Pump power calculation: how to size a pump for any system

Buying the wrong pump is expensive, both upfront and in ongoing energy costs. Too small and you can't deliver the required flow. Too large and you're running at poor efficiency, wasting electricity every day the system operates. Here's how to calculate what size pump motor you need.

The three numbers you need

Pump sizing comes down to three things:

• Flow rate (Q): how much fluid the system needs to move (m³/s or m³/h)
• Total head (H): the total energy per unit weight the pump must supply (m)
• Pump efficiency (η): how much of the motor's energy actually goes into the fluid

From these three, you can calculate the power (in watts, kilowatts, or horsepower) that the motor driving the pump must supply.

The pump power formula

• P: shaft (motor input) power (W)
• ρ: fluid density (kg/m³); water = 1000
• g: 9.81 m/s²
• Q: volumetric flow rate (m³/s)
• H: total head (m)
• η: overall pump efficiency (e.g., 0.75 for 75%)

The numerator (ρgQH) is the hydraulic power, the power actually transferred to the fluid. Dividing by efficiency gives the shaft power, what the motor must supply.

What is "total head"?

Total head H is the sum of all energy the pump must overcome, expressed in meters:

• Friction head loss: energy lost to pipe friction (use the Head Loss Calculator)
• Static head: elevation difference between pump inlet and discharge point (meters)
• Pressure head: any required delivery pressure above atmospheric (ΔP/ρg)
• Velocity head: usually negligible for pump sizing (V²/2g)

H = h_friction + h_static + h_pressure. For a horizontal system delivering to atmosphere: H ≈ h_friction only.

Step-by-step example: building water supply

A pump must supply water to a building's top floor, 25 m above the pump. Required flow: Q = 10 m³/h through 80 m of 80 mm pipe (f = 0.022). Delivery pressure required at top: 1.5 bar above atmospheric.

Step 1: find flow velocity

Step 2: calculate friction head loss

Use the Head Loss Calculator for this step.

Step 3: calculate total head

Step 4: calculate pump power (η = 70%)

Select a 2.2 kW motor (next standard size above 1.58 × 1.15 service factor = 1.82 kW). Try this with your own numbers in the Pump Power Calculator.

What is pump efficiency?

No pump is 100% efficient. Energy is lost to fluid turbulence inside the impeller, mechanical friction at seals and bearings, and fluid leakage back across impeller clearances. The overall efficiency η accounts for all these losses.

• Small centrifugal pumps (< 5 kW): η ≈ 50 to 65%
• Medium pumps (5 to 50 kW): η ≈ 65 to 80%
• Large pumps (> 50 kW): η ≈ 80 to 90%
• High-efficiency pumps (recent designs): up to 92 to 94%

Always use the efficiency at your operating point, not the peak efficiency. Pumps are least efficient when running far from their Best Efficiency Point (BEP).

Check NPSH before you order anything

The power calculation tells you which motor to buy. It tells you nothing about whether the pump will survive at its inlet. If pressure at the impeller eye falls to the vapour pressure of the liquid, the fluid boils, the bubbles collapse against the impeller, and the pump cavitates. It sounds like gravel and it destroys impellers.

The check compares two numbers. NPSH available comes from your system. NPSH required comes from the manufacturer curve for that pump at that flow. NPSHa must beat NPSHr with room to spare, usually 0.5 to 1 m.

Take the building supply above, drawing 20°C water from a tank 2 m below the pump, with 0.4 m of friction in the suction line. Atmospheric pressure is 101,325 Pa and water vapour pressure at 20°C is 2,340 Pa:

Now run the same pump on 80°C water, as a heating circuit might. Vapour pressure climbs to 47,400 Pa and density falls to 972 kg/m³:

Nothing changed except fluid temperature. This is why hot water and condensate pumps are usually fed from a tank mounted above them rather than lifted, and why you should never size a pump on power alone.

The pump runs where the two curves cross

The 40.6 m of head calculated above describes one operating point. A real pump does not deliver a fixed head. Its curve falls as flow rises, because a centrifugal impeller moves more fluid only by generating less pressure.

Your piping has a curve too, running the other way. Static head stays flat no matter what, but friction loss climbs with roughly the square of flow, so the system curve rises steeply. The pump settles wherever the two lines intersect, and that point is the only flow you actually get.

Two things follow. Overestimating friction loss pushes your design point up and left, so you buy a bigger pump that then runs throttled and inefficient. And a system that is nearly all static lift has a flat curve, which means flow barely changes when the pump wears, while a friction-dominated system loses flow quickly. Ask the supplier for the curve and check where your point lands relative to the Best Efficiency Point before signing off.

Frequently asked questions