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

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).

Frequently Asked Questions