Physics calculators

Pump Power Calculator

Updated Jul 28, 2026 By Jehan Wadia
Rate Formulas
Unit System
Switching mode reloads that system's default values and units. Every field keeps its own unit menu, so you can still mix units freely.
Pump & Fluid Inputs
Fill in any 3 of the 4 fields below. Leave the field you want to solve for blank.
The four solvable variables are Flow Rate, Head / Pressure, Pump Efficiency and Shaft Power. Fluid density and gravity are always required.
Volumetric flow through the pump.
Total differential (discharge minus suction) developed by the pump.
Dimensionless. Enter 0.60 for a 60%-efficient pump.
Left blank by default, so the calculator solves for it (Pshaft = ρ·g·Q·h ÷ η).
Auto-fills the density field below; you can always type over it.
Mass-density units are multiplied by g to get specific weight; specific-weight units are used directly.
Writes SG × 1000 kg/m³ (or SG × 62.428 lb/ft³) into the density field.
Default: 9.81 m/s² (Earth standard). Editable for other planets or academic cases.
The results table always lists W, kW and hp together.
Results
Solved for Shaft Power
 
Hydraulic Power
 
Shaft Power
 
Power Loss / Efficiency
 
QuantityWkWhp
Hydraulic Power
Shaft Power
Power Loss (pump)
Normalized InputSIImperial / US
Flow rate (Q)
Differential head (h)
Equivalent pressure (p = γh)
Mass density (ρ)
Specific weight (γ = ρg)
Gravity (g)
Pump efficiency (η)
Power Gauges (scaled to shaft power)
Step-by-Step Solution
Shaft Power vs. Pump Efficiency
Where the Motor Power Goes

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. If you only know the pipe size and velocity, work it out first with the pipe flow calculator.

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. For static lift on the suction side, the hydrostatic pressure calculator is handy, and pipe losses can be estimated with the friction loss calculator.

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. To convert the answer into current draw, try the kW to amps calculator.

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. The specific gravity calculator can help you find it.

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. If you want the general definition of power as work over time, see the power calculator.

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. Once you know the shaft power, the electricity cost calculator turns running hours into dollars.

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 — check the viscosity calculator and the Reynolds number calculator for that side of the problem. When sizing a backup supply for the motor, the generator sizing calculator is a good next stop.

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 — see the horsepower calculator for more conversions.
  • Motors are often chosen a bit larger than the shaft power to leave a safety margin.
  • Need the volume of liquid in the line or tank first? Use the pipe volume calculator or the tank volume calculator.

Formulas used

Specific weight from density
\gamma = \rho\, g
Mass density from specific weight
\rho = \frac{\gamma}{g}
Head from differential pressure
h = \frac{p}{\rho\, g} = \frac{p}{\gamma}
Hydraulic (fluid) power
P_{hyd} = \rho\, g\, Q\, h = \gamma\, Q\, h
Shaft (motor input) power
P_{shaft} = \frac{P_{hyd}}{\eta} = \frac{\rho\, g\, Q\, h}{\eta}
Flow rate (solved)
Q = \frac{P_{shaft}\, \eta}{\gamma\, h}
Pump efficiency (solved)
\eta = \frac{\gamma\, Q\, h}{P_{shaft}}
Power lost inside the pump
P_{loss} = P_{shaft} - P_{hyd} = (1 - \eta)\, P_{shaft}

Frequently asked questions

What is the difference between hydraulic power and shaft power?

Hydraulic power is the useful power that reaches the liquid. Shaft power is the power the motor must put into the pump.

Shaft power is always bigger because pumps lose some power to friction, leaks, and heat. The gap between the two numbers is the power loss.

Why is my shaft power field blank when I open the calculator?

That is on purpose. The calculator solves for whatever field you leave blank, and shaft power is the most common answer people want.

If you want a different answer, type a shaft power value and clear one of the other three fields instead.

Can I solve for pump efficiency instead of power?

Yes. Enter flow rate, head, and shaft power, then leave the efficiency box empty. Press Calculate and the tool works out the efficiency for you.

You can also click the small Solve for this field link under the efficiency box to clear it fast.

