Pump Horsepower Calculator - Shaft & Hydraulic Power

A pump horsepower calculator turns a pump's flow rate, differential head, fluid density, and efficiency into the shaft power the motor must supply and the hydraulic power the fluid actually receives. It accepts volumetric flow with a unit selector, head in metres or feet, fluid density, gravity, pump efficiency, and optional RPM, then returns hydraulic power in watts, shaft power in watts and mechanical horsepower, and a dimensionless specific speed when RPM is provided. Use it to size a centrifugal pump, confirm a textbook problem, or check a nameplate before specifying a motor.

• Centrifugal pump selection: Pick the right motor rating by estimating shaft power from design flow and head, then compare to pump catalog curves.
• Classroom fluid-power problems: Solve textbook exercises in fluid mechanics, turbomachinery, and chemical engineering unit operations.
• Plumbing and HVAC design checks: Estimate pump power for chilled water loops, boiler feed systems, and stormwater lift stations during preliminary design.
• Pump performance verification: Cross-check manufacturer curves and field measurements by computing hydraulic and shaft power at the operating point.

Because pump power depends on the net force the impeller applies to the fluid, the Forces & Newton's Laws Calculator helps you sanity-check the head term by switching between force and pressure viewpoints.

The calculator applies the standard turbomachinery power equations to the inputs you provide. Hydraulic power is rho times g times Q times H, and shaft power divides that hydraulic power by the pump efficiency. When you supply a rotational speed, it also reports the dimensionless specific speed used to compare pump geometries.

• Q: Volumetric discharge in m3/s. The calculator converts m3/h, L/s, and US gpm into m3/s before any power calculation.
• H: Differential head in metres, including static lift plus pipe, fitting, and equipment friction losses. Feet are converted internally.
• rho: Mass density of the pumped fluid in kg/m3. Water at 4 C is 1000 kg/m3; seawater about 1025 kg/m3; light oils 800 to 900.
• g: Local acceleration due to gravity in m/s2. Defaults to 9.81 m/s2.
• eta: Overall pump efficiency as a decimal between 0 and 1. Centrifugal pumps typically run 0.6 to 0.85 at design point.
• N: Pump rotational speed in RPM, used only for specific speed. Internally converted to rad/s with N_rad = 2 * pi * N / 60.

Hydraulic power Ph equals flow in m3/h times density times gravity times head divided by 3.6 million, and shaft power Ps equals Ph divided by the pump efficiency, per Engineering Toolbox.

When the same shaft power and head are expressed in joules per second versus watt-hours, the Work, Energy & Power Calculator confirms the unit conversions and reinforces that efficiency is the ratio of output to input power.

Four ideas drive every pump horsepower problem. Knowing each one lets you sanity-check the calculator instead of trusting it blindly.

Treat efficiency as the link between what the fluid gains and what the motor pays for; treat specific speed as the link between pump type and operating regime. If your answers fall outside the typical band for a chosen pump family, re-examine the efficiency input first.

Because pump shaft power is also the product of torque and angular speed, the Torque, Power & Speed Calculator converts between motor RPM, torque, and the same wattage the calculator reports as Ps.

Enter the operating point, supply the fluid and efficiency, and read off hydraulic power, shaft power, and optional specific speed.

1. 1 Choose flow unit and enter flow: Pick m3/s, m3/h, L/s, or US gpm from the dropdown and type the volumetric discharge your pump must deliver.
2. 2 Set differential head: Add the static lift from suction reservoir to discharge plus pipe, fitting, and equipment friction losses. Use metres or feet.
3. 3 Fill in fluid density and gravity: Use 1000 kg/m3 for fresh water, 1025 kg/m3 for seawater, or the supplier's value for glycol or oil. Default gravity is 9.81 m/s2.
4. 4 Set pump efficiency: Start with the manufacturer curve value. Use 0.6 to 0.7 for small centrifugal pumps, 0.75 to 0.85 for mid-size units, and 0.85 to 0.95 for positive-displacement pumps.
5. 5 Add RPM for specific speed (optional): Enter the impeller speed in revolutions per minute to also compute dimensionless specific speed. Leave at zero to hide the output.
6. 6 Read the results and adjust: Hydraulic power tells you what the fluid receives, shaft power tells you what the motor must supply, and the horsepower value lets you size the motor against standard ratings.

To size a motor for a 50 m3/h pump moving water through 25 m of total head at 75 percent efficiency: choose m3/h, set flow to 50, head to 25 m, density to 1000, gravity to 9.81, efficiency to 0.75, leave RPM at zero. The result is Ph = 3,406.25 W, Ps = 4,541.67 W (6.09 hp). A 7.5 kW (10 hp) motor would carry the load with margin.

Once you have sized the pump, the Hydraulic Retention Time Calculator pairs naturally with this tool to confirm the residence time inside the basin or tank the pump feeds.

A dedicated pump horsepower solver removes unit-conversion errors and lets you compare operating points in seconds.

• Two readings from one calculation: Hydraulic power in watts and shaft power in watts and horsepower appear together, so you can compare fluid demand with the motor nameplate.
• Live unit conversion: Switch flow between m3/s, m3/h, L/s, and US gpm, and head between metres and feet, without re-keying numbers.
• Density-aware results: Default water density is 1000 kg/m3 but you can drop in seawater (1025), glycol mixtures, or light oils.
• Optional specific speed: Adding RPM gives the dimensionless specific speed used to position a unit inside the radial, mixed, or axial family of impeller designs.
• Friction-aware shaft power: An efficiency input turns the ideal hydraulic model into a realistic shaft power estimate, so motor selection accounts for slip and recirculation.
• Classroom-ready outputs: Each result matches the SI textbook convention, so homework, lab reports, and engineering assignments can use the calculator's output directly.

Use it to sketch motor sizes during a preliminary design or to double-check a nameplate after a maintenance swap.

When the same system includes gravity flow or pressure-driven distribution, the Water Potential Calculator covers the energy-per-unit-mass viewpoint that complements the wattage view this calculator provides.

Pump power depends on the operating point, the fluid, and the assumed efficiency. A few levers move the answer more than others.

• The model assumes steady, single-phase, incompressible flow. Two-phase mixtures, slurries above about 5 percent solids, or compressible gases need a different power treatment.
• Friction losses are absorbed into the single efficiency factor. Real pumps have hydraulic, volumetric, and mechanical loss terms that move differently with flow and RPM.
• Specific speed uses the SI form. The customary form with N in RPM, Q in gpm, H in ft gives a different numeric value, so do not mix forms against a manufacturer's chart.

If a real pump 'feels' harder to drive than the calculator suggests, the operating point has slid off the best-efficiency line, so the efficiency number should fall with it. For compressible gases, slurries, or non-Newtonian fluids, swap this calculator for a specialist tool.

According to Wikipedia - Pump, the shaft power required by a pump equals the hydraulic power delivered to the fluid divided by the overall efficiency, and centrifugal pumps convert mechanical shaft work into fluid kinetic energy through the impeller before converting that kinetic energy into pressure head.

According to OpenStax University Physics Vol. 1, the power delivered by a fluid under pressure equals the pressure difference times the volumetric flow rate, which for incompressible flow in SI units reduces to density times gravity times flow times head.