Fan Laws Calculator

Concepts behind this calculation

Scale same-diameter fan airflow, pressure and shaft power by a new speed or target actual airflow, retaining density or explicitly accounting for two inlet-air densities.

Fan laws describe corresponding operating points of the same fan when speed changes. The speed ratio r changes actual inlet volume flow directly, while pressure and mechanical shaft power respond more strongly. The baseline airflow, pressure, speed, and shaft power must all describe one operating point; assembling them from unrelated catalog ratings creates a fictional starting condition.

When inlet density changes, the explicit-density methods also adjust pressure and shaft power by the new-to-baseline total-air density ratio. They do not turn actual CFM into standard CFM or hold mass flow constant. A target airflow identifies a point on the assumed similarity path; a real system with changed resistance or a fixed pressure requirement may operate elsewhere.

How to use this calculator

1. Choose Solve for to match a new speed or Target airflow.
2. Enter Baseline fan speed, Baseline airflow, Baseline fan pressure, and Baseline shaft power from one compatible point.
3. Enter New fan speed or Target airflow. For density methods, document Fan, operating-point and density reference, confirm Same-fan similarity and airflow basis, and enter both total inlet-air densities.
4. Review the predicted point together with its mass-flow and equipment implications.

Calculation method and applicability

r = N₂/N₁ = Q₂,actual/Q₁,actual. With fixed diameter: Q₂ = Q₁r; P₂ = P₁(ρ₂/ρ₁)r²; BHP₂ = BHP₁(ρ₂/ρ₁)r³. Original modes set the density ratio to 1.

N = actual fan shaft speed (RPM); Q = actual inlet volume flow (CFM); P = matching fan pressure (in. w.g.); ρ = total inlet-air density (lb/ft³); BHP = mechanical shaft horsepower; r = dimensionless speed/actual-flow ratio. Subscripts 1 and 2 identify the baseline and new states.

Input definitions and units

Solve for

Keep fan diameter and geometry fixed. Original methods retain density; explicit-density methods also scale pressure/shaft BHP with the supplied total inlet-air density ratio. Choices: Performance at a new speed; Speed for a target airflow; New speed with explicit inlet-air densities; Target actual airflow with explicit inlet-air densities.

Baseline fan speed (RPM)

Use fan RPM, not motor RPM when a belt drive changes the ratio.

Baseline airflow (CFM)

Actual volume flow at the baseline fan inlet state, paired with the baseline RPM, pressure and shaft BHP. SCFM is not an interchangeable actual-flow input.

Baseline fan pressure (in. w.g.)

Use the same fan total or static pressure definition at both points.

Baseline shaft power (BHP)

Mechanical power at the fan shaft; this is not electrical input kW.

New fan speed (RPM)

Check the fan and drive manufacturer speed limit before changing speed. Applies to Solve for: Performance at a new speed or New speed with explicit inlet-air densities.

Target airflow (CFM)

Actual volume flow at the new inlet state on the same fan-similarity path, not SCFM or a fixed mass-flow target. Real fan/system curves may limit the attainable point. Applies to Solve for: Speed for a target airflow or Target actual airflow with explicit inlet-air densities.

Fan, operating-point and density reference

Identify the fixed fan geometry, compatible baseline operating point, matching total/static pressure definition and actual inlet density sources. Record the new-state basis and independent applicability of similarity; a plausible result does not authenticate the supplied data. Applies to Solve for: New speed with explicit inlet-air densities or Target actual airflow with explicit inlet-air densities.

Same-fan similarity and airflow basis

Confirm unchanged diameter/geometry, actual inlet volume-flow and total-air density definitions, matching pressure and mechanical fan-shaft power, and applicable dynamically similar operating points. No fixed-pressure system or changed efficiency is solved here. Choices: Not established; Fixed geometry, compatible inlet states and fan similarity established. Applies to Solve for: New speed with explicit inlet-air densities or Target actual airflow with explicit inlet-air densities.

Baseline total inlet-air density (lb total air/ft³)

Total air mass per actual baseline inlet volume, including water vapor if present. This is not dry-air mass per volume or a universal standard-air default. Supply the actual applicable property. Applies to Solve for: New speed with explicit inlet-air densities or Target actual airflow with explicit inlet-air densities.

New total inlet-air density (lb total air/ft³)

Use total air mass per actual new inlet volume on the same basis. Density must be independently established; no temperature/elevation/humidity conversion or weather lookup is performed. Applies to Solve for: New speed with explicit inlet-air densities or Target actual airflow with explicit inlet-air densities.

How to interpret the result

Read the airflow, RPM, pressure, and BHP as a matched predicted point. Check that point against the actual fan/system curves and equipment limits before treating it as attainable.

Worked examples

Assumptions and limits

• All methods hold fan diameter and geometry fixed and require dynamically similar operating points. No impeller trimming or geometrical scaling to another fan is modeled.
• Original methods retain density. Explicit-density methods use the supplied total inlet-air density ratio for pressure and shaft power, not for actual volume flow. Densities are not inferred from weather, temperature, elevation or RH.
• Density methods report total-air mass as 60 × actual CFM × total-air density at each inlet state. This differs from dry-air density, SCFM and a reference-state mass-conserving conversion.
• Classical ASHRAE 2024 laws neglect Reynolds-number effects; no Mach/compressibility correction, stall-region change or efficiency curve is calculated. Confirm the approximation applies at both points.
• Use compatible baseline fan total/static pressure and mechanical shaft BHP, not an arbitrary TESP value, motor nameplate horsepower or electrical kW. No motor, belt, VFD or startup-loss model is applied.
• A system with a flow-independent pressure term, changed dampers/filters/resistance or another nonhomologous operating region needs independently applicable fan/system curves. The scaled point is not guaranteed attainable.
• Predicted shaft BHP is not annual electrical savings or an allowed speed/power decision. Fan/drive/motor limits, worst-case inlet density and actual controls must be checked separately.
• Required reference and basis confirmation record user assumptions, not source authenticity. Nonfinite and underflowed positive derived outputs are withheld; zero baseline pressure and/or BHP remain valid arithmetic boundaries.

Sources

• Greenheck: fan performance and fan lawsManufacturer application guide; similarity relationships, not a permission to exceed equipment limits.
• ASHRAE 2024 Systems and Equipment, Chapter 21: FansNamed 2024 classical fan laws, Table 2 Law 1a–1c. With diameter fixed, volume scales with speed, while pressure and shaft power also scale with inlet density. Reynolds/Mach and bearing/drive deviations remain outside the model.
• Greenheck Vektor-MD performance catalog: Air Density Correction FactorsPrinted page 9 example: 17,000 CFM, factor 1.14, 4 actual / 4.56 standard in. wg, approximately 1,450 RPM and 20 standard / 17.5 operating BHP. Supplied-point density arithmetic reproduces within stated rounding tolerance; product selection, density table lookup and motor choice are not implemented.
• MEPBase: Fan Laws CalculatorActual density-ratio form executed in IP units with fixed diameter. At 1,750→1,400 RPM and density ratio 0.8, baseline 5,000 CFM / 2.5 in. wg / 3.5 BHP gave 4,000 CFM / 1.28 in. wg / 1.43 HP at peer display precision. Motor and savings outputs are not adopted.
• Longwell: Fan Laws CalculatorDirect manufacturer peer controls expose both inlet densities, speeds and diameters. This implementation retains one diameter and does not reuse sound-level, motor, trimming or diameter predictions; no live Longwell numerical result is claimed.