HVAC Fan Laws Calculator

The three basic fan laws (affinity laws)

For a similar fan at constant air density, changing speed (or diameter on a homologous curve) scales airflow, pressure, and power as follows. This calculator holds diameter fixed and scales by RPM or target CFM.

Diameter laws: When impeller diameter changes at constant RPM, Q ∝ D, P ∝ D², H ∝ D³ (same exponents). Use OEM fan software for diameter changes—this page is speed/airflow oriented for sheave and VFD planning.

Formula & explanation

Let ratio r = N₂/N₁ (or Q₂/Q₁ when scaling by airflow). Then:

• CFM₂ = CFM₁ × r
• SP₂ = SP₁ × r²
• BHP₂ = BHP₁ × r³

Density / altitude caveat: Affinity laws assume constant air density. At altitude or with hot/cold process air, correct density (or use manufacturer altitude factors) before trusting BHP and SP₂. Do not apply sea-level ratios blindly to high-elevation AHUs.

Worked examples (50% airflow turndown)

Baseline point: 10,000 CFM, 1.5 in. wg, 5 BHP at 1,750 RPM. Target 5,000 CFM (50% turndown) → ratio r = 0.5.

• Law 1 (airflow): Q₂ = 10,000 × 0.5 = 5,000 CFM; N₂ = 1,750 × 0.5 = 875 RPM.
• Law 2 (static pressure): SP₂ = 1.5 × 0.5² = 0.375 in. wg — pressure drops with the square of speed.
• Law 3 (power): BHP₂ = 5 × 0.5³ = 0.625 BHP — theoretical brake power falls with the cube (12.5% of baseline).

When fan laws break down

• Large RPM changes — beyond ~±20–30% from the catalog point, efficiency and noise shift; laws are screening, not field commissioning data.
• Air density change — altitude, temperature, or moisture changes mass flow at the same volumetric CFM; correct density before trusting BHP and SP₂.
• System curve change — dampers, dirty filters, or resized ducts move the operating intersection; affinity laws scale one point on a fixed curve, not a new system.
• Different fan or impeller — laws apply to geometrically similar fans on homologous curves, not when swapping models or trimming wheels without OEM data.

VAV note: theoretical vs practical power

At 50% CFM, Law 3 predicts BHP at 12.5% of design—ideal for variable-volume planning. In practice, VAV systems rarely hit the cube law because minimum airflow, reheat, static reset, and fan/motor efficiency at part load add parasitic power. Use affinity results as an upper-bound savings screen; measure or use VFD/BMS data for operating cost.

References

• AMCA — fan testing standards and catalog performance conventions.
• ASHRAE fan and air-handling guidance — system curves and fan selection.
• Engineering Toolbox — fan affinity laws — summary of speed and diameter scaling.

Best for: sheave changes, VFD/VAV turndown screens, and “what if we raise RPM 10%?” planning.

Not ideal for: selecting a different fan model, density-corrected OEM curves, or unstable fan regions—use manufacturer software (e.g. catalog fan selectors).

Need system resistance first? Estimate duct path ESP with the duct static pressure calculator. Need CFM from ventilation? Use ACH to CFM.

Worked example

Baseline: 10,000 CFM, 1.5 in. wg, 5 BHP at 1,750 RPM. Raise speed to 1,925 RPM (+10%).

• Ratio r = 1925/1750 ≈ 1.10
• CFM₂ ≈ 11,000 · SP₂ ≈ 1.82 in. wg · BHP₂ ≈ 6.66

Check that the motor and starter can handle ~33% more power, and that duct ESP still matches the new SP₂. Re-screen ducts with HVAC duct size if velocity limits are exceeded.

FAQ