Pump Head & Shaft Power Calculator (H, P=ρgQH/η) | Online Free Tool | Elysia Tools
Elysia Tools
Navigation
Math & Numbers
Pump Head & Shaft Power Calculator (H, P=ρgQH/η)
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.
Execution
Run this tool
Fill in the form, run the tool, and review the result in one place.
Samples
Examples that match this tool
Related
Continue with connected tools and hubs
Result
Ready for a run
Run the tool to preview files, text, structured data, or streamed output here.
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
1Enter discharge pressure, flow rate, and their units; suction pressure and static head difference are optional.
2Set the liquid density, pump efficiency, gravity, and optional discharge and suction nozzle diameters.
3The calculator converts the inputs and applies H = (p_d − p_s)/(ρg) + Δz + (v_d² − v_s²)/(2g).
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.
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.