Math Solutions: Pump Performance and Efficiency Calculations

By Dan Theobald, Environmental Services


Water Online’s “Math Solutions” series, presented by wastewater consultant and trainer Dan Theobald (“Wastewater Dan”), instructs operators on Pump Performance and Efficiency calculations.


Pump performance and efficiency calculations on your certification exams or operating you plant may require various head pressure calculations, different horsepower calculations or certain efficiency calculations.


Depending on your required math solution pertaining to pumps, calculations and unit of expression require explicit formulas.


Some common pump performance and efficiency terms are defined and their calculations are accessible below:


Definitions and Solutions of various Pump Performance Efficiency Calculations


Suction Lift Head Pressure:

Define-Suction Lift Head Pressure-Ft.:

Suction Lift Head Pressure Feet is the distance from where the liquid is taken to the centerline of the pump.

Calculate-Suction Lift Head Pressure-Ft.:


Discharge Head Pressure:

Define-Discharge Head Pressure-Ft.:

Discharge Head Pressure Feet is the distance in feet that the liquid leaves a pump.

Calculate-Discharge Head Pressure-Ft.:



Total Dynamic Head (TDH) Pressure-Ft:

Define-Dynamic Head (TDH) Pressure-Ft:

Total Dynamic Head (TDH) Pressure Feet is the total equivalent height in feet that a fluid is to be pumped, taking into account friction losses in the pipe.

Calculate-Dynamic Head (TDH) Pressure-Ft:


Water Horsepower:

Define-Water Horsepower:

Water Horsepower is a ratio of water horsepower out divided by the mechanical horsepower into the pump.

Calculate-Water Horsepower:



Brake Horsepower:

Define-Brake Horsepower:

Brake Horsepower is the horsepower available at the output shaft of a motor.

Calculate-Brake Horsepower:



Wire-to-Water Horsepower:

Define-Wire-to-Water Horsepower:

Wire-to-Water (Electrical or Motor) horsepower is calculated by dividing Brake Horsepower by Motor Efficiency.

Calculate-Wire-to-Water Horsepower:


Wire-to-Water Efficiency Percentage (%):

Define-Wire-to-Water Efficiency Percentage (%):

The combined efficiency of a motor and pump system. Calculated by multiplying the motor efficiency by the pump efficiency.

Calculate-Wire-to-Water Efficiency Percentage (%):


Play List of all my ‘Math Solutions’




This is the Pump Performance and efficiency calculations presentation in my series of “Math Solutions.” If you have specific wastewater math queries, please submit a question.


About Dan Theobald:

Known in the industry as “Wastewater Dan,” Daniel L. Theobald, proprietor of Environmental Services (, is a professional wastewater and safety consultant/trainer. He has more than 24 years of hands-on industry experience operating many variants of wastewater treatment processing units and is eager to share with others his knowledge about water conservation.


Theobald serves as an active consultant for industries looking to achieve and maintain improved wastewater treatment at reduced cost. He is a Lifetime Member of the Who’s Who Registry of Professionals and holds numerous certifications from wastewater management regulatory boards and professional organizations. Theobald contributed one chapter to the Water Environment Federation’s ( Manual of Practice # 37 (MOP-37), a technical manual resource guide for biological nutrient removal, published in 2013.

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