Pump Power Calculator estimates hydraulic and shaft power from flow rate, total head, fluid density, and pump efficiency with formulas, examples, FAQs, and references.

Pump Power / Head Calculator

What this calculator does

The Pump Power Calculator determines the hydraulic power required to move a fluid, the mechanical shaft power required to drive the pump, and the electrical input power required by the motor.

Inputs explained

  • Flow rate (Q): The volume of fluid moved over time (L/s, m³/h, GPM).
  • Total head (H): Total dynamic head (vertical lift + pipe friction loss) in meters or feet.
  • Fluid: Select common fluids (Water, Sea water, Diesel) or enter custom density.
  • Pump efficiency (η_pump): Percentage of mechanical power converted to fluid power (default 70%).
  • Motor efficiency (η_motor): Percentage of electrical power converted to mechanical power (default 90%).

How it works / Method

First, hydraulic power is calculated using the fluid density, flow rate, head, and gravity. Then, shaft power (Brake Horsepower, BHP) is calculated by dividing hydraulic power by pump efficiency. Finally, motor input power is found by dividing shaft power by motor efficiency.

Formulas used

  • Hydraulic Power (W) = ρ × g × Q × H
  • Hydraulic Power (kW) = (ρ × Q × H × 9.81) / 1000
  • Shaft Power (kW) = Hydraulic kW ÷ (η_pump / 100)
  • BHP (HP) = Shaft kW × 1.341
  • Motor Input Power (kW) = Shaft kW ÷ (η_motor / 100)

Units: ρ in kg/m³, Q in m³/s, H in meters, g = 9.81 m/s², Power in kW & HP.

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Formulas

Hyd. Power(ρ × Q × H × g) / 1000
Shaft kWHyd kW / η_pump
Motor kWShaft kW / η_motor

Quick Reference: Pump Efficiency

Pump TypeTypical Efficiency
Centrifugal60% - 80%
Submersible50% - 70%
Positive Displacement80% - 90%
Standard Motor85% - 95%

Related Calculators

Motor Current kW to Amps Energy Cost

Step-by-step example

Scenario: Pumping water (ρ=1000) at 10 L/s against a 20m total head. Pump efficiency 70%, Motor 90%.

Formula: Hyd kW = (ρ × Q × H × g) / 1000

  1. Convert Q: 10 L/s = 0.01 m³/s.
  2. Hydraulic kW = (1000 × 0.01 × 20 × 9.81) / 1000 = 1.962 kW.
  3. Shaft kW = 1.962 / 0.70 = 2.803 kW.
  4. BHP = 2.803 × 1.341 = 3.76 HP.
  5. Motor Input kW = 2.803 / 0.90 = 3.11 kW.

Result: Shaft power is ~2.8 kW. Recommend standard 3.7 kW (5 HP) motor.

Use cases

  • Sizing agricultural irrigation pumps and motors.
  • Building commercial water supply and booster stations.
  • Designing HVAC chilled water loops and cooling towers.
  • Calculating power needs for sewage lift stations.
  • Industrial fluid transfer sizing (e.g., diesel or chemicals).

Assumptions & limitations

  • Assumes steady-state incompressible flow.
  • 'Total Head' must include both static lift and dynamic friction loss in the pipes; if you only use vertical lift, the motor will be undersized.
  • Motor slip and power factor are not modeled in the core kW calculation, but affect current draw.
  • Fluid viscosity affects pump efficiency; highly viscous fluids require derating factors not included here.
  • Consult manufacturer pump curves for actual duty point efficiency.

Sources & references

Related calculators

Frequently Asked Questions

Hydraulic power formula: P (kW) = (ρ × g × Q × H) ÷ 1000, where ρ is fluid density (1000 kg/m³ for water), g = 9.81 m/s², Q is flow in m³/s, and H is head in meters. To get shaft power, divide by pump efficiency. Example: 0.01 m³/s at 20 m head = (1000 × 9.81 × 0.01 × 20) ÷ 1000 = 1.96 kW hydraulic. With 70% pump efficiency, shaft power is about 2.8 kW.

Hydraulic horsepower (HP) = (Q × H × SG) ÷ 3960, where Q is flow in US GPM, H is total head in feet, and SG is specific gravity (1 for water). Example: 100 GPM × 100 ft head ÷ 3960 = 2.53 HP hydraulic. Divide by pump efficiency (typically 0.55–0.75) to get brake horsepower. So a real motor selection might be 4 HP for that duty. Keep this formula handy — it's the backbone of every pump quotation.

Shaft power = hydraulic power ÷ pump efficiency. Pump efficiency typically ranges from 50% on small domestic pumps to 80% on large industrial ones. So if your hydraulic load is 2 kW and the pump is 65% efficient, shaft power = 2 ÷ 0.65 = 3.08 kW. To pick the motor, divide once more by motor efficiency (around 0.85–0.92) and add a 15–25% safety margin. Pumps near their best-efficiency point save the most energy long-term.

For a typical flow rate, plug into P = (ρ × g × Q × H) ÷ 1000. Lifting 0.005 m³/s (5 L/s) of water 50 m: (1000 × 9.81 × 0.005 × 50) ÷ 1000 = 2.45 kW hydraulic. With a 65% pump and 90% motor, electrical input ≈ 2.45 ÷ (0.65 × 0.9) = 4.18 kW. Round up to a 5.5 kW motor. Always include friction head from pipe length and bends, otherwise the pump will fall short on actual delivery.

Hydraulic power is the useful work done on the fluid: lifting and pressurizing it. Shaft power is what the motor actually has to deliver to the pump shaft, and it's higher because of pump losses (friction, recirculation, leakage). The ratio is the pump efficiency. Example: 2 kW hydraulic ÷ 0.7 efficiency = 2.86 kW shaft power. Knowing this distinction stops juniors from spec'ing a motor that's too small and tripping the overload on day one.

Combine head and flow into hydraulic power, then divide by pump and motor efficiencies. P_electrical (kW) = (ρ × g × Q × H) ÷ (1000 × η_pump × η_motor). For 0.01 m³/s at 30 m with 70% pump and 90% motor: (1000 × 9.81 × 0.01 × 30) ÷ (1000 × 0.7 × 0.9) ≈ 4.67 kW. Always size the next standard motor up — 5.5 kW in this case — so you don't run on the edge.

Yes. The calculator gives shaft power, then you divide by motor efficiency and apply a service factor (1.15 to 1.25) to pick the next standard motor size. Example: 3 kW shaft ÷ 0.9 efficiency × 1.2 service = 4 kW, so a 5.5 kW motor is the safe pick. Always check the manufacturer's pump curve at the actual operating point — calculators give a starting figure, but the curve confirms the duty.