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Pump Affinity Law: Head vs Speed

H2H1=(N2N1)2\frac{H_2}{H_1} = \left(\frac{N_2}{N_1}\right)^{2}
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Worked example: 16 m at 1160 rpm; 25 m needs 1450 rpm. Press Try an example to run it live, then adjust anything.

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Where Pump Affinity Law: Head vs Speed fits

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Pump Water HorsepowerPump Brake HorsepowerPump Affinity Law: Head vs Impeller DiameterPump Specific Speed (Ns)
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See also

Pump Specific Speed (Ns): Both use pump total head and shaft speed.Pump Affinity Law: Head vs Impeller Diameter: Both use pump total head.Pump Brake Horsepower: Both use pump total head.Pump Water Horsepower: Both use pump total head.Total Dynamic Head: Both use pump total head.Fan Affinity Law: Airflow vs Speed: Both use shaft speed.
4 more relatedFan Affinity Law: Power vs Speed: Both use shaft speed.Fan Affinity Law: Static Pressure vs Speed: Both use shaft speed.Pump Affinity Law: Flow vs Speed: Both use shaft speed.Pump Affinity Law: Power vs Speed: Both use shaft speed.
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Pump Affinity Law: Head vs Speed explained

N2N1H1H2

Head is a velocity effect: the impeller tip speed sets how much energy the liquid leaves with, and energy goes as velocity squared. Trim a 1750 rpm pump making 120 ft of head down to 1450 rpm and you keep 120 × (1450/1750)² ≈ 82.4 ft. Note the head is expressed in feet or metres of the pumped liquid, not of water: the affinity laws are blind to specific gravity, which is exactly why manufacturers publish curves in feet rather than psi.

The classic field error is reading a psi gauge and scaling that by the square. Convert to head first. A pump on 1.2 SG brine showing 52 psi is making 52 × 2.31/1.2 ≈ 100 ft of head, and it is that 100 ft, not the 52 psi, that follows the speed-squared rule.

Pump Affinity Law: Head vs Speed formula

H2H1=(N2N1)2\frac{H_2}{H_1} = \left(\frac{N_2}{N_1}\right)^{2}
Where
  • H1H_1= Head at speed 1 (m)
  • N1N_1= Speed 1 (rpm)
  • H2H_2= Head at speed 2 (m)
  • N2N_2= 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). Pump Affinity Law: Head vs Speed Formula & Calculator. https://formula.expert/solvers/pump-affinity-head-speed

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