Fan Law Calculator

Calculate

Airflow at the known operating point in CFM

Static pressure at the known operating point in in. w.g.

Brake horsepower (shaft power) at the known operating point in HP

Known fan speed (RPM), impeller diameter (in or mm), or air density (lb/ft³ or kg/m³) — depending on the selected fan law

New fan speed (RPM), impeller diameter (in or mm), or air density (lb/ft³ or kg/m³) — depending on the selected fan law

Overview

The Fan Law Calculator predicts how fan performance changes when operating conditions are adjusted. The three fan laws — also called the affinity laws — are fundamental relationships in HVAC and mechanical engineering that describe how airflow (CFM), static pressure (SP), and brake horsepower (BHP) scale with changes in fan speed (RPM), impeller diameter, or air density.

Select which fan law to apply, enter the known operating point, and specify the new condition. The calculator instantly computes the new airflow, pressure, and power. Engineers use fan laws during system balancing, VFD (variable frequency drive) sizing, fan selection, and troubleshooting to predict performance without re-testing.

These relationships assume geometrically similar fans operating in the same system. They are accurate for moderate changes (typically ±20–30%) and are widely referenced in ASHRAE Handbook — HVAC Systems and Equipment, AMCA Publication 201, and manufacturer selection software.

How to Use This Calculator

  1. Select fan law — choose from Fan Law 1 — Change in Speed, Fan Law 2 — Change in Impeller Diameter, Fan Law 3 — Change in Air Density.

  2. Enter known airflow — in m³/h or CFM.

  3. Enter known static pressure — in Pa or in. w.g..

  4. Enter known brake horsepower — in kW or HP.

  5. Enter known rpm / diameter / density.

  6. Enter new rpm / diameter / density.

  7. Click "Calculate" — get new airflow, new static pressure, new brake horsepower.

Use the result to support your engineering design and analysis decisions.

Inputs & Outputs

Inputs

  • •Fan Law — Options: Fan Law 1 — Change in Speed (RPM), Fan Law 2 — Change in Impeller Diameter, Fan Law 3 — Change in Air Density
  • •Known Airflow (m³/h / CFM)
  • •Known Static Pressure (Pa / in. w.g.)
  • •Known Brake Horsepower (kW / HP)
  • •Known RPM / Diameter / Density
  • •New RPM / Diameter / Density

Outputs

  • •New Airflow (m³/h / CFM)
  • •New Static Pressure (Pa / in. w.g.)
  • •New Brake Horsepower (kW / HP)
  • •Airflow Change (%)
  • •Pressure Change (%)
  • •Power Change (%)

Formula

Fan Law Formulas

The three fan laws describe how airflow, pressure, and power scale with changes in speed, diameter, or density.

Fan Law 1 — Change in Speed (RPM)

CFM₂ = CFM₁ × (RPM₂ / RPM₁)
SP₂  = SP₁  × (RPM₂ / RPM₁)²
BHP₂ = BHP₁ × (RPM₂ / RPM₁)³

Airflow varies directly with speed. Pressure varies with the square of speed. Power varies with the cube of speed.

Fan Law 2 — Change in Impeller Diameter

CFM₂ = CFM₁ × (D₂ / D₁)³
SP₂  = SP₁  × (D₂ / D₁)²
BHP₂ = BHP₁ × (D₂ / D₁)⁵

Airflow varies with the cube of diameter. Pressure varies with the square. Power varies with the fifth power.

Fan Law 3 — Change in Air Density

CFM₂ = CFM₁  (unchanged)
SP₂  = SP₁ × (ρ₂ / ρ₁)
BHP₂ = BHP₁ × (ρ₂ / ρ₁)

Airflow (volume) does not change with density. Pressure and power both vary directly with density.

