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Fan Affinity Law: Power vs Speed

P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}
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Worked example: 4 kW at 600 rpm; 13.5 kW needs 900 rpm. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

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See also

Pump Affinity Law: Power vs Speed: Both use shaft power and shaft speed.Fan Affinity Law: Airflow vs Speed: Both use shaft speed.Fan Affinity Law: Static Pressure vs Speed: Both use shaft speed.Fan Brake Horsepower: Both use shaft power.Pump Affinity Law: Flow vs Speed: Both use shaft speed.Pump Affinity Law: Head vs Speed: Both use shaft speed.
5 more relatedPump Brake Horsepower: Both use shaft power.Pump Efficiency from Hydraulic and Shaft Power: Both use shaft power.Pump Specific Speed (Ns): Both use shaft speed.Ship Propulsive Power by the Admiralty Coefficient: Both use shaft power.Steam Turbine Power Output: Both use shaft power.
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Fan Affinity Law: Power vs Speed explained

N2N1P1P2

Multiply the linear flow law by the square-law pressure and you get a cube: a 5 hp fan sped from 800 to 1000 rpm needs 5 × 1.25³ ≈ 9.77 hp. That factor of nearly two for a 25% speed change is the most expensive line item in HVAC retrofit work, and it is precisely why a variable-air-volume system that spends most of the year at 60% airflow uses only about 22% of design fan energy.

Every experienced service technician has a story about a re-sheave that tripped the overloads within an hour. The rule of thumb: never raise fan speed without checking that the new power fits inside the motor's service factor. Run the numbers first: 15% more rpm is 52% more power, and there is no such thing as a small speed increase.

Fan Affinity Law: Power vs Speed formula

P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}
Where
  • P1P_1= Fan power at speed 1 (W)
  • N1N_1= Fan speed 1 (rpm)
  • P2P_2= Fan power at speed 2 (W)
  • N2N_2= Fan speed 2 (rpm)
In this toolkit

The pump and fan affinity laws

7 formulasHow flow, head and power scale with impeller speed and diameter — the first, second and third power relationships behind every VFD retrofit.

Revised 16 October 2026
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formula.expert. (2026, October 16). Fan Affinity Law: Power vs Speed Formula & Calculator. https://formula.expert/solvers/fan-affinity-power-speed

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