Pump Efficiency Formula: Calculate Hydraulic, Shaft, and Overall Efficiency

The pump efficiency formula is useful hydraulic output power divided by input power, multiplied by 100%. The arithmetic is short. The important part is choosing the right input boundary: shaft power for the bare pump, or electrical power for the complete motor-and-pump system. This guide shows both methods, works the same duty point in metric and US units, and explains how to check a result before comparing it with a curve.

Searches for a water pump efficiency formula, centrifugal pump efficiency formula, pump efficiency equation, or wire to water efficiency all lead to the same first decision: define the input boundary. That decision remains outside a pump efficiency formula calculator; the calculator only evaluates the values and units supplied.

Which Efficiency Are You Calculating?

Before entering a number, draw the boundary around the equipment included in the calculation. That is the Measurement-Boundary Check. Two calculations may use the same hydraulic output and produce different, equally valid percentages because one stops at the pump shaft and the other starts at the electrical supply.

The adjective “overall” is not enough to identify a boundary. Some pump literature uses overall efficiency for hydraulic output divided by shaft input. Energy regulations may use a driver-input or multi-load-point metric. Name the numerator and denominator every time.

Which Input Reading Belongs in the Denominator?

One quick way to avoid the wrong denominator is to trace energy from the electrical supply to the electric motor, from motor shaft torque to the pump, and from the impeller to the liquid. Stop the map at the point where your input was actually measured. A shaft-torque reading belongs to a pump-only equation. A three-phase power-analyzer reading belongs to an overall or wire-to-water equation. A motor nameplate belongs to neither unless the task is rating selection rather than measurement.

Step 1: Calculate Hydraulic Output Power

Hydraulic power is the useful rate of energy delivered to the liquid:

P_hydraulic = ρ × g × Q × H

Here, ρ is liquid density in kg/m³, g is gravitational acceleration in m/s², Q is flow in m³/s, and H is total dynamic head in metres. The result is watts. For water near ordinary test temperatures, the common metric shortcut is:

P_hydraulic (kW) ≈ Q (m³/h) × H (m) × SG ÷ 367

Specific gravity, SG, accounts for liquid density relative to water. The constant 367 is a rounded unit-conversion shortcut, not a new physical law. If density and temperature matter to the required precision, use ρgQH with the measured density instead.

In US customary units, water horsepower is:

Water horsepower = Q (gpm) × H (ft) × SG ÷ 3,960

Use total dynamic head, not discharge pressure alone. Total head accounts for the pressure difference between discharge and suction, elevation terms, and velocity-head differences at the measurement sections. When gauges use different diameters or elevations, a simple pressure subtraction can be incomplete.

Head is energy per unit weight, which is why the same centrifugal pump curve can express head independently of liquid density while power changes with density. Pressure and head are related, but they are not interchangeable without the liquid’s density. This distinction becomes especially important when a water-tested pump is evaluated on a denser or lighter process liquid.

Use output and input readings from the same stabilized duty point. Mixing a current flow-and-head reading with catalog peak power does not describe measured pump efficiency.

Step 2: Identify Shaft or Electrical Input Power

For pump-only efficiency, the denominator is shaft input power at the measured duty point. Torque and rotational speed can establish it directly, or a test report may provide brake power for the same pump, impeller diameter, speed, and liquid. The motor nameplate rating is capacity information; it is not a live shaft-power reading.

For wire-to-water efficiency, measure real electrical input power. On a three-phase motor, that normally means a suitable power analyzer that accounts for voltage, current, power factor, phase balance, waveform, and any variable-frequency drive inside the chosen boundary. Multiplying nameplate voltage and current is not a reliable substitute.

One common field error is a boundary mismatch: motor nameplate capacity is used as though it were measured input. For example, a 15 kW nameplate does not prove that the shaft received 15 kW at the recorded duty point. Keep the torque-and-speed record or the power-analyzer export with the calculation so the denominator can be checked later.

If your task is to size a motor rather than calculate a measured efficiency, use BBP’s broader pump power formula guide. This page stays on the other side of that relationship: known output and known input produce efficiency.

Metric Pump Efficiency Worked Example

Consider a water pump operating at 100 m³/h and 30 m total dynamic head. The shaft measurement shows 13.0 kW.

