What are the pump affinity laws?

For the same pump, flow scales with the ratio, head scales with the ratio squared, and power scales with the ratio cubed.

What is required in Speed mode?

Enter the initial speed n₁ and new speed n₂ in rpm. Baseline flow, head, and power are optional.

What is required in Diameter mode?

Enter the initial diameter D₁ and new diameter D₂, using meters, centimeters, or millimeters.

Can I calculate only the scaling ratio?

Yes. If Q₁, H₁, and P₁ are all omitted, the calculator returns only the ratio.

Which units are supported?

Flow supports m³/s, L/s, L/min, and m³/h; head supports m and ft; power supports W, kW, and hp; diameter supports m, cm, and mm.

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Pump Affinity Laws Calculator (Q∝n, H∝n², P∝n³)

Apply the pump affinity laws to the same pump at different speeds or with a different impeller diameter. Speed mode: ratio = n2/n1; diameter mode: ratio = D2/D1. Then Q2 = Q1·ratio, H2 = H1·ratio², P2 = P1·ratio³. Q1, H1 and P1 are optional baseline-condition inputs; if all three are omitted, only the ratio is returned. Flow in m³/s/L/s/L/min/m³/h, head in m/ft, power in W/kW/hp, impeller diameter in m/cm/mm; SI equivalents (m³/s, m, W) are also reported.

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2 examples

Speed mode: n1=1750 rpm, n2=3500 rpm (ratio=2), Q1=10 L/s, H1=20 m, P1=1000 W -> Q2=20 L/s, H2=80 m, P2=8000 W

ratio = n2/n1 = 3500/1750 = 2. Flow Q2 = Q1·ratio = 10·2 = 20 L/s (0.02 m³/s). Head H2 = H1·ratio² = 20·4 = 80 m. Power P2 = P1·ratio³ = 1000·8 = 8000 W.

{"result":"Pump affinity laws (speed). n1=1750 rpm, n2=3500 rpm, ratio=2. Q: 10 L/s → 20 L/s (0.01 → 0.02 m³/s). H: 20 m → 80 m (20 → 80 m). P: 1000 W → 8000 W (1000 → 8000 W).","metadata":{"input":{"mode":"speed","speedN1":1750,"speedN2":3500,"diameterUnit":"m","flowQ1":10,"flowUnit":"L/s","headH1":20,"headUnit":"m","powerP1":1000,"powerUnit":"W"},"result":{"ratio":2,"mode":"speed","flowQ1":10,"flowQ2":20,"flowUnit":"L/s","flowQ1_m3_s":0.01,"flowQ2_m3_s":0.02,"headH1":20,"headH2":80,"headUnit":"m","headH1_m":20,"headH2_m":80,"powerP1":1000,"powerP2":8000,"powerUnit":"W","powerP1_W":1000,"powerP2_W":8000}}}

Diameter mode: D1=0.2 m, D2=0.25 m (ratio=1.25), Q1=50 L/min, P1=2 kW -> Q2=62.5 L/min, P2=3.9063 kW (3906.25 W)

ratio = D2/D1 = 0.25/0.2 = 1.25. Flow Q2 = Q1·ratio = 50·1.25 = 62.5 L/min (0.001 m³/s). Head not supplied. Power P2 = P1·ratio³ = 2·1.953125 = 3.90625 kW (3906.25 W) → 3.9063 kW at 4 dp.

{"result":"Pump affinity laws (diameter). D1=0.2 m, D2=0.25 m, ratio=1.25. Q: 50 L/min → 62.5 L/min (0.0008 → 0.001 m³/s). P: 2 kW → 3.9063 kW (2000 → 3906.25 W).","metadata":{"input":{"mode":"diameter","diameterD1":0.2,"diameterD2":0.25,"diameterUnit":"m","flowQ1":50,"flowUnit":"L/min","powerP1":2,"powerUnit":"kW"},"result":{"ratio":1.25,"mode":"diameter","flowQ1":50,"flowQ2":62.5,"flowUnit":"L/min","flowQ1_m3_s":0.0008,"flowQ2_m3_s":0.001,"headH1":null,"headH2":null,"headUnit":"m","headH1_m":null,"headH2_m":null,"powerP1":2,"powerP2":3.9063,"powerUnit":"kW","powerP1_W":2000,"powerP2_W":3906.25}}}

Inputs

Options are grouped so long tools stay easier to scan.

13 options

SettingsAdjust formats, ranges, numbers, and modes.13

ModeselectOptionalSpeed mode uses the speed ratio n2/n1. Diameter mode uses the impeller diameter ratio D2/D1.Speed n₁ (rpm)numberRequiredInitial pump speed n1 (rpm). Required when Mode = Speed.Speed n₂ (rpm)numberOptionalNew pump speed n2 (rpm). Required when Mode = Speed.Impeller Diameter D₁numberOptionalInitial impeller diameter D1. Enter in the selected Diameter Unit. Required when Mode = Diameter.Impeller Diameter D₂numberOptionalNew impeller diameter D2. Enter in the selected Diameter Unit. Required when Mode = Diameter.Diameter UnitselectOptionalInitial Flow Q₁numberOptionalInitial flow Q1 at the baseline speed / diameter. Enter in the selected Flow Unit. Optional.Flow UnitselectOptionalInitial Head H₁numberOptionalInitial head H1 at the baseline speed / diameter. Enter in the selected Head Unit. Optional.Head UnitselectOptionalInitial Power P₁numberOptionalInitial power P1 at the baseline speed / diameter. Enter in the selected Power Unit. Optional.Power UnitselectOptionalDecimal PlacesnumberOptional

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Pump Affinity Laws Calculator (Q∝n, H∝n², P∝n³)

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Examples

1. Doubling pump speed

2. Evaluating a larger impeller

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3. Returning a ratio only