Pump Power
Calculator
Compute hydraulic and brake power for motor sizing, with full step-by-step solutions.
Formula
Quick Answer
Pump power comes in two flavors: hydraulic power (the useful work delivered to the fluid) and brake power (the actual shaft power the motor must supply, always larger due to pump inefficiency). Hydraulic power = ρgQH; brake power = hydraulic power / efficiency. This calculator computes both from flow rate, head, fluid density, and pump efficiency.
Pump Power Calculator
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How to Use the Pump Power Calculator
- 1
Enter the flow rate and head
Enter the volumetric flow rate Q and the total head H the pump must develop (from the NPSH or system curve calculation).
- 2
Enter the fluid density
Enter the fluid density ρ, use 998 kg/m³ for water at room temperature, or your specific fluid's value.
- 3
Enter the pump efficiency
Enter the pump's efficiency η (from its datasheet or performance curve), typically 50–85% for centrifugal pumps.
- 4
Read hydraulic and brake power
Read the hydraulic (fluid) power and the brake (shaft) power the motor needs to supply, brake power is always higher.
Need to check suction-side cavitation risk too? Use the NPSH Available Calculator, or see the full Fluid Mechanics topic guide.
What Is Pump Power?
A pump does two distinct jobs worth separating: it delivers useful energy to the fluid (hydraulic power), and it draws mechanical energy from its driver, usually an electric motor, to do so (brake power). Because no pump is perfectly efficient, brake power is always larger than hydraulic power; the gap between them is lost to internal friction, recirculation, and leakage inside the pump.
This calculator computes both from the four quantities every pump datasheet or system design gives you: volumetric flow rate, total developed head, fluid density, and pump efficiency.
Derivation: From Energy Balance to Brake Power
Hydraulic power is the rate of useful work done raising a mass flow of fluid through a head H. Starting from the mechanical energy balance, the work per unit weight of fluid is H, so the power delivered to a mass flow rate ṁ = ρQ is:
This is the power actually transferred to the fluid, independent of the pump itself. The pump, however, cannot deliver 100% of its input shaft work to the fluid: mechanical friction in bearings and seals, internal fluid recirculation, and disk friction all consume part of the input. The pump efficiency η captures all of these losses in one ratio, giving the brake (shaft) power the motor must actually supply:
Where Q and H Actually Come From
This calculator takes Q and H as inputs, but neither is arbitrary, a real pump settles wherever its own curve crosses the system curve, computed live below.
When You Need a Pump Power Calculation
- Motor sizing. Selecting the right electric motor for a pump requires the brake power at the design flow and head, plus a service-factor margin.
- Energy and operating-cost estimates. Brake power directly sets the electrical draw of a pump, which is the basis for running-cost and energy-audit calculations.
- Pump selection from a system curve. Once the total dynamic head is known from a system-curve analysis (including friction losses), power tells you which pump class or size is required.
- Cavitation and suction design cross-checks. Power sizing and NPSH margin are solved together when specifying a new pump, see the NPSH calculator.
Worked Example
Sizing a Water Transfer Pump
Problem: A centrifugal pump moves water (ρ = 998 kg/m³) at Q = 0.05 m³/s against a total head of H = 30 m. The pump is 70% efficient. Find the hydraulic and brake power.
Answer: Hydraulic power ≈ 14.69 kW, brake power ≈ 20.98 kW, the motor must be rated for at least ~21 kW, typically rounded up to a standard 22 or 25 kW motor with margin.
Common Mistakes
- Forgetting to divide by efficiency. Hydraulic power alone understates what the motor must supply, always divide by η to get brake power for motor sizing.
- Using static lift instead of total dynamic head. H must include friction losses in the piping, not just the elevation difference between source and destination.
- Mixing up flow rate units. Q must be in m³/s for this formula, a flow rate given in L/min or gpm must be converted first, or the result is off by orders of magnitude.
- Assuming 100% efficiency. Even well-designed centrifugal pumps rarely exceed 85–90% efficiency at their best efficiency point, and efficiency drops further away from it.
Key Takeaways
- Hydraulic power = ρgQH, the useful work delivered to the fluid.
- Brake power = hydraulic power / η, what the motor must actually supply.
- Brake power is always ≥ hydraulic power, since no pump is 100% efficient.
- Use total dynamic head (static head + friction losses), not just static lift.
- Add a service-factor margin above calculated brake power when selecting a motor.
Frequently Asked Questions
Motor sizing and utility-cost estimates need brake power, not hydraulic power, sizing off the smaller number leaves the motor unable to actually drive the pump at its rated point. See the derivation below for how the gap between them (lost to internal friction, leakage, and recirculation) is exactly what efficiency η quantifies.
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