Variable Reference

Variable Meaning Units
CFM₁ / CFM₂ Airflow at known / new condition CFM or m³/h
SP₁ / SP₂ Static pressure at known / new condition in. w.g. or Pa
BHP₁ / BHP₂ Brake horsepower at known / new condition HP or kW
RPM₁ / RPM₂ Fan speed at known / new condition RPM
D₁ / D₂ Impeller diameter at known / new condition in or mm
ρ₁ / ρ₂ Air density at known / new condition lb/ft³ or kg/m³

What Are the Fan Laws?

The fan laws — also known as the affinity laws — are three fundamental relationships that describe how fan performance parameters change when operating conditions are modified. They apply to all centrifugal turbomachines, including fans, blowers, and pumps.

The three fan laws relate airflow (CFM), static pressure (SP), and brake horsepower (BHP) to changes in:

  1. Fan speed (RPM) — Fan Law 1
  2. Impeller diameter — Fan Law 2
  3. Air density — Fan Law 3

These relationships are derived from dimensional analysis and fluid mechanics principles. They assume geometrically similar fans operating within the same system (same ductwork and resistance characteristics).

Fan Law 1 — Speed Change

Fan Law 1 is the most commonly used fan law in HVAC practice. It describes how performance changes when fan speed (RPM) is varied while everything else remains constant:

  • Airflow varies directly with speed: CFM₂ = CFM₁ × (RPM₂/RPM₁)
  • Pressure varies with the square of speed: SP₂ = SP₁ × (RPM₂/RPM₁)²
  • Power varies with the cube of speed: BHP₂ = BHP₁ × (RPM₂/RPM₁)³

The cubic power relationship is critically important for energy management. A 20% speed increase requires 73% more power, while a 20% speed reduction saves about 49% of power. This is why variable frequency drives (VFDs) are one of the most effective energy conservation measures in HVAC systems.

Fan Law 2 — Diameter Change

Fan Law 2 describes performance changes when the impeller diameter is changed while speed remains constant:

  • Airflow varies with the cube of diameter: CFM₂ = CFM₁ × (D₂/D₁)³
  • Pressure varies with the square of diameter: SP₂ = SP₁ × (D₂/D₁)²
  • Power varies with the fifth power of diameter: BHP₂ = BHP₁ × (D₂/D₁)⁵

This law is most accurate for small diameter changes (typically less than 15%) on geometrically similar fans. The fifth-power relationship for power means even small diameter increases cause very large power increases.

Fan Law 3 — Density Change

Fan Law 3 describes what happens when air density changes while the fan speed and diameter remain constant:

  • Airflow (volume) remains unchanged: CFM₂ = CFM₁
  • Pressure varies directly with density: SP₂ = SP₁ × (ρ₂/ρ₁)
  • Power varies directly with density: BHP₂ = BHP₁ × (ρ₂/ρ₁)

This law is essential for altitude corrections. At higher elevations, air is less dense, so the fan develops less pressure and requires less power — even though it moves the same volume of air. Engineers must apply density corrections when selecting fans for locations significantly above sea level.

Practical Applications

VFD Sizing and Energy Savings

Variable frequency drives allow continuous fan speed adjustment to match actual airflow demand. Using Fan Law 1, engineers can predict the power savings at reduced speeds. For a typical VAV (variable air volume) system, annual fan energy savings of 30–50% are common when VFDs replace constant-speed operation.

System Balancing

During commissioning, if measured airflow differs from design, fan laws predict the speed adjustment needed to achieve the target. For example, if a fan delivers 2,800 CFM at 1,000 RPM but the design calls for 3,000 CFM, the required speed is 1,000 × (3,000/2,800) = 1,071 RPM.

Altitude Correction

Fans selected at sea-level conditions must be corrected for altitude. At 5,000 feet, standard air density is approximately 0.0659 lb/ft³ versus 0.075 lb/ft³ at sea level. Using Fan Law 3, pressure and power are both reduced by the density ratio (0.879), which affects coil performance and system resistance.

