Pump Power Calculator
Pump power is what a motor must provide to move fluid against pressure and gravity. Get it wrong and you'll underpower (pump stalls) or overpower (wasted energy and cost) your system. This calculator gives you hydraulic power and shaft power - including motor sizing in hp for equipment selection. Use the Head Loss Calculator to find H before starting here.
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Why Pump Power Calculation Matters
When you're designing a pumped system - a water supply network, a cooling circuit, an oil transfer system - you need to know how powerful a motor to buy. Too small, and the pump can't deliver the required flow. Too large, and you're paying for energy you'll never use, and the pump may operate far from its best efficiency point (BEP), causing vibration and shortened lifespan.
The calculation always starts with head: what total head must the pump overcome? That includes friction losses (from this site's Head Loss Calculator), elevation change, and required delivery pressure.
The Formula Explained
P = ρ × g × Q × H / η - P - shaft (input) power required (W)
- ρ - fluid density (kg/m³)
- g - gravitational acceleration = 9.81 m/s²
- Q - volumetric flow rate (m³/s)
- H - total head (m)
- η - pump efficiency (e.g. 0.75 for 75%)
Hydraulic power (power delivered to the fluid) = ρ × g × Q × H. Shaft power accounts for pump inefficiency by dividing by η.
Worked Example
A water pump must deliver Q = 0.05 m³/s against a total head of H = 25 m. Pump efficiency is 72%. Find the required motor power.
Hydraulic power = ρ × g × Q × H
= 1000 × 9.81 × 0.05 × 25 = 12,262 W = 12.3 kW
Shaft power = 12,262 / 0.72
= 17,031 W ≈ 17.0 kW (22.8 hp)
You'd select a standard motor size just above 17 kW - typically an 18.5 kW or 22 kW motor to allow for startup torque and operating margin.
Frequently Asked Questions
What head value should I use - friction only or total?
Use total head: the sum of friction head loss (from the Darcy-Weisbach equation), static elevation difference (discharge level minus pump centerline), and any additional pressure head required at delivery. The Head Loss Calculator only gives you the friction component - add the others manually.
What motor size should I order?
Never order a motor exactly matching the calculated shaft power. Add a service factor of 10–15% for design margin, then round up to the next standard motor size (e.g., 1.5 kW, 2.2 kW, 3 kW, 4 kW, 5.5 kW, 7.5 kW...). This protects against unexpected head increases and system aging.
How do I convert m³/s to other flow units?
1 m³/s = 1000 L/s = 3600 m³/h = 15,850 US GPM. For small systems, flows in L/s or L/min are more practical. Divide L/s by 1000 to get m³/s.
Related Tools
💧 Head Loss Calculator
Calculate friction head loss - the main input H for this calculator.
🔄 Volumetric Flow Rate Calculator
Find Q from pipe diameter and velocity for use in this calculator.
📉 Pressure Drop Calculator
Find pressure drop in Pa - convert to head by dividing by ρg.
📊 Moody Chart Calculator
Get friction factor to calculate head loss for pump sizing.