Pump Head and Power Calculator
Calculate the hydraulic power required to drive a pump based on flow rate, total head (static plus friction), fluid density, and pump efficiency. Use this when selecting a pump motor or auditing energy consumption in a piping system.
About this calculator
The hydraulic (shaft) power required by a pump is given by P = (Q·ρ·g·H) / η, where Q is the volumetric flow rate in m³/s, ρ is the fluid density in kg/m³, g = 9.81 m/s² is gravitational acceleration, H is the total head in metres (static head plus friction losses), and η is the pump efficiency as a decimal. This equation is derived from the steady-flow energy equation (Bernoulli with losses). Total head H represents the energy per unit weight that the pump must add to the fluid. The formula converts flow rate from L/min to m³/s by dividing by 60,000. A pump's efficiency η accounts for hydraulic, volumetric, and mechanical losses inside the pump casing and impeller — typical values range from 0.60 to 0.85 for centrifugal pumps.
How to use
A centrifugal pump moves water (ρ = 1,000 kg/m³) at 300 L/min against a static head of 15 m with 5 m of friction loss. Pump efficiency η = 0.70. Total head H = 15 + 5 = 20 m. Q = 300 / 60,000 = 0.005 m³/s. P = (Q·ρ·g·H) / η = (0.005 × 1,000 × 9.81 × 20) / 0.70. Numerator: 0.005 × 1,000 × 9.81 × 20 = 981 W. P = 981 / 0.70 ≈ 1,401 W ≈ 1.40 kW. Select a motor of at least 1.5 kW to provide a standard safety margin.
Frequently asked questions
What is the formula for pump power and how is it calculated from flow rate and head?
Pump shaft power is calculated as P = (Q·ρ·g·H) / η, where Q is flow rate (m³/s), ρ is fluid density (kg/m³), g is 9.81 m/s², H is total head (m), and η is pump efficiency. The numerator Q·ρ·g·H gives the ideal hydraulic power — the rate at which energy is added to the fluid. Dividing by efficiency accounts for internal losses in the pump, so the motor must supply more power than the fluid actually receives. The result gives the minimum shaft power; motor sizing should add a further service factor of 10–25%.
What is total dynamic head and how does it differ from static head?
Static head is the vertical height the fluid must be lifted against gravity, measured in metres. Total dynamic head (TDH) adds friction losses in pipes, fittings, valves, and heat exchangers to the static head. Friction losses depend on flow velocity, pipe diameter, pipe roughness, and the number and type of fittings — they increase with the square of flow velocity. A pump must overcome both components: if static head is 20 m but friction losses add another 8 m, the pump must develop 28 m TDH. Underestimating friction losses is a common cause of pumps failing to deliver the design flow rate.
How does pump efficiency affect the motor power I need to install?
Pump efficiency directly scales the required motor power. A pump moving 500 W of hydraulic power at 80% efficiency requires 500/0.80 = 625 W of shaft power, while the same pump at 60% efficiency would need 500/0.60 = 833 W — a 33% increase. In large industrial systems this difference translates to significant energy costs over time. Pump efficiency is highest near the best efficiency point (BEP) on the pump curve; operating far from BEP due to oversizing or throttling wastes energy and accelerates wear. Always select a pump whose BEP is close to the design operating point.