Pump Efficiency Formula: How to Calculate and Improve It

End-suction chilled water pumps with pressure gauges on suction and discharge. Those two gauges are all you need to calculate total head -- and with a power meter, the pump's real efficiency. [REPLACE with your own project photograph or a licensed image.]

TL;DR

What Is Pump Efficiency?

Pump efficiency is the ratio of the hydraulic power the pump delivers to the fluid to the shaft power delivered into the pump. Everything that does not come out as useful flow and head comes out as heat, noise and vibration.

That definition contains a distinction people routinely blur, and it is worth nailing down before any arithmetic: pump efficiency is not motor efficiency, and neither is the same as wire-to-water efficiency.

If you measure electrical input at the panel and divide hydraulic power by it, you have calculated wire-to-water efficiency, not pump efficiency -- and you will report a number several points lower than the pump's actual performance. On a VFD-driven pump there is a third loss to account for as well, usually 2–4%.

Overall Efficiency Is a Product of Three Sub-Efficiencies

For readers who want the layer underneath, a pump's overall efficiency decomposes into three components that multiply together:

• Hydraulic efficiency -- losses from friction, turbulence, shock at the impeller inlet and flow separation inside the volute. Largest of the three, and most sensitive to how far you are operating from BEP.
• Volumetric efficiency -- losses from internal recirculation, where fluid that has already been pressurised leaks back through wear ring clearances to the suction side. This is the component that degrades most predictably with age.
• Mechanical efficiency -- losses in bearings, seals and disc friction on the impeller shrouds. Generally the smallest of the three.

Typical Efficiency Ranges

Efficiency scales with size. Losses that are proportional to surface area matter less as volume grows, so a large pump is inherently more efficient than a small one of the same design quality. Judging a 3 kW pump against a 300 kW pump's efficiency is a category error.

Indicative ranges for clean cold water at BEP with a standard end-suction or split-case design. Actual catalogue values vary with specific speed, impeller type and manufacturer. Always work from the selected pump's certified curve, not a range table.

The Pump Efficiency Formula

The working form most MEP engineers use, because it takes flow in the units a flow meter reports and returns a percentage directly:

Where does 3.67 come from? It is not arbitrary. Hydraulic power is ρgQH. Substituting water density 1000 kg/m³, gravity 9.81 m/s², and converting m³/h to m³/s by dividing 3600:

The SI Base-Unit Form

If your flow is already in m³/s -- as it often is in academic problems and process work -- use the unconverted form. It also handles fluids other than water, since density stays explicit:

Water Horsepower vs Brake Horsepower

The same relationship in imperial units, which you will meet on any US-origin pump curve and in most manufacturer selection software.

• Water horsepower (WHP) -- also called hydraulic horsepower. The power actually imparted to the fluid. This is the useful output.
• Brake horsepower (BHP) -- the power delivered to the pump shaft by the driver, measured as if by a brake dynamometer on the shaft. Always larger than WHP.

The 3960 constant carries the same job as 367 in the metric form: it converts gallons per minute and feet into horsepower, via water's weight of 8.34 lb/gal and the definition of one horsepower as 33,000 ft·lb/min (33,000 ÷ 8.34 ≈ 3,957, rounded to 3,960 by convention).

Live Pump Efficiency Calculator

Enter your measured or catalogue values. The calculator handles unit conversion, reports both metric and imperial forms, and separates pump efficiency from wire-to-water efficiency.

Worked Calculation Example

A centrifugal pump on a condenser water duty. Site measurements taken at the design operating point:

• Flow rate Q = 0.2 m³/s
• Total head H = 27 m
• Shaft power input P = 65 kW
• Fluid: clean water, ρ = 1000 kg/m³

1. Calculate hydraulic power
   P_hyd=ρgQH

   =1000×9.81×0.2×27
   P_hyd = 52,974 W = 52.97 kW
2. Divide output by input
   η=52.9765
   η = 0.815, or 81.5%
3. Cross-check using the practical form

   First convert the flow: 0.2 m³/s × 3600 = 720 m³/h.

   η%=720×273.67×65

   =19,440238.55
   η = 81.5% — both methods agree
4. Account for the losses
   P_loss=65−52.97
   12.03 kW lost inside the pump

   Dissipated as heat into the fluid, bearing and seal friction, and noise. On a closed chilled water loop, that heat is a load the chiller then has to remove.