Why did I get an error saying efficiency is over 100%?

That means your three input numbers do not fit together. The flow and head you entered would need more power than the shaft power you typed.

Check your units first. A wrong unit on flow, head, or power is the usual cause.

Do I have to use water as the fluid?

No. Pick any fluid from the drop-down list, such as seawater, diesel, gasoline, crude oil, ethanol, glycerin, milk, SAE 30 oil, or slurry. The density fills in for you.

For any other liquid, choose Custom and type the density yourself.

What does the Specific Gravity Apply button do?

It turns a specific gravity number into a density and writes it into the density box.

Type 0.85, press Apply, and you get 850 kg/m³ in metric mode or about 53.1 lb/ft³ in imperial mode.

Can I enter specific weight instead of density?

Yes. The density unit menu includes lbf/ft³, N/m³, and kN/m³. These are specific weight units.

When you pick one, the tool uses it directly and divides by gravity to find the mass density.

How do I switch between head and pressure?

Use the small Head and Pressure buttons above the input box. Head lets you enter meters, feet, cm, mm, or inches. Pressure lets you enter kPa, Pa, MPa, bar, psi, or atm.

Pressure mode needs a density value, because the tool converts pressure to head with h = p ÷ (ρ · g).

Can I mix metric and imperial units?

Yes. Every field has its own unit menu. You can enter GPM for flow, meters for head, and hp for power all at once.

The mode buttons only load starting values and units. They do not lock you in.

What size motor should I buy from this result?

Pick a motor a bit bigger than the shaft power shown. Many engineers add 10% to 25% as a safety margin.

Then round up to the next standard motor size that you can actually buy.

Does the calculator include motor efficiency?

No. It only uses pump efficiency. The shaft power shown is the power going into the pump shaft.

To find the electrical power drawn from the wall, divide the shaft power by the motor efficiency too.

Why does a heavier liquid need more power?

Density sits right in the formula. Twice the density means twice the weight of liquid to lift each second.

So pumping slurry at 1300 kg/m³ takes about 30% more power than water at the same flow and head.

What head number should I use?

Use the total differential head, which is the discharge head minus the suction head. It includes the vertical lift plus all friction losses in the pipes and fittings.

Do not use only the vertical lift. That gives an answer that is too low.

What is a normal pump efficiency to enter?

Most centrifugal pumps run from 50% to 85%. Small pumps sit lower, large ones sit higher.

If you do not know, 0.60 to 0.70 is a fair guess. Use the pump curve from the maker for a real number.

What does the donut chart show?

It splits your shaft power into two slices. One slice is the power that reaches the liquid. The other slice is the power lost inside the pump.

The center of the donut shows the total shaft power.

What does the efficiency line chart tell me?

It shows how much shaft power you would need at efficiencies from 30% to 100%. The flat dashed line is the hydraulic power, which never changes.

The orange dot marks your pump. It shows fast how much money a low efficiency costs you.

Can I change gravity?

Yes. The gravity field is editable, so you can run problems on the Moon, Mars, or for class work.

Leave it at 9.81 m/s² or 32.174 ft/s² for normal Earth jobs.

Why do I see a message asking for three of four fields?

The formula links four values: flow, head, efficiency, and shaft power. You need three of them to find the fourth.

If you fill in all four or only two, the tool cannot tell what to solve, so it asks you to fix it.

Does this work for positive displacement pumps?

Yes, the same power formula applies. Just use the right head or pressure rise and the right efficiency for that pump type.

Positive displacement pumps often run at higher efficiency than centrifugal pumps.

Does the calculator check for cavitation or NPSH?

No. This tool only works out power, head, flow, and efficiency.

Cavitation depends on suction pressure, fluid vapor pressure, and temperature, so you need a separate NPSH check for that.

Why does the step-by-step section show a horsepower cross-check?

It repeats the answer using the common US formula: hp = (γ × Q × h) ÷ 550, with specific weight in lbf/ft³, flow in ft³/s, and head in feet.

It proves both unit systems give the same result.

Can I use this for air or gas?

Not really. This formula is for liquids, which barely change volume under pressure.

Gases compress, so fans, blowers, and compressors need different math.