HVAC Fan Laws Calculator
Scale fan CFM, static pressure, and brake HP with affinity laws from RPM or target airflow — for AHU, exhaust, and VAV planning.
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Quick Calculator
Enter baseline point 1. Results for point 2 update instantly.
Advanced — scaling mode
About this calculator
Affinity-law screening for speed or airflow changes after you know duct ESP from the duct static pressure calculator. Browse all HVAC tools on the HVAC Calculators hub. Not a substitute for catalog fan curves or motor overload checks.
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.
| Fan law | Quantity | Scales with | Formula (speed change) |
|---|---|---|---|
| 1 | Airflow (CFM) | RPM (or diameter) | Q₂ = Q₁ × (N₂/N₁) |
| 2 | Static pressure | RPM² | P₂ = P₁ × (N₂/N₁)² |
| 3 | Brake HP / power | RPM³ | H₂ = H₁ × (N₂/N₁)³ |
| — | From target CFM | — | N₂/N₁ = Q₂/Q₁ (then apply laws 2–3) |
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.
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
What are the three basic fan laws?
Law 1: airflow scales with speed (CFM₂/CFM₁ = N₂/N₁). Law 2: static pressure scales with speed squared. Law 3: power (BHP) scales with speed cubed. All assume similar fans and constant density.
What is the fan law formula?
With ratio r = N₂/N₁: Q₂ = Q₁·r, P₂ = P₁·r², H₂ = H₁·r³. If you know target CFM instead of RPM, set r = Q₂/Q₁ and solve for N₂ = N₁·r.
How do you calculate fan CFM from a speed change?
CFM₂ = CFM₁ × (RPM₂ / RPM₁). Static pressure scales with the square of that ratio, and brake horsepower with the cube.
What is the difference between fan laws and duct static pressure?
Fan laws scale an existing fan operating point when speed or airflow changes. Duct static pressure estimates the system resistance the fan must overcome. Use both: check duct ESP, then use fan laws for VAV or sheave changes.
When are fan affinity laws not valid?
They assume similar fans, constant air density, and operation on a homologous curve. They are not a substitute for catalog fan selection when density, altitude, system curve, or fan type changes significantly.