Pump Power Calculator — Motor kW from Flow Rate, Head & Efficiency
Calculate pump hydraulic power and required motor kW from flow rate, total head, fluid density, and pump efficiency.
Calculator
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Hydraulic power: 19.62 kW
Shaft power (approx.): 26.16 kW
Formula
Hydraulic power P_h = ρ × g × Q × H (W), where Q in m³/s, H in m, ρ in kg/m³, g = 9.81 m/s². Shaft power P_shaft = P_h / η_pump. Input power P_input = P_shaft / η_motor. Motor kW rating = P_input × 1.1 to 1.25 (design margin).
Example calculation
Water pump: Q = 180 m³/h = 0.05 m³/s, TDH = 40 m, pump η = 0.72, motor η = 0.92. P_h = 1000×9.81×0.05×40 = 19,620 W = 19.62 kW. P_shaft = 19.62/0.72 = 27.25 kW. P_input = 27.25/0.92 = 29.62 kW. Select 37 kW motor (next standard size above 29.62 × 1.15 safety margin = 34.1 kW).
Engineering notes
Total dynamic head (TDH) = static head + friction head + velocity head + pressure head differential. Friction head must be calculated separately using Darcy-Weisbach. η_overall = η_pump × η_motor. For preliminary sizing: η_pump = 0.65–0.70 (small pumps < 10 kW), 0.72–0.80 (medium 10–100 kW), 0.80–0.88 (large > 100 kW). Motor standard frame sizes (IS 325): 0.37, 0.55, 0.75, 1.1, 1.5, 2.2, 3.7, 5.5, 7.5, 11, 15, 18.5, 22, 30, 37, 45, 55, 75, 90, 110, 132, 160, 200, 250, 315 kW.
When to use this calculator
- Pump motor selection — calculate required motor kW before specifying any pump driver
- Energy audit — estimate annual electricity consumption for pumping circuits at known operating hours
- Fire pump sizing — determine hydraulic kW for firefighting pumps per NFPA 20 or IS 12288
- Project costing — include pump power in the electrical load list for MCC and transformer sizing
- System comparison — compare power and efficiency of alternative pump selections for the same duty point
Frequently asked questions
- How do I calculate pump motor kW from flow rate and head?
- Use: Motor kW = (ρ × g × Q × H) / (η_pump × η_motor × 1000), where ρ = fluid density (kg/m³), g = 9.81 m/s², Q = flow rate (m³/s), H = total dynamic head (m). Divide by 1000 to convert W to kW. Then select the next standard motor size above the calculated value. Add a 10–25% design margin to account for head estimation error and future capacity increase: motor kW = calculated input kW × 1.15.
- What is total dynamic head (TDH) and how do I calculate it?
- TDH = Static head + Friction head + Minor losses + Pressure differential head. Static head: elevation difference between suction and discharge liquid levels (m). Friction head: pressure drop in pipes and fittings (calculate with Darcy-Weisbach or use the pressure drop calculator on this site). Minor losses: equivalent length method for elbows, valves, tees. Pressure head: (P_discharge − P_suction) / (ρg) in metres — add if pumping into a pressurised vessel, subtract if discharging to atmosphere or lower-pressure vessel.
- What pump efficiency should I use for motor sizing if I have no datasheet?
- For preliminary sizing: small centrifugal pumps under 5 kW hydraulic power: η_pump = 55–65%. Medium pumps 5–50 kW: η_pump = 68–76%. Large pumps above 50 kW: η_pump = 78–85%. Premium efficiency pumps (IE3-equivalent hydraulic): 82–88% above 100 kW. Motor efficiency (IE2, standard): 87–92% for 5–100 kW. IE3 motors: 90–95%. Overall efficiency η_overall = η_pump × η_motor: use 0.55–0.70 for small pump+motor sets, 0.65–0.78 for industrial installations.
- How do I convert flow rate from m³/h or LPM to m³/s for the formula?
- Divide m³/h by 3,600 to get m³/s. Divide LPM (litres per minute) by 60,000 to get m³/s. Multiply US gpm by 0.0000631 to get m³/s. Examples: 100 m³/h = 0.02778 m³/s; 500 LPM = 0.00833 m³/s; 100 US gpm = 0.00631 m³/s.
- Can this calculator be used for viscous liquids like heavy oil or slurry?
- The hydraulic power formula P = ρgQH is valid for any fluid — use the correct density ρ for your liquid. However, for viscous fluids above ~50 cP (centipoise), the pump efficiency degrades compared to water performance. Apply Hydraulic Institute (HI 9.6.7) viscosity correction factors to derate the pump head, flow, and efficiency from the water curve. For slurries, also reduce speed and use abrasion-resistant impeller materials (hard metal or rubber); slurry specific gravity increases effective density.
- What is NPSHa and how do I check for cavitation?
- NPSHa (Net Positive Suction Head available) = (P_atm + P_static_suction − P_vapour) / (ρg) − h_f_suction, in metres. For water at 20°C: P_vapour = 0.24 m head. NPSHa must exceed NPSHr (required, from pump curve) by at least 0.5–1.0 m margin. Low NPSHa causes cavitation — implosion of vapour bubbles that erodes impeller, creates noise (like gravel in the pump), and reduces flow and head. Solutions: lower pump, raise sump level, increase suction pipe diameter, reduce suction pipe length and fittings.
- How do I size a pump for a system with multiple parallel or series pumps?
- Series pumps (to increase head): total head = sum of individual heads; flow rate stays the same. Each pump must be rated for the same flow but can have different head ratings. Parallel pumps (to increase flow): total flow = sum of individual flows at the same head. The system curve intersects the combined pump curve at the operating point. For parallel operation, both pumps should have similar H-Q curves to ensure equal load sharing. Running two identical pumps in parallel typically gives only 60–80% of double the flow (not 100%) because the system head increases with flow.