Pump & Fan Affinity Law Calculator Pumps & Fans
One operating point and a speed (or impeller) change, scaled by the affinity laws.
Inputs are seeded with an example — edit them to your numbers.
Input
Speeds take any consistent unit (RPM, Hz, %). Flow, head, and power pass through unchanged, so the outputs carry whatever units you entered — head (ft) for pumps, static pressure (in. w.c.) for fans, power in bhp or kW.
Output — at N₂
Q₂ / H₂ / P₂ carry the same units you entered above — this tool just scales the magnitudes.
Worked example
A VFD slows a pump from 60 Hz to 50 Hz — 83 % speed — at an operating point of 100 GPM, 50 ft head, 10 bhp.
- Ratio:
50 ÷ 60 = 0.833. - Flow:
100 × 0.833 = 83.3 GPM(linear). - Head:
50 × 0.833² = 34.7 ft(square). - Power:
10 × 0.833³ = 5.8 bhp(cube).
A 17 % speed cut costs about 17 % of flow but nearly halves the power. The cube law is the energy case for variable-speed pumping — and the reason the savings shrink fast once you stop riding the curve down (see Pump Control).
The laws scale points on the pump or fan’s own curve; whether the machine actually rides down the affinity parabola is a system question. The cube-law payoff assumes a mostly-friction system curve — little or no static lift — with efficiency holding roughly constant. Add real static head — an open cooling tower, irrigation, anything that lifts water out of a sump (open-loop work; a closed loop recovers its own elevation and carries none) — and the operating point leaves the parabola, so the savings flatten short of the cube. Speed is the exact case for the curve; the system decides how much of it you keep.
Input
Diameters take any consistent unit (in, mm). The diameter laws hold only for modest trims of the same casing — past roughly 10–15 % the efficiency falls off and the simple ratios drift.
Output — at D₂
Q₂ / H₂ / P₂ carry the same units you entered above — this tool just scales the magnitudes.
The laws
| Quantity | By speed (N) | By diameter (D) |
|---|---|---|
| Flow Q | ∝ N₂/N₁ | ∝ D₂/D₁ |
| Head / pressure H | ∝ (N₂/N₁)² | ∝ (D₂/D₁)² |
| Power P | ∝ (N₂/N₁)³ | ∝ (D₂/D₁)³ |
Speed is the exact, reversible case — slow a pump and speed it back up and it returns to the same point. Impeller trim is permanent metal and only approximate: good for a one-time match of an oversized pump to its duty, not for control.
Before acting on P₂, check the motor. The cube law works both ways: a 10 % speed increase asks the motor for 33 % more power. This page scales the load — as a cross-check and a teaching aid — but whether the motor survives the new speed is decided by the nameplate HP, the service factor, and the overload settings. Confirm those before raising a maximum frequency; the calculator predicts the load, it doesn’t protect the motor.