Pump Affinity Laws Calculator (Speed & Impeller Diameter)
By Santaji GadepatilinUpdated November 5, 2026
The affinity laws predict how a centrifugal pump's flow, head and power change with speed or impeller diameter: flow scales with the ratio, head with its square and power with its cube. This pump affinity laws calculator applies them for a VFD speed change or an impeller trim — useful when comparing centrifugal vs positive displacement pumps or sizing a VFD.
How to use the pump affinity laws calculator
Enter the pump’s known duty point — flow, head and shaft power — at the original speed and impeller diameter, then enter the new speed and/or new diameter. Keep D₂ = D₁ for a pure speed change, or N₂ = N₁ for an impeller trim.
Pump affinity laws
Q₂ = Q₁ (N₂/N₁)(D₂/D₁) · H₂ = H₁ (N₂/N₁)²(D₂/D₁)² · P₂ = P₁ (N₂/N₁)³(D₂/D₁)³
Worked example
A pump delivers 100 m³/h at 50 m head and absorbs 18.5 kW at 1,450 rpm. A VFD slows it to 1,160 rpm (ratio 0.80):
- Q₂ = 100 × 0.80 = 80.0 m³/h
- H₂ = 50 × 0.80² = 32.0 m
- P₂ = 18.5 × 0.80³ = 9.47 kW — a 49% power reduction
Speed reduction table (100 m³/h, 50 m, 18.5 kW at 1,450 rpm)
| Speed | Flow | Head | Power | Power saving |
|---|---|---|---|---|
| 100% (1450 rpm) | 100.0 m³/h | 50.0 m | 18.50 kW | 0% |
| 90% (1305 rpm) | 90.0 m³/h | 40.5 m | 13.49 kW | 27% |
| 80% (1160 rpm) | 80.0 m³/h | 32.0 m | 9.47 kW | 49% |
| 70% (1015 rpm) | 70.0 m³/h | 24.5 m | 6.35 kW | 66% |
| 60% (870 rpm) | 60.0 m³/h | 18.0 m | 4.00 kW | 78% |
| 50% (725 rpm) | 50.0 m³/h | 12.5 m | 2.31 kW | 88% |
Notes
- Efficiency is assumed constant — real savings are slightly lower because motor and VFD losses rise at low load.
- Check that the reduced head still overcomes the static head of the system.
- For fans and blowers the same laws apply; see the fan affinity laws calculator.
Frequently asked questions
What are the pump affinity laws?
Q₂/Q₁ = N₂/N₁, H₂/H₁ = (N₂/N₁)² and P₂/P₁ = (N₂/N₁)³. The same relations hold approximately for a change in impeller diameter D at constant speed.
How much energy does slowing a pump save?
Power falls with the cube of speed, so running at 80% speed needs about 51% of the power — a 49% saving — if the system has little static head.
Do the affinity laws work with high static head?
Not directly. They move the pump along curves of constant efficiency, but a system with large static head does not follow those curves — find the new duty point on the system curve instead.
How accurate are they for impeller trimming?
Reasonably for trims up to about 10–15% of diameter. Beyond that efficiency drops and the actual head and flow fall below the predicted values.