1. Hydraulic output = 100 × 30 ÷ 367 = 8.174 kW.
2. Pump efficiency = 8.174 ÷ 13.0 = 0.6288.
3. Convert the decimal once: 0.6288 × 100% = 62.9%.

If the measured electrical input is 14.5 kW instead, the wire-to-water efficiency is 8.174 ÷ 14.5 × 100% = 56.4%. Nothing happened to the hydraulic duty point. The percentage fell because the second boundary includes motor and drive losses.

To calculate pump efficiency consistently, record flow rate, head, and input before doing the pump efficiency calculation. The result becomes useful for engineering and maintenance only when the operating condition is also recorded. Plants may monitor efficiency over time, but a lower value does not by itself identify wear: valve position, speed, liquid, and meter uncertainty can move the result. Compare like with like and look for a repeatable change larger than the measurement uncertainty.

Peak efficiency is a curve property, not a guaranteed value at every operation. An efficient selection places the required duty near the relevant peak without violating NPSH, reliability, or control requirements. Positive-displacement equipment also needs its own performance method; do not transfer the centrifugal-pump shortcut blindly. The minimum documentation set is the measurement boundary, pump configuration, liquid, speed, instruments, and timestamp.

US Customary Pump Efficiency Worked Example

The same approximate duty point converts to about 440 gpm and 98.4 ft. Suppose measured shaft input is 17.43 bhp.

1. Water horsepower = 440 × 98.4 ÷ 3,960 = 10.93 hp.
2. Pump efficiency = 10.93 ÷ 17.43 = 0.627.
3. Efficiency = 62.7%.

The small difference from the metric result comes from rounded converted inputs. This avoids two common problems—a rounding error and a unit mismatch—when the original measurement sheet is retained and flow, head, and power are converted from one duty point. Do not treat the last decimal as a test discrepancy when the inputs were rounded first.

The Input-Power Boundary Trace: Hydraulic, Volumetric, Mechanical, Motor, and Overall Efficiency

The Input-Power Boundary Trace helps locate losses without pretending every efficiency term was measured independently.

You may estimate wire-to-water efficiency as motor efficiency × pump efficiency, but only when both figures apply at the same load, speed, voltage, liquid, and operating point. Catalog peak motor efficiency multiplied by pump efficiency read at another flow is not a measured system result.

This decomposition is diagnostic, not permission to invent component percentages. Pump-only overall efficiency can be measured directly even when hydraulic, volumetric efficiency, and mechanical efficiency are not separately known. Treat a multiplication of unverified sub-efficiencies as a model, label its inputs, and do not present it as an instrumented result.

How to Measure Pump Efficiency in the Field

1. Define the boundary. Decide whether the denominator is shaft input, motor input, or supply input including a drive.
2. Stabilize the operating point. Record speed, valve position, liquid temperature, and system condition. Do not pair a flow reading from one minute with a power reading from another operating state.
3. Measure flow with an appropriate, installed, calibrated flowmeter and record its uncertainty.
4. Determine total head. Use suction and discharge pressure or head, elevation, and velocity terms at defined measurement sections.
5. Measure input power. Use a torque/speed method for shaft power or a suitable analyzer for real electrical power.
6. Repeat and compare. Take repeated readings, calculate uncertainty, then compare only with a curve or acceptance basis for the same configuration.

Flow measurement quality depends on meter technology, straight-run conditions, liquid properties, installation orientation, and calibration. Pressure instruments need appropriate range and elevation correction. Torque, speed, volume, temperature, and electrical power each carry uncertainty. Because efficiency is a quotient assembled from several measurements, a one-percentage-point change may not be meaningful when the combined uncertainty is larger.

Formal test methods have application limits. The official ISO 9906:2012 scope is framed around acceptance testing with liquids that behave like clean, cold water. ASME PTC 8.2 states a Newtonian-viscosity liquid scope. Correct ρgQH calculations for viscous or non-Newtonian process liquids do not automatically make a clean-water acceptance curve the right comparison.

The US Department of Energy has also supported sensor-based pump-efficiency measurement. That illustrates why concurrent measurements matter; it does not certify any particular field sensor or replace calibration records.

Read the Efficiency Curve and Find the Best Efficiency Point

The pump efficiency curve plots efficiency against flow at a stated speed, impeller diameter, and test condition. The best efficiency point (BEP) is the maximum of the relevant efficiency curve. The Hydraulic Institute pump-curves reference shows efficiency, input power, head, flow, and NPSH on the same performance framework.