5. Find what the motor actually draws

   Assuming a motor efficiency of 93%:

   P_elec=650.93=69.9kW

   η_{wire-to-water}=52.9769.9
   75.8% wire-to-water

   Note the gap: 81.5% at the pump, 75.8% at the meter. Quote the wrong one in a report and your numbers will not reconcile with the electricity bill.

81.5% is a good result for a pump of this size. But it tells you nothing on its own about whether the pump is well selected -- only that at this particular duty point it is converting shaft power efficiently. For that judgement you need the curve.

Best Efficiency Point (BEP)

A pump does not have "an efficiency." It has an efficiency curve. The Best Efficiency Point is the flow rate at which that curve peaks -- the flow the impeller was hydraulically designed for, where fluid enters the vanes at the correct angle with minimum shock loss and hydraulic forces around the impeller are most nearly balanced.

Move away from BEP in either direction and two things happen at once. Efficiency falls, which costs money. And the radial hydraulic load on the impeller becomes unbalanced, which costs bearing life, seal life and eventually shaft life. The second effect is the one that gets underestimated.

Why Engineers End Up Off BEP

Almost always the same reason: the pump was selected against an inflated system head calculation. Safety factors get stacked -- 10% on the pressure drop piping friction estimate, another 10% on the coil pressure drop, a round-up to the next standard impeller -- and the pump is delivered oversized. Once installed, the excess head has to go somewhere, so the balancing valve is throttled. The pump now operates left of its design point, wasting energy across a valve, and often outside the POR.

This is why the design-stage head calculation matters far more than it appears to. An honest system curve produces a pump that lands on BEP; a padded one produces a pump that never can.

Interactive Pump Efficiency Curve

Below is a representative centrifugal pump curve -- head, efficiency and shaft power plotted against flow, with the BEP and the ANSI/HI operating regions marked. Drag the slider to move the operating point and watch what happens to efficiency, power and the reliability verdict.

The Same Curve as a Table

Illustrative curve generated from a symmetric efficiency model for teaching purposes. Real pump curves are asymmetric -- efficiency typically falls off more steeply to the right of BEP than to the left. Always work from the manufacturer's certified curve.

Factors That Influence Pump Efficiency

Design Factors -- Fixed at Selection

• Specific speed (N_s). The dimensionless shape parameter N√Q / H^0.75 that classifies impeller geometry from radial to mixed to axial flow. Attainable peak efficiency is a function of specific speed -- there is an optimum band, and duties that fall far outside it simply cannot reach high efficiency regardless of build quality.
• Impeller design and surface finish. Vane profile, number of vanes, inlet angle and cast surface roughness all set the hydraulic loss floor. On small pumps especially, surface finish is a meaningful fraction of total loss.
• Volute or diffuser design. The casing has to convert velocity to pressure with minimum turbulence, and it can only do this optimally at one flow -- which is precisely what defines BEP.
• Impeller trim. A trimmed impeller is cheaper than a new pump but costs efficiency, because the trimmed vane tips no longer match the volute cutwater. Expect a few points of loss on a significant trim.
• Physical size. As covered in Table 1, bigger is inherently more efficient. Clearances and surface friction do not scale down proportionally.

Operating Factors -- What Degrades It in Service

• Wear ring clearance opening up. The single biggest cause of gradual efficiency loss. As clearances widen, more already-pressurised fluid recirculates internally back to suction, and volumetric efficiency falls. Restoring wear rings to original clearance is one of the highest-return pump overhaul actions available.
• Operating far from BEP. Off-design flow means shock loss at the impeller inlet and flow separation in the volute. As Table 3 shows, running at 50% of BEP costs over 20 efficiency points on this curve.
• Throttled discharge valves. Throttling to control flow burns energy across a valve to correct a selection error. The pump itself may still be efficient; the system is not. This is exactly the waste a VFD eliminates.
• Cavitation. When suction pressure falls below the vapour pressure of the liquid, vapour bubbles form and collapse violently on the impeller. Efficiency drops, noise rises to a distinctive gravel-in-the-casing sound, and impeller material is progressively eroded away.
• Fluid viscosity. Glycol solutions in chilled water systems raise both density and viscosity. Higher viscosity increases disc friction and hydraulic loss, reducing head and efficiency relative to the water-based catalogue curve -- corrections must be applied, not ignored.
• Fouled strainers and pipework. Rising system resistance shifts the operating point left along the pump curve. The pump has not changed; its duty point has.

Pump Affinity Laws and VFD Savings

The affinity laws describe how a pump's performance scales when you change its speed or impeller diameter. For a speed change on a fixed impeller: