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 Calculator - Flow, Head and Efficiency

Agarapu Ramesh — Editor and content reviewer
Editorially reviewed Reviewed by Agarapu Ramesh, science educator (chemistry). LinkedIn
Last reviewed: May 2026 | Standard electrical engineering formulas

Pump power is the work needed to lift or move fluid. The core formula is rho x g x flow x head, then you divide by efficiency. The head number matters more than people think. A few extra metres can change the motor size.

Formula at a glance

  • hydraulic W = density x 9.81 x flow m3/s x head m
  • shaft W = hydraulic W / pump efficiency
  • HP = W / 745.7

Field note: A pump that looks right from flow alone can be wrong once you add pipe friction. The pump curve is where the real answer lives.

⚙

Calculator Tool

Enter values to compute

%
%
Results
Click Calculate

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

How to use the Pump Power Calculator

Use this as a pump power check, then compare it with the pump curve and the real pipe layout. Flow and head look simple until elbows, valves and friction join the party.

Worked example

Example: water at 0.01 m3/s through 20 m head needs 1,962 W hydraulic power. At 70% pump efficiency, shaft power is about 2.8 kW.

Practical checks before you trust the number

  • Use total dynamic head, not just vertical lift.
  • Friction losses in pipe, elbows and valves add head.
  • Pick the motor after checking pump curve and service factor.

Common mistake

A pump that looks right from flow alone can be wrong once you add pipe friction. The pump curve is where the real answer lives.

Sources and 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.