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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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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
SP2SP1=(N2N1)2\frac{SP_2}{SP_1} = \left(\frac{N_2}{N_1}\right)^{2}
Where
  • SP1SP_1= Static pressure at speed 1
  • N1N_1= Fan speed 1
  • SP2SP_2= Static pressure at speed 2
  • N2N_2= Fan speed 2
Missing one of these? Work it out first, then come back
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7 formulasHow flow, head and power scale with impeller speed and diameter — the first, second and third power relationships behind every VFD retrofit.