Troubleshooting

When field-measured performance does not match fan law predictions, it often indicates a system problem — such as a damaged impeller, incorrect rotation, excessive system effect, or duct leakage. Fan laws provide the theoretical baseline against which actual performance is compared.

Important Limitations

Fan laws are approximations that work best within moderate operating ranges. Key limitations include:

  • System curve changes: Fan laws assume the system resistance curve stays the same. Adding or removing ductwork, dampers, or filters changes the system curve.
  • Efficiency variation: Fan efficiency changes across the operating range. Fan laws assume constant efficiency, which is only approximately true near the design point.
  • Stability limits: Fans operating near stall or surge do not follow fan law predictions reliably.
  • Motor limits: The calculated new BHP must not exceed the motor's rated capacity. Always check motor nameplate before increasing speed.

For critical applications, always verify fan law predictions against the manufacturer's certified fan performance curves.

Key Facts

  • Fan laws are also called the affinity laws and apply to all centrifugal machines including fans, pumps, and blowers.
  • A 20% increase in fan speed increases power consumption by approximately 73% (1.2³ = 1.728).
  • A 10% speed reduction saves approximately 27% in fan energy (0.9³ = 0.729).
  • Fan laws assume the fan operates in the same system (same ductwork and resistance curve).
  • Variable frequency drives (VFDs) exploit Fan Law 1 to achieve significant energy savings by reducing fan speed during part-load conditions.
  • Fan Law 2 (diameter change) is most accurate for small diameter changes (< 15%) on geometrically similar fans.
  • Fan Law 3 (density change) explains why fans at high altitude deliver the same volume but less mass airflow and require less power.

Applications

  • VFD (variable frequency drive) sizing and energy savings estimation.
  • Fan selection and performance prediction at different operating speeds.
  • System balancing — predicting airflow and pressure at adjusted fan speed.
  • Altitude correction — adjusting fan performance for non-standard air density.
  • Troubleshooting — verifying whether measured performance matches expected fan law predictions.
  • Energy audits — estimating savings from reducing fan speed during part-load operation.
  • Retrofit analysis — predicting performance when replacing a fan with a different impeller diameter.

Example Calculation

Example: Fan Law 1 — Speed Change

Given (known operating point):

  • Airflow = 3,000 CFM
  • Static Pressure = 1.5 in. w.g.
  • Brake Horsepower = 5.0 HP
  • Known RPM = 1,000
  • New RPM = 1,200

Calculation:

Ratio = 1200 / 1000 = 1.20

New CFM = 3000 × 1.20    = 3,600 CFM
New SP  = 1.5  × 1.20²   = 1.5 × 1.44 = 2.16 in. w.g.
New BHP = 5.0  × 1.20³   = 5.0 × 1.728 = 8.64 HP

Result:

  • New Airflow = 3,600 CFM (+20%)
  • New Static Pressure = 2.16 in. w.g. (+44%)
  • New BHP = 8.64 HP (+73%)

Interpretation: A 20% speed increase delivers 20% more airflow but requires 73% more power. The motor must be rated for at least 8.64 HP (next standard size: 10 HP). This cubic relationship is why VFDs are so effective at saving energy — even a small speed reduction yields significant power savings.

Example: Fan Law 3 — Density Change (Altitude)

Given:

  • Airflow = 3,000 CFM at sea level
  • Static Pressure = 1.5 in. w.g.
  • BHP = 5.0 HP
  • Sea-level density = 0.075 lb/ft³
  • Density at 5,000 ft = 0.0659 lb/ft³

Calculation:

Ratio = 0.0659 / 0.075 = 0.879

New CFM = 3,000 CFM (unchanged)
New SP  = 1.5 × 0.879 = 1.32 in. w.g.
New BHP = 5.0 × 0.879 = 4.39 HP

Result: At 5,000 ft elevation, the fan moves the same volume of air but develops 12% less pressure and requires 12% less power because the air is less dense.

