How do I calculate pump power from flow rate and head?

Hydraulic power is ρgQH. At 10 L/s against 30 m of water that is 998 × 9.80665 × 0.010 × 30 = 2,936 W. Divide by the pump efficiency to get the shaft power the motor must supply.

What efficiency should I assume for a pump?

It depends on size and duty. Small centrifugal pumps are often 30% to 50%, medium ones 55% to 75%, and large pumps up to the high 80s. The default of 0.70 is a reasonable midpoint for a medium pump near its best-efficiency point. Use the manufacturer's curve when you have it.

What is total head and how do I find it?

Total head is the energy the pump must add per unit weight of fluid: the static lift, plus the pressure difference between the delivery and suction points converted to head, plus friction and minor losses in the piping. The pipe head loss calculator gives the friction part.

How do I convert a pressure rise to head?

Divide by the density and gravity: H = ΔP/(ρg). A 300 kPa rise in water is about 30.6 m of head.

How do I choose a motor size from shaft power?

Pick the next standard rating at or above the shaft power, then allow a margin for the operating range and the service factor. The calculator lists the next standard IEC rating as an indication. Confirm with the pump curve, since power can rise at flows away from the design point.

Pump Power Calculator

Pump hydraulic power, shaft power, and an indicative motor size from flow rate, total head or pressure rise, fluid density, and efficiency.

Scratchpad (not saved)

Save to create a persistent, shareable workspace.

What This Calculator Does

A pump adds energy to a fluid at a rate set by the flow and the head it works against. The hydraulic power is the energy the fluid receives, $P_h = \rho g Q H$, and the shaft power is what the motor must deliver, which is larger by the pump efficiency. This calculator takes the flow, the total head (or a pressure rise converted to head), the fluid density, and the efficiency, then returns both powers in kW and horsepower. It also lists the next standard motor rating above the shaft power from a fixed table of common sizes, which is indicative only. The total head usually comes from the pipe head loss calculator plus the static lift.

It combines Flow Rate Q, Flow Unit, Head Input, Total Head H to estimate Shaft power, Hydraulic power, Indicative motor size (next standard rating).

Formula & Method

Hydraulic power:

P_h = \rho\,g\,Q\,H

Shaft power:

P_{shaft} = \frac{P_h}{\eta}

Head from a pressure rise:

H = \frac{\Delta P}{\rho\,g}

where

\rho

is fluid density,

g = 9.80665

m/s²,

Q

is volumetric flow,

H

is total head,

\Delta P

is the pressure rise across the pump, and

\eta

is the pump efficiency, between 0 and 1. One horsepower is 745.7 W. Total head is the static lift plus the friction and minor losses in the piping, plus any difference in pressure or velocity head between the suction and discharge.

Notation used in the formulas: $R$ = Shaft power; $x_{1}$ = Flow Rate Q; $x_{2}$ = Flow Unit; $x_{3}$ = Head Input; $x_{4}$ = Total Head H; $x_{5}$ = Head Unit; $x_{6}$ = Pressure Rise ΔP.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it to estimate the motor size for a pumping duty, to compare the running power of two operating points, or to see what efficiency does to energy cost. The power rises in proportion to both flow and head, so a throttled pump at lower flow still draws power at the higher head.

Worked Examples

Water at 10 L/s against 30 m of head (metric)

Given: Q = 10 L/s, H = 30 m, water ρ = 998 kg/m³, η = 0.70 Method: hydraulic power from ρgQH, then divide by efficiency for the shaft. Q = 0.010 m³/s Ph = 998 × 9.80665 × 0.010 × 30 = 2,936 W Pshaft = 2,936 / 0.70 = 4,194 W = 4.19 kW = 5.62 hp The next standard rating above 4.19 kW is 5.5 kW (a 4 kW motor falls short).

Pump specified by pressure rise (imperial)

Given: Q = 100 US gal/min, pressure rise 40 psi, water, η = 0.65 Method: convert the pressure rise to head, then use the same power equation. Q = 100 × 6.309×10⁻⁵ = 6.309×10⁻³ m³/s ΔP = 40 psi = 275.8 kPa, so H = 275,790 / (998 × 9.80665) = 28.2 m (92.4 ft) Ph = 275,790 × 6.309×10⁻³ = 1,740 W Pshaft = 1,740 / 0.65 = 2,677 W = 2.68 kW = 3.59 hp. A 3 kW motor is the next standard rating above 2.68 kW.

