Pump & Fan Speed vs Power Calculator
Affinity laws for VFD-driven pumps and fans: how flow, pressure and power change with speed or frequency, and the yearly energy difference.
Formulas (affinity laws)
- Speed ratio r = n2 ÷ n1 ≈ f2 ÷ f1 (drive frequency ratio, slip ignored)
- Flow Q2 = Q1 × r
- Pressure / head H2 = H1 × r²
- Power P2 = P1 × r³
- Yearly energy difference = (P1 − P2) × operating hours
Flow, pressure and power by speed (rated = 100 %)
| Speed | At 60 / 50 Hz | Flow | Pressure | Power |
|---|---|---|---|---|
| 100 % | 60 / 50 Hz | 100 % | 100 % | 100 % |
| 90 % | 54 / 45 Hz | 90 % | 81 % | 72.9 % |
| 80 % | 48 / 40 Hz | 80 % | 64 % | 51.2 % |
| 70 % | 42 / 35 Hz | 70 % | 49 % | 34.3 % |
| 60 % | 36 / 30 Hz | 60 % | 36 % | 21.6 % |
| 50 % | 30 / 25 Hz | 50 % | 25 % | 12.5 % |
Lowering speed by 20 % gives 0.8³ = 51.2 % power, roughly half. The DOE fan sourcebook says the same: «reducing fan rotational speed by 20 percent decreases fan power by 50 percent» (rounded).
When the laws do not hold
- Systems with high static head or static pressure: the affinity laws are the theoretical result for friction-only systems. A pump lifting to a height can approach shut-off with only a small speed cut, so flow can drop far more than the formula says. The DOE pumping sourcebook says drives must be evaluated carefully for high-static-head systems.
- Low-load efficiency: at much lower speed, motor efficiency and power factor drop (DOE fan sourcebook). «Energy saved» above ignores efficiency changes and leans to the upper bound.
- Frequency ratio = speed ratio is an approximation. Induction motors run slower by the slip; see the motor speed calculator for the real speed.
- When replacing damper or valve throttling with a drive, use a measured power at the old operating point as the baseline.
Where it is used
- Estimating flow and power per operating frequency when adding a VFD to a fan or pump.
- Explaining the savings of running HVAC fans or cooling water pumps at a lower frequency.
- Choosing a frequency for a target flow (friction-dominated systems).
FAQ
What happens to power when I go from 60 Hz to 48 Hz?
The speed ratio is 0.8, so power is 0.8³ = 0.512, about 51 %. A 22 kW rated point becomes about 11.3 kW (theoretical, friction-dominated system).
Is flow proportional to speed?
Under the affinity laws, yes (Q ∝ n). Pressure goes with the square and power with the cube.
Why are real savings smaller than calculated?
Static head in the system, lower motor and drive efficiency at light load, and the drive's own losses. The calculation is close to a theoretical upper bound.
For frequency versus actual motor speed (poles, slip), use the Motor Speed Calculator. For motor rated current and input power, use the Motor Current Calculator.
Basis
U.S. Department of Energy, «Improving Fan System Performance: A Sourcebook for Industry» (DOE/GO-102003-1294, 2003): fan laws on p.4 (flow ∝ n, pressure ∝ n², power ∝ n³), «20 percent speed reduction → 50 percent power reduction» and the drop in motor efficiency and power factor at low load on p.18. The same form for pumps and the caution for high-static-head systems: «Improving Pumping System Performance» (2nd ed., 2006) pp.17, 49. DOE fan sourcebook (PDF) · DOE pumping sourcebook (PDF).