Standards & References

  • ASHRAE Handbook — HVAC Systems and Equipment — Chapter 21: Fans, fan laws and performance characteristics
  • AMCA Publication 201 — Fans and Systems, fan law applications and system effect factors
  • AMCA Publication 203 — Field Performance Measurement of Fan Systems
  • ASHRAE 90.1 — Energy Standard for Buildings, fan power limitation requirements
  • SMACNA HVAC Systems Duct Design — System resistance and fan selection methodology

Limitations

  • Fan laws assume geometrically similar fans operating in the same system (same ductwork and resistance curve).
  • Accuracy decreases for changes greater than ±20–30% from the known operating point.
  • Fan Law 2 (diameter change) is only valid for small diameter changes on fans with similar geometry.
  • Fan laws do not account for efficiency changes — fan efficiency varies across the operating range.
  • Results assume the fan is operating in a stable region of its performance curve, not in stall or surge.
  • Motor and drive losses are not included — actual electrical input will be higher than calculated BHP.
  • For axial fans, the diameter law exponents differ from centrifugal fan values shown here.

Common Mistakes to Avoid

  • Applying fan laws beyond their valid range (> 30% change) without verifying system curve effects.
  • Forgetting that Fan Law 1 power scales with the cube of speed — a small speed increase causes a large power increase.
  • Using Fan Law 2 (diameter) for fans that are not geometrically similar.
  • Ignoring motor nameplate limits — the new BHP must not exceed the motor's rated horsepower.
  • Confusing volume flow (CFM) with mass flow — Fan Law 3 keeps volume constant but mass flow changes with density.
  • Applying fan laws to fans operating in stall or surge regions where performance is unstable.
  • Not accounting for drive losses when converting between shaft power (BHP) and electrical input power.

Frequently Asked Questions

What are the fan laws?
The fan laws (also called affinity laws) are three sets of proportional relationships that predict how fan airflow, pressure, and power change when speed, impeller diameter, or air density is varied. They are derived from dimensional analysis and apply to all centrifugal turbomachines including fans, blowers, and pumps.
Why does power increase so much with speed?
Power varies with the cube of speed (Fan Law 1). This means a 20% speed increase requires 73% more power (1.2³ = 1.728). Conversely, reducing speed by just 20% saves about 49% of fan power (0.8³ = 0.512). This cubic relationship is the fundamental reason variable frequency drives (VFDs) are so effective at saving energy in HVAC systems.
When should I use Fan Law 1 vs Fan Law 2 vs Fan Law 3?
Use Fan Law 1 (speed) when changing fan RPM via a VFD, pulley change, or motor replacement. Use Fan Law 2 (diameter) when evaluating a different impeller size on the same fan housing — but only for small changes (< 15%). Use Fan Law 3 (density) when the same fan operates at a different altitude, temperature, or barometric pressure that changes air density.
Are fan laws accurate for large speed changes?
Fan laws are most accurate for moderate changes, typically within ±20–30% of the known operating point. For larger changes, the system curve may shift, fan efficiency changes, and the fan may move into an unstable operating region. Always verify large changes against the manufacturer's fan curve.
Do fan laws apply to axial fans?
The speed law (Fan Law 1) applies to axial fans with the same exponents. However, the diameter law (Fan Law 2) uses different exponents for axial fans because the geometry scaling differs from centrifugal fans. Consult the manufacturer for axial fan diameter corrections.
How do fan laws relate to VFD energy savings?
VFDs (variable frequency drives) reduce fan speed to match actual airflow demand. Because power varies with the cube of speed, even a small speed reduction yields large energy savings. For example, running a fan at 80% speed uses only about 51% of full-speed power. This makes VFDs one of the most cost-effective energy conservation measures in HVAC systems.

Frequently Used Together

Engineers often use these calculators in combination for complete project workflows:

Fan Efficiency Calculator

Altitude Correction For Hvac

Sound Attenuation In Ducts Calculator

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