Typical Pump Efficiencies and Standard Motor Sizes

Efficiency depends strongly on size and on how close the pump runs to its best-efficiency point. The ranges below are rules of thumb. Use the manufacturer's pump curve when you have it.

Pump type	Typical overall efficiency
Small centrifugal (under 1 kW)	30% to 50%
Medium centrifugal (1 to 50 kW)	55% to 75%
Large centrifugal (over 50 kW)	75% to 88%
Positive displacement (gear, piston)	60% to 90%

The motor suggestion uses these IEC ratings in kW: 0.37, 0.55, 0.75, 1.1, 1.5, 2.2, 3, 4, 5.5, 7.5, 11, 15, 18.5, 22, 30, 37, 45, 55, 75, 90, 110, 132, 160, 200, 250, 315. The list is indicative. Available sizes and the service margin to add vary by region, duty, and standard.

Reference

The hydraulic power relation is covered in Çengel and Cimbala, Fluid Mechanics, and in Karassik et al., Pump Handbook. The Hydraulic Institute standards give the accepted definitions of pump head and efficiency.

Common Mistakes

Using the static lift alone as the head. Total head also includes friction and minor losses in the piping and any pressure at the discharge.
Using a motor efficiency where the pump efficiency belongs. This calculator returns shaft power. Electrical input power is higher by the motor efficiency.
Entering efficiency as a percentage. Enter 0.70, not 70.
Using water density for a heavier or lighter fluid. Power scales with density.
Sizing the motor to the exact shaft power with no margin. Operating points drift, so check the pump curve across its full range, not only at the design point.

When Not To Use This Calculator

Final motor selection. The list of standard sizes here is indicative; confirm with the pump curve, the service factor, and the applicable standard.
Compressors and fans handling compressible gas, where the work depends on the thermodynamic process.
Viscous fluids, where pump efficiency and head fall with viscosity and correction factors are required.
Variable-speed duty, where efficiency and head change across the operating range.

Frequently Asked Questions

How do I calculate pump power from flow rate and head?: Hydraulic power is ρgQH. At 10 L/s against 30 m of water that is 998 × 9.80665 × 0.010 × 30 = 2,936 W. Divide by the pump efficiency to get the shaft power the motor must supply.
What efficiency should I assume for a pump?: It depends on size and duty. Small centrifugal pumps are often 30% to 50%, medium ones 55% to 75%, and large pumps up to the high 80s. The default of 0.70 is a reasonable midpoint for a medium pump near its best-efficiency point. Use the manufacturer's curve when you have it.
What is total head and how do I find it?: Total head is the energy the pump must add per unit weight of fluid: the static lift, plus the pressure difference between the delivery and suction points converted to head, plus friction and minor losses in the piping. The pipe head loss calculator gives the friction part.
How do I convert a pressure rise to head?: Divide by the density and gravity: H = ΔP/(ρg). A 300 kPa rise in water is about 30.6 m of head.
How do I choose a motor size from shaft power?: Pick the next standard rating at or above the shaft power, then allow a margin for the operating range and the service factor. The calculator lists the next standard IEC rating as an indication. Confirm with the pump curve, since power can rise at flows away from the design point.

Inputs Used

Flow Rate Q: Volumetric flow the pump delivers.
Flow Unit: Unit for the value entered above.
Head Input: Used directly in the calculation.
Total Head H: Static lift plus friction and minor losses. Used when Head Input is total head.
Head Unit: Unit for the value entered above.
Pressure Rise ΔP: Discharge pressure minus suction pressure. Used when Head Input is pressure rise.
Pressure Unit: Unit for the value entered above.
Fluid (Density ρ): Used directly in the calculation.
Custom Density ρ: Used only when the fluid is set to Custom.
Custom Density Unit: Unit for the custom density.
Pump Efficiency η: A fraction between 0 and 1, for example 0.70 for 70%.

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