There is a subtle boundary issue: a bare-pump efficiency curve and an overall motor-and-pump efficiency curve need not peak at exactly the same flow. Current US regulatory definitions distinguish bare-pump and overall-efficiency concepts. Always identify which curve and denominator produced the stated BEP.

Regulatory pump energy indices can combine prescribed load points and reference performance. They are not synonyms for the single-point percentage calculated on this page. The 2024 US circulator-pump final rule is one example of a broader rating framework. Apply it only to equipment inside its scope.

If a field point appears inefficient, compare it with the curve for the same speed and impeller before diagnosing wear. Curves for another trim or liquid are weak evidence even when the flow is similar. Keep the curve revision and test configuration with the field record.

If speed or impeller diameter changes, use the pump affinity laws as an estimate, then return to the applicable manufacturer curve. Affinity calculations often assume efficiency stays approximately constant; the actual efficiency curve decides whether that approximation is acceptable.

The Efficiency Sanity Check: Diagnose Impossible or Misleading Results

An efficiency above 100% is not a high-performing pump; it is a data problem. The Efficiency Sanity Check starts with incompatible units and boundaries because they can produce a polished but physically impossible answer. It then checks whether all readings came from the same operating point.

Frequently Asked Questions

What is the formula for pump efficiency?

Pump efficiency is useful hydraulic output power divided by input power, multiplied by 100%. First calculate hydraulic output from density, gravity, flow, and total head. For pump-only efficiency, divide by measured shaft input. For wire-to-water efficiency, divide by measured electrical input for the complete boundary. The output and input must represent the same operating point.

Keep the efficiency as a decimal during the calculation and multiply by 100 only once at the end. If the resulting value exceeds 100%, check units, head, density, and power boundaries before interpreting it.

How do you calculate overall pump efficiency?

Define what “overall” includes. If it means the bare pump, divide hydraulic output by shaft input. If it means the motor-and-pump set or wire-to-water system, divide hydraulic output by measured electrical input. Multiplying motor and pump efficiencies is an estimate only when both efficiencies apply at the same load, speed, and duty point. Do not substitute the motor nameplate rating for measured input, and do not combine pump and motor values taken at different load, speed, or duty points.

What is a good pump efficiency?

There is no defensible universal percentage. Pump type, size, speed, impeller trim, liquid, and operating point all affect the result. Compare a measured value with the applicable manufacturer curve or acceptance criterion for that exact configuration. Generic industry percentages cannot replace a matched curve and a stated test boundary.

Can pump efficiency be more than 100%?

No. Any result above 100% means the calculated hydraulic output exceeds the selected input, which violates the energy balance. Check flow and head units, liquid density, gauge locations, instrument scaling, power factor, and whether the denominator is shaft or electrical power.

How does BEP affect pump efficiency?

Efficiency normally reaches its maximum near the best efficiency point of the applicable tested curve and falls as the duty point moves away. The exact shape is not necessarily symmetric. Also confirm whether the curve represents bare-pump efficiency or overall efficiency before comparing it with field data.

What to Send BBP for a Duty-Point Review

For a meaningful review, send flow, total dynamic head, liquid and temperature, density or specific gravity, frequency and speed, suction conditions, pump model, impeller diameter, and the method used to measure input power. Include the curve or test report you are comparing against.

Without these records, a low result cannot be separated reliably from a unit, boundary, or instrumentation problem. If repeated readings remain below the matched curve outside combined uncertainty, the next review can examine wear, bypass flow, speed, and operating position.

BBP’s centrifugal pump range includes end-suction and high-flow configurations. See the end suction pump and double suction pump pages for configuration context. Curve matching or test-report clarification can establish whether two efficiency figures are truly comparable; it should not be replaced by a generic promise.

References & Sources

• Hydraulic Institute Data Tool: Pump Curves
• US Department of Energy: Wireless Sensor for Pump Efficiency
• ISO 9906:2012 scope
• ASME PTC 8.2: Centrifugal Pumps
• 10 CFR Part 431 Subpart Y
• 2024 Energy Conservation Standards for Circulator Pumps

Formula examples are derived illustrations, not product acceptance-test results.