Pump Power Calculator

Pump Power Formula Explained

Hydraulic power is the useful work done on the fluid:

P_h = rho x g x Q x H / 1000

Where P_h = hydraulic power (kW), rho = fluid density (kg/m3), g = 9.81 m/s2, Q = flow rate (m3/s), H = total head (m). Shaft power adds pump efficiency:

P_shaft = P_h / eta

Example: pumping water (1000 kg/m3) at 100 m3/h against 50 m head with 70% efficiency: Q = 100/3600 = 0.0278 m3/s, P_h = 1000 x 9.81 x 0.0278 x 50 / 1000 = 13.6 kW, P_shaft = 13.6 / 0.7 = 19.5 kW.

Typical Pump Efficiencies

| Pump Type | Typical Efficiency |

|---|---|

| Large centrifugal (best point) | 80 - 90% |

| Medium centrifugal | 70 - 85% |

| Small centrifugal | 50 - 70% |

| Positive displacement (screw, gear) | 70 - 90% |

| Multistage centrifugal | 75 - 85% |

Efficiency varies with flow rate and specific speed. Operating far from the best efficiency point (BEP) drops efficiency sharply and increases energy cost. Always select the pump so the duty point sits near BEP.

Worked Example: Sizing a Pump Motor

A process needs 100 m3/h of water (density 1000 kg/m3) at 50 m total head. With a centrifugal pump at 70% efficiency:

P_shaft = 1000 x 9.81 x (100/3600) x 50 / 0.7 / 1000 = 19.5 kW

Select a standard motor size above this: 22 kW (30 HP). Add service factor and check starting torque for the actual pump curve. For viscous or high-density fluids, use the actual density — pumping 1200 kg/m3 fluid raises shaft power to 23.3 kW, requiring a 30 kW motor.

Power Unit Conversion

Pump and motor power is expressed in several units depending on region and industry:

| Convert | Multiply by |

|---|---|

| kW to mechanical hp | 1.341 |

| hp to kW | 0.7457 |

| kW to BTU/hr | 3412 |

| kW to kcal/h | 860 |

Example: a 22 kW motor is 22 x 1.341 = 29.5 hp (standard 30 hp frame) and consumes 22 x 3412 = 75,064 BTU/hr at full load. Energy cost is always calculated from kW (input power), not hp.

Affinity Laws and Variable Speed Power

For a fixed pump and impeller, changing speed N changes flow, head and power:

Q2/Q1 = N2/N1, H2/H1 = (N2/N1)^2, P2/P1 = (N2/N1)^3.

Because power varies with the cube of speed, a small speed reduction saves a lot of energy. Running a 19.5 kW pump at 90% speed needs only 0.9^3 = 0.729 of the power, about 14.2 kW - a 27% saving. This is why variable-speed drives are the primary energy-saving measure for pumps. Use the pump affinity law calculator for detailed speed-change results.

Centrifugal vs Positive Displacement: Same Power Math, Different Machines

The pump power equation is identical for every pump type — centrifugal or positive displacement: shaft power P = rho x g x Q x H / eta. What changes between machine types is not the power math but the flow-head characteristic, the efficiency curve and the best operating range. A centrifugal pump delivers variable flow against a BEP-centred head, while a positive displacement pump (gear, screw, lobe, piston, plunger, diaphragm) delivers near-constant flow regardless of head. Use this calculator for the hydraulic power duty point in both cases, then choose pump type by flow rate, viscosity, discharge pressure and flow-stability requirements — a decision covered separately in the Positive Displacement Pumps guide and the Pump Selection Guide shown in the related section.