Fan Laws Calculator — Speed, Diameter & Density Changes
The fan laws predict how a fan's airflow, pressure, power and noise change when you alter its speed, its impeller diameter or the density of the air. Enter the known operating point and the change; the calculator returns the new point and the energy saving.
No signup · Works on mobile · Formulas shown below · Updated 2026-08-23
Fan Affinity Laws Calculator
Q ∝ N·D³ · P ∝ N²·D²·ρ · W ∝ N³·D⁵·ρ. Leave diameter and density unchanged to see a pure speed change.
Results
Engineering estimate for preliminary sizing. Verify against the fan curve, local codes and your system measurements before purchase. Ask a Longwell engineer to check your duty point free of charge.
The fan laws (affinity laws)
For a given fan operating on a fixed system (the same ducts, filters and dampers), the three fan laws relate a change in speed N, impeller diameter D and air density ρ to the new airflow Q, pressure P and power W:
The most-used consequence: because power follows the cube of speed, a fan running at 80 % speed draws only 0.8³ = 51 % of full-speed power. At 50 % speed it draws 12.5 %. That is why EC fans and variable-speed drives pay back so fast on any fan that runs at part load.
The laws hold while the fan operates at the same point on its dimensionless curve — i.e. the system curve is a pure square law (P ∝ Q²) and passes through the origin. Fixed pressure in the system (a pressurised room, a minimum duct static setpoint) breaks that assumption; then use the fan curve directly.
Speed change cheat sheet
Speed ratio
Airflow
Pressure
Power
Sound (approx.)
50 %
50 %
25 %
12.5 %
−15 dB
60 %
60 %
36 %
21.6 %
−11 dB
70 %
70 %
49 %
34.3 %
−7.7 dB
80 %
80 %
64 %
51.2 %
−4.8 dB
90 %
90 %
81 %
72.9 %
−2.3 dB
110 %
110 %
121 %
133 %
+2.1 dB
120 %
120 %
144 %
173 %
+4.0 dB
Worked example: trimming an oversized exhaust fan
Given: 500 mm axial fan at 1,450 rpm delivers 10,000 m³/h at 300 Pa, drawing 1.5 kW. The space only needs 8,000 m³/h.
Speed ratio = 8,000 / 10,000 = 0.80 → new speed 1,160 rpm
Pressure = 300 × 0.8² = 192 Pa (fine — the system needs less pressure at lower flow)
Power = 1.5 × 0.8³ = 0.77 kW → saves 0.73 kW
At 6,000 h/year and $0.15/kWh: 0.73 × 6,000 × 0.15 = $657 per year — from a 0–10 V signal to an EC fan or a $300 VSD.
Sound drops ~4.8 dB — clearly audible.
Frequently Asked Questions
What are the three fan laws?
Airflow is proportional to speed; pressure to speed squared; power to speed cubed. The same laws apply to impeller diameter (D, D², D³ for the dimensionless form, or D³, D², D⁵ when holding speed constant) and, for pressure and power, to air density.
If I slow a fan by 20 %, how much energy do I save?
About 49 %: 0.8³ = 0.512, so the fan draws 51 % of its original power. Airflow drops to 80 % and pressure to 64 %. The saving is real only when system resistance is unchanged.
Can I use the fan laws to pick a bigger fan?
Only within the same fan family (geometrically similar impellers). A 560 mm version of a 500 mm fan at the same rpm gives (560/500)³ = 1.40× the airflow, 1.25× the pressure and 1.76× the power. Between different designs, compare catalog curves instead.
Do the fan laws apply to EC fans?
Yes — they describe the aerodynamics, not the motor. EC fans simply make speed changes easy (0–10 V, PWM or Modbus) and keep motor efficiency high at part load, so the cube-law savings are actually realised at the wall socket.
Why does my pressure not fall with the square of speed?
Because part of your system pressure is fixed, not flow-dependent — e.g. a room held at +20 Pa or a duct static setpoint. The fan laws assume the whole system curve is P ∝ Q². With a fixed component, slowing the fan moves it to a different point on its curve; read the curve directly.
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This calculator is free to reference in articles, forums, specifications and course material. Please credit it with a link:
<a href="https://www.longwellfans.com/resources/fan-laws-calculator/">Fan Affinity Laws Calculator</a> by LONGWELL Fans
APA: LONGWELL Fans. (2026). Fan Affinity Laws Calculator. https://www.longwellfans.com/resources/fan-laws-calculator/
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