Calculate pump efficiency and hydraulic power, or estimate shaft power and flow for an entered duty, using total dynamic head and fluid density in metric or US units. Distinguish pump-shaft losses from electrical wire-to-water efficiency.

Use matched steady-duty flow, total head and power. Shaft, electrical and hydraulic power are different measurement boundaries.

Use the pump discharge-to-suction total-head increase, not elevation alone.

Electrical input and annual energy

Required for electrical input; optional for shaft-based results. Cover all losses from electrical input to pump shaft.

Optional. Enter hours to estimate electrical energy; requires motor/drive efficiency.

Pump Efficiency Formula

For steady incompressible flow, hydraulic output power is Pₕ = ρgQH. Pump efficiency uses shaft input power at the pump as its denominator:

ηpump = Pₕ / Pshaft = ρgQH / Pshaft
  • ηpump is pump efficiency as a fraction; multiply by 100 for %. The entered efficiency percentages are divided by 100 before use.
  • ρ is fluid density in kg/m³. Specific-gravity mode uses ρ = 1000 × SG with a fixed reference density of 1000 kg/m³.
  • g is the acceleration due to gravity (≈ 9.81 m/s² near Earth’s surface)
  • Q is volumetric flow in m³/s after conversion; US gpm means US liquid gallons per minute.
  • H is total head added across the pump, in metres of the pumped fluid: discharge total head minus suction total head, including pressure, elevation, and velocity-head differences. It is not just vertical lift.
  • Pshaft is mechanical power entering the pump shaft, in W. If measured power is electrical input Pe, use Pshaft = Pe × ηmotor/drive for the stated electrical-to-shaft boundary.

Wire-to-water efficiency is ηwire = Pₕ/Pe = ηpump × ηmotor/drive, with efficiencies expressed as fractions and all values taken at the same operating point. The motor/drive value must include the losses between the selected electrical measurement point and pump shaft. Hydraulic output, shaft input, and electrical input are separate quantities.

The inverse calculations are Pshaft = ρgQH/ηpump and Q = ηpumpPshaft/(ρgH). They estimate a duty from assumed efficiency; a manufacturer pump curve and the system curve are still needed to establish actual operation. This model uses positive flow, total head and density, with efficiencies greater than 0 and at most 100%. It excludes shutoff, reverse flow, and turbine operation.

Example Problem

How to calculate pump efficiency?

To calculate pump efficiency, you first need to determine the variables presented in the equation above. The first of these is the density of the fluid. For this example, we will assume the fluid is water at about 20 °C and has a density of 998 kg/m^3.

Next, use a flow rate of 0.020 m³/s (20 L/s), measured or specified at the same operating point as the head and input power.

Next, use a total pump head of 15 m at that flow, including the relevant pressure, elevation and velocity-head differences.

Next, use 4200 W (4.2 kW) of mechanical shaft input to the pump. Electrical input would additionally include motor/drive losses and would require the corresponding efficiency conversion.

Finally, with the stated g = 9.81 m/s² approximation, calculate pump efficiency as ηpump = (ρgQH)/Pshaft.

So, η = (998 * 9.81 * 0.020 * 15) / 4200

= 2937.114 / 4200

= 0.6993128571…

= 69.9312857…% (about 69.9%). The hydraulic output is 2937.114 W; pump losses are 4200 − 2937.114 = 1262.886 W.

FAQ

What factors can affect pump efficiency?

Pump efficiency can be affected by several factors including the design of the pump, the condition of the pump (wear and tear), the type of fluid being pumped, the viscosity of the fluid, and how well the pump is matched to the system it’s being used in. Improper installation or maintenance can also significantly impact efficiency.

How can you improve the efficiency of a pump?

Maintenance, appropriate pump selection, compatible fluids and operation near the intended duty can help performance. Piping changes and speed control may reduce total system energy use, but do not automatically raise the pump’s own efficiency. Check the pump curve, motor/drive losses and manufacturer operating limits for the proposed change.

Why is calculating pump efficiency important?

Efficiency calculations help compare input energy with hydraulic duty and identify potential losses. Optional operating hours estimate electrical energy at the stated constant duty as E = Pe(kW) × hours; blank hours omit the energy estimate, and electrical-energy estimates require the motor/drive efficiency. The 0–8784 h input range accommodates one leap year. This is an energy-use estimate, not a calculation of savings, and does not replace pump/system selection checks.

Pump Efficiency Calculator screenshot