Fan Laws (Flow, Head, Power, Speed) Calculator

Formula Used

Flow law: Q₂ / Q₁ = N₂ / N₁

Head law: H₂ / H₁ = (N₂ / N₁)²

Power law: P₂ / P₁ = (N₂ / N₁)³

These fan laws apply when the fan geometry remains similar and air properties stay reasonably constant. The calculator uses the speed ratio r = N₂/N₁, then computes Q₂ = Q₁r, H₂ = H₁r², and P₂ = P₁r³.

For reverse calculations, the calculator rearranges the same formulas: N₂ = N₁(Q₂/Q₁), N₂ = N₁√(H₂/H₁), and N₂ = N₁(P₂/P₁)^1/3.

How to Use This Calculator

Enter the known base operating point: flow, head, power, and speed.
Choose suitable engineering units for display clarity.
Select the solve mode based on your design question.
Enter either target speed, target flow, target head, or target power.
Press Calculate Fan Laws to see results above the form and in the detailed section.
Review the comparison table and Plotly graph for proportional changes.
Use the CSV button for spreadsheet-friendly export.
Use the PDF button to save a printable report.

Scenario	Base Flow	Base Head	Base Power	Base Speed	Target Speed	Estimated Flow	Estimated Head	Estimated Power
Case A	4.00 m³/s	700 Pa	8.00 kW	1200 RPM	1500 RPM	5.00 m³/s	1093.75 Pa	15.63 kW
Case B	5.20 m³/s	920 Pa	14.00 kW	1450 RPM	1600 RPM	5.74 m³/s	1119.55 Pa	18.79 kW
Case C	3.50 m³/s	600 Pa	6.20 kW	1000 RPM	900 RPM	3.15 m³/s	486.00 Pa	4.52 kW

FAQs

1. What do fan laws predict?

Fan laws predict how flow, pressure head, and power change when fan speed changes under similar geometry and comparable air conditions.

2. Why does power rise faster than flow?

Power follows the cube of the speed ratio. Even a moderate speed increase can create a much larger motor load than the matching flow increase.

3. Can I use this for reverse calculations?

Yes. The calculator can estimate required speed from a target flow, target head, or target power using rearranged fan law equations.

4. Does this work if impeller diameter changes?

This page is set up for speed-based scaling with similar geometry. Diameter-change studies need separate affinity treatment and careful manufacturer verification.

5. Are the results exact for every installation?

No. Real systems can deviate because of efficiency drift, density shifts, losses, duct changes, and operating point movement on the fan curve.

6. Which units should I use?

Use any consistent units for your engineering workflow. The laws depend on ratios, so the chosen unit labels mainly improve clarity and reporting.

7. Why is head based on the square of speed?

Pressure head reflects dynamic effects tied to velocity changes. Since velocity scales with speed, head scales with the square of that ratio.

8. When should I avoid using fan laws alone?

Avoid relying only on fan laws for safety-critical work, stall-prone conditions, major density changes, non-similar fans, or certified equipment selection.