Introduction
A pump moves liquid, and that takes power. This pump power calculator tells you how much power a pump needs. Just enter the flow rate, the head (or pressure), and the pump efficiency. The tool gives you the shaft power in watts, kilowatts, and horsepower.
The math is simple: P = ρ · g · Q · h ÷ η. Here ρ is the fluid density, g is gravity, Q is the flow rate, h is the head, and η is the pump efficiency. The calculator does this work for you and shows every step.
You can also work backward. Fill in any 3 of the 4 main fields and leave one blank. The tool solves for the blank one. So you can find the flow rate, the head, or the efficiency instead of the power.
Pick metric or imperial units, and change the unit on each field if you want. Choose a fluid like water, diesel, or crude oil, and the density fills in on its own. You also get charts that show how efficiency changes the power you need, and how much power is lost inside the pump.
How to use our Pump Power Calculator
Fill in any three of these four values (flow rate, head or pressure, pump efficiency, and shaft power), plus the fluid density and gravity. Leave one field blank and the calculator solves for it, then shows hydraulic power, shaft power, power loss, gauges, charts, and a step-by-step solution.
Unit System: Pick SI (metric) or Imperial (US). This loads default values and units for that system. You can still change the unit next to any field.
Flow Rate (Q): Type how much fluid moves through the pump, then pick the unit, such as m³/h, L/s, or GPM.
Head or Pressure: Choose "Head" to enter lift in meters or feet, or choose "Pressure" to enter the pressure rise in kPa, bar, or psi. Then type the value and pick its unit.
Pump Efficiency (η): Enter how well the pump works. Use 0.60 in decimal mode or 60 in percent mode.
Shaft Power (Pshaft): Enter the motor input power in W, kW, MW, or hp. Leave it blank if you want the calculator to find it.
Select a Fluid: Pick water, seawater, diesel, oil, slurry, or another fluid to auto-fill its density. Choose "Custom" to type your own.
Fluid Density (ρ or γ): Enter the density, like 1000 kg/m³ for water, and pick the unit. Specific weight units such as lbf/ft³ or N/m³ also work.
Specific Gravity override: Know the SG instead? Type it, like 0.85, and press Apply to write the matching density into the density field.
Acceleration due to Gravity (g): Leave this at 9.81 m/s² (or 32.174 ft/s²) for Earth. Change it only for other planets or class problems.
Display unit for gauges & charts: Choose W, kW, MW, or hp for the gauges and graphs. The results table always shows W, kW, and hp side by side.
Buttons: Press Calculate to see your answer, Reset to load the sample values again, or Clear Fields to empty every box.
What Is Pump Power?
Pump power is the amount of energy a pump needs each second to move a liquid. A pump has to lift the liquid and push it through pipes. The harder that job is, the more power the motor must supply.
The Pump Power Formula
Hydraulic power is the useful power that actually goes into the liquid:
Phydraulic = ρ × g × Q × h
Shaft power is the power the motor must put into the pump:
Pshaft = (ρ × g × Q × h) ÷ η
What Each Symbol Means
- ρ (rho) – fluid density, or how heavy the liquid is for its size. Water is about 1000 kg/m³ (62.4 lb/ft³).
- g – gravity, 9.81 m/s² or 32.174 ft/s² on Earth.
- Q – flow rate, the volume of liquid moved each second (m³/s, L/s, or GPM).
- h – head, the height the pump can raise the liquid, in meters or feet.
- η (eta) – pump efficiency, a number from 0 to 1. A value of 0.70 means 70% of the motor power reaches the liquid.
Head and Pressure
Head and pressure describe the same push in two ways. You can switch between them with p = ρ × g × h. So 10 meters of water head equals about 98 kPa, and 100 feet of water head equals about 43 psi. You need the liquid's density to change pressure into head.
Why Efficiency Matters
No pump is perfect. Some power is lost to friction, leaks, and heat inside the pump. Most centrifugal pumps run near 50% to 85% efficient. Lower efficiency means a bigger motor and a higher power bill for the same flow. Efficiency can never be more than 100%, so if a math result goes above that, one of the input numbers is wrong.
Where This Is Used
Engineers use pump power math to pick motor sizes, guess energy costs, and check if an old pump still does its job. It works for water, seawater, fuel, oil, milk, and slurry. Thicker or heavier liquids need more power at the same flow and head, because density is part of the formula. Thick fluids also change the flow pattern in the pipe.
Quick Tips
- Double the flow rate and the power roughly doubles.
- Double the head and the power roughly doubles.
- 1 hp equals about 746 watts.
- Motors are often chosen a bit larger than the shaft power to leave a safety margin.