ × (N₂/N₁)²
W₂ = W₁ × (N₂/N₁)³

Where: Q = volumetric flow rate (m^3/s), P = pressure rise (Pa), W = shaft power (W), N = rotational speed (RPM). These equations also apply to centrifugal pumps (pump similarity laws).

Variable speed drive energy savings

A 10% speed reduction saves approximately 27% of power (0.90^3 = 0.729).
A 20% speed reduction saves approximately 49% of power (0.80^3 = 0.512).
A 30% speed reduction saves approximately 66% of power (0.70^3 = 0.343).
Actual savings depend on the system resistance curve. Pure friction systems achieve the full cubic savings; systems with static head components achieve less.

Fan affinity laws calculator: frequently asked questions

What are the fan affinity laws?

The fan affinity laws (also called the fan laws or pump laws) describe how flow rate, pressure, and power scale with changes in fan speed or impeller diameter. For speed changes: Q2/Q1 = N2/N1, P2/P1 = (N2/N1)^2, W2/W1 = (N2/N1)^3. For diameter changes at constant speed: Q2/Q1 = (D2/D1)^3, P2/P1 = (D2/D1)^2, W2/W1 = (D2/D1)^5.

Why is the power relationship a cube of speed?

Fluid power is the product of pressure and flow rate. Since flow rate scales with speed (linear) and pressure scales with speed squared, power scales as the product: N^1 * N^2 = N^3. This cube relationship means that even a small reduction in fan speed has a large effect on power consumption and is the basis for variable-speed drive energy savings.

What energy savings result from a 20% speed reduction?

A 20% reduction in fan speed (N2/N1 = 0.80) reduces power to (0.80)^3 = 0.512 of the original, saving approximately 49% of the fan power. This is the theoretical saving; actual savings depend on system resistance curve behaviour.

Do the affinity laws apply to centrifugal pumps?

Yes. The affinity laws apply to both centrifugal fans and centrifugal pumps (also called the pump similarity laws). They assume the system resistance curve is quadratic (friction-dominated) and the fan or pump operates at the same efficiency point after scaling.

What is the AMCA standard for fan performance?

AMCA Publication 201 (Fans and Systems) and AMCA Standard 210 (Laboratory Methods of Testing Fans for Aerodynamic Performance Rating) are the primary standards. AMCA 210 defines standardised test conditions and performance measurement methods for fans.

Official sources

AMCA Publication 201 Fans and Systems: AMCA Publication 201.
ASHRAE Handbook: Fundamentals (Chapter 21, Duct Design): ashrae.org/technical-resources/ashrae-handbook.

Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.