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Fan Affinity Law: Static Pressure vs Speed

SP2SP1=(N2N1)2\frac{SP_2}{SP_1} = \left(\frac{N_2}{N_1}\right)^{2}
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Worked example: 1.0 kPa at 900 rpm sped to 1170 rpm → 1.69 kPa. 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.

Where Fan Affinity Law: Static Pressure vs Speed fits

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Fan Brake Horsepower
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See also

Fan Brake Horsepower: Both use fan pressure.Fan Affinity Law: Airflow vs Speed: Both use shaft speed.Fan Affinity Law: Power vs Speed: Both use shaft speed.Pump Affinity Law: Flow vs Speed: Both use shaft speed.Pump Affinity Law: Head vs Speed: Both use shaft speed.Pump Affinity Law: Power vs Speed: Both use shaft speed.
1 more relatedPump Specific Speed (Ns): Both use shaft speed.
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Fan Affinity Law: Static Pressure vs Speed explained

N2N1SP1SP2

Static pressure is the air's velocity energy converted at the fan discharge, and velocity energy goes as the square of speed. Take a fan making 1.0 kPa at 900 rpm up to 1170 rpm and it makes 1.0 × 1.3² = 1.69 kPa. Duct designers meet this law in reverse when a system is starved: doubling the speed to fix a 50% airflow shortfall means quadrupling the pressure the ductwork, flex connectors and access doors must contain.

Trade practice still measures fan static in inches of water gauge (1 in w.g. ≈ 249 Pa ≈ 0.0833 ft H₂O), so if your gauge reads inches, convert before entering it here. The square law also explains why a dirty filter is self-limiting rather than self-correcting: the added resistance moves the operating point up a fixed fan curve, so airflow falls while pressure rises, and the occupant complains about comfort long before the fan complains about load.

Fan Affinity Law: Static Pressure vs Speed formula

SP2SP1=(N2N1)2\frac{SP_2}{SP_1} = \left(\frac{N_2}{N_1}\right)^{2}
Where
  • SP1SP_1= Static pressure at speed 1 (kPa)
  • N1N_1= Fan speed 1 (rpm)
  • SP2SP_2= Static pressure at speed 2 (kPa)
  • 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: Static Pressure vs Speed Calculator. https://formula.expert/solvers/fan-affinity-pressure-speed

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