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Pump Head & Shaft Power Calculator (H, P=ρgQH/η)

· Last updated：2026-07-22

Compute the total dynamic head H = (p_d - p_s)/(ρ·g) + Δz + (v_d² - v_s²)/(2g) of a centrifugal pump (m), then the fluid power P_fluid = ρ·g·Q·H and shaft power P_shaft = P_fluid/η. p_d and p_s are gauge pressures (suction may be negative for suction lift). Nozzle velocities v = 4Q/(π·D²) come from the flow rate and the discharge/suction nozzle diameters; if a nozzle diameter is left blank its velocity head is omitted. Pressure in Pa/kPa/bar/atm/psi, flow in m³/s/L/s/L/min/m³/h, density in kg/m³/g/cm³; power output in W/kW/hp.

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Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Math & Numbers
Input types
number, select
Output type
json
Sample coverage
4
API ready
Yes

Overview

The Pump Head & Shaft Power Calculator computes total dynamic head, fluid power, and shaft power for a centrifugal pump using gauge pressures, elevation difference, flow rate, fluid density, nozzle diameters, efficiency, and gravity.

When to use

  • Estimate pump total dynamic head from discharge and suction gauge pressures.
  • Calculate hydraulic fluid power and required shaft power at a known flow rate and efficiency.
  • Include discharge and suction velocity heads when nozzle diameters are available.

How it works

  1. 1Enter discharge pressure, flow rate, and their units; suction pressure and static head difference are optional.
  2. 2Set the liquid density, pump efficiency, gravity, and optional discharge and suction nozzle diameters.
  3. 3The calculator converts the inputs and applies H = (p_d − p_s)/(ρg) + Δz + (v_d² − v_s²)/(2g).
  4. 4It returns head in meters, fluid power, and shaft power in W, kW, and hp.

Use cases

  • Pump selection and preliminary sizing for water and other liquids.
  • Checking operating conditions against a pump's expected head and power demand.
  • Estimating motor or shaft power requirements from pressure, flow, density, and efficiency.

Examples

1. Basic water-pump head and power estimate

Pump designer

Background

A designer needs a quick estimate for a water pump delivering 10 L/s against a 2 bar discharge gauge pressure.

Problem

Calculate total dynamic head and shaft power without including nozzle velocity heads.

How to use

Enter discharge pressure 2 bar, suction pressure 0 bar, flow rate 10 L/s, density 1000 kg/m³, and efficiency 75%. Leave both nozzle diameters blank.

dischargePressure=2; pressureUnit=bar; suctionPressure=0; flowRate=10; flowUnit=L/s; density=1000; densityUnit=kg/m³; efficiency=75%

Outcome

The calculator returns approximately 20.3874 m of head, 2000 W of fluid power, and 2666.6667 W of shaft power, or 2.6667 kW.

2. Pump calculation with discharge and suction velocity heads

Hydraulic engineer

Background

A system carries 20 L/s with a 300 kPa discharge pressure and different discharge and suction nozzle diameters.

Problem

Account for the velocity-head difference as well as the pressure head.

How to use

FAQ

What pressure type does the calculator use?

It uses gauge pressure for both discharge and suction. Suction pressure may be negative for suction lift.

Which pressure units are supported?

You can enter pressure in Pa, kPa, bar, atm, or psi.

Which flow-rate units are supported?

The calculator accepts m³/s, L/s, L/min, and m³/h.

Are nozzle diameters required?

No. If a discharge or suction diameter is blank, the corresponding velocity-head term is omitted.

How is shaft power calculated?

Shaft power equals fluid power divided by pump efficiency, with efficiency entered as a percentage.

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Enter 300 kPa discharge pressure, 0 kPa suction pressure, 20 L/s flow, 0.1 m discharge diameter, 0.15 m suction diameter, water density of 1000 kg/m³, and 70% efficiency.

dischargePressure=300; pressureUnit=kPa; suctionPressure=0; flowRate=20; flowUnit=L/s; density=1000; densityUnit=kg/m³; dischargeDiameter=0.1; suctionDiameter=0.15; nozzleDiameterUnit=m; efficiency=70%

Outcome

The result is approximately 30.8463 m of total dynamic head, 6052.0366 W of fluid power, and 8645.7665 W of shaft power, or 8.6458 kW.