Fan Law Calculator

What Are the Fan Laws?

The fan affinity laws (sometimes called the fan similarity laws) are three relationships that apply to centrifugal fans operating on the same duct system at different speeds. They are derived from fluid mechanics principles and describe how performance variables scale with rotational speed.

The three laws, expressed in terms of a speed ratio R = RPM₂ / RPM₁:

• Airflow: CFM₂ = CFM₁ × R — airflow changes proportionally with speed
• Static Pressure: SP₂ = SP₁ × R² — static pressure changes with speed squared
• Horsepower: HP₂ = HP₁ × R³ — brake horsepower changes with speed cubed

Why Each Variable Changes at a Different Rate

Airflow scales linearly

Airflow is directly proportional to fan speed because the fan blade tips sweep through air at a rate determined by how fast they spin. Double the speed and the fan moves twice as much air volume per minute through the same duct system — hence the linear (first-power) relationship.

Static pressure scales with the square of speed

Static pressure is related to the kinetic energy imparted to the air. Kinetic energy is proportional to velocity squared, and velocity scales with speed. Therefore, a 20% increase in fan speed produces a 44% increase in static pressure (1.2² = 1.44). This explains why static pressure rises much faster than you might expect when overspeeding a fan.

Horsepower scales with the cube of speed

Brake horsepower is the product of airflow and pressure (work done per unit time). Since airflow scales as speed¹ and pressure scales as speed², their product — power — scales as speed³. This is the most consequential of the three laws. A fan running 20% faster requires 73% more horsepower (1.2³ ≈ 1.73). Running a fan 50% faster demands over three times the original horsepower. Motor overload is a real risk when fan speed is increased without checking nameplate limits.

Example Calculation

A rooftop unit fan runs at 1,000 RPM, delivering 5,000 CFM at 1.0 in. w.g. static pressure on a 5.0 HP motor. The TAB technician needs to increase airflow by adjusting the sheave ratio. New target speed: 1,200 RPM.

• Speed ratio: 1,200 / 1,000 = 1.20
• New CFM: 5,000 × 1.20 = 6,000 CFM
• New SP: 1.0 × 1.20² = 1.0 × 1.44 = 1.44 in. w.g.
• New HP: 5.0 × 1.20³ = 5.0 × 1.728 = 8.64 HP

The motor would need to handle 8.64 HP. If the motor nameplate is 7.5 HP, the technician cannot achieve 1,200 RPM without risking motor overload — even though the airflow increase sounds modest.

When Fan Laws Are Useful

• Sheave ratio changes — estimating new fan performance before making a physical change to the belt-drive system
• VFD speed adjustments — understanding how reducing fan speed to 80% saves significant energy (power drops to 0.8³ = 51% of original)
• Troubleshooting — checking whether a reported fan speed is consistent with measured airflow and static pressure
• Education — understanding why energy-efficient HVAC design focuses on reducing system resistance rather than increasing fan speed

Limitations and Assumptions

• The fan laws assume the duct system resistance is unchanged. If dampers are repositioned, filters loaded, or coils dirty, the operating point shifts independently of speed.
• The laws apply to centrifugal fans (forward-curved, backward-curved, airfoil). They are approximations for axial fans and may not apply at all to positive-displacement fans.
• Motor efficiency and slip are not accounted for. Actual shaft power may differ from nameplate brake horsepower especially at reduced speeds.
• Belt and sheave losses reduce actual power delivered to the fan. VFD drives introduce their own efficiency curves.
• Fan laws assume operation near the fan's best efficiency point (BEP). Far from BEP, deviation from ideal relationships increases.