In this pump power calculator, we will show you how to find the shaft power of a pump in just a few steps.
We will also help you understand what pump power means, the formulas used in both US and SI units, and how to apply them.
What is pump power?
Why do we need it in fluid systems?
How do we calculate it with flow rate, head, and efficiency? Find all the answers here!
Pump Power Calculator
Shaft Power (US Units)
US gpmft
(0-1)
Understanding Pump Power Formulas
1. Formula in US Units
Shaft Power (hp) = (Q × H × SG) / (3960 × η)
- Q = Flow rate (US gpm)
- H = Total head (ft)
- SG = Specific Gravity of fluid
- η = Pump efficiency (decimal)
- 3960 = Unit conversion constant (relates gpm × ft × SG → hp)
2. Formula in SI Units
Hydraulic Power (kW) =
(ρ × g × Q × H) / 1000
Shaft Power (kW) =
Phydraulic / η
- ρ = Fluid density (kg/m³)
- g = Acceleration due to gravity (9.81 m/s²)
- Q = Flow rate (m³/s)
- H = Total head (m)
- η = Pump efficiency (decimal)
- 1000 = Conversion from Watts to kilowatts
3. Relation Between US & SI Formulas
Both formulas calculate shaft power, but use different measurement systems:
- In US units, the 3960 constant comes from combining unit conversions (1 hp = 550 ft·lbf/s, flow in gpm, head in ft).
- In SI units, no constant like 3960 is needed, because the formula uses ρ, g, and Q in standard units.
Essentially, the US formula is a shortcut derived from the SI equation after applying all necessary conversions for gallons, feet, and horsepower.
4. Worked Example
Problem: A pump delivers 150 US gpm of water (SG = 1.0) against a head of 100 ft with 80% efficiency. Find the shaft power.
Step 1: Given Data
- Q = 150 gpm
- H = 100 ft
- SG = 1.0
- η = 0.80
Step 2: Apply US Formula
Pshaft = (Q × H × SG) / (3960 × η)
= (150 × 100 × 1.0) / (3960 × 0.80)
Step 3: Calculate
Numerator = 150 × 100 = 15000
Denominator = 3960 × 0.80 = 3168
Pshaft = 15000 / 3168 ≈ 4.74 hp
Step 4: Convert to SI
1 hp ≈ 0.746 kW
Pshaft = 4.74 × 0.746 ≈ 3.54 kW
Thus, both formulas give consistent results when converted across unit systems.
Reference Table for Pump Power Calculations
| Parameter | Symbol | Typical Unit | Notes |
|---|---|---|---|
| Flow Rate | Q | US gpm / m³/hr / m³/s | 1 US gpm = 0.0631 L/s = 0.227 m³/hr |
| Total Head | H | ft / m | 1 ft = 0.3048 m |
| Specific Gravity | SG | – (dimensionless) | SG = ρfluid / ρwater (ρwater ≈ 1000 kg/m³) |
| Density of Water | ρ | kg/m³ | ρ ≈ 1000 kg/m³ at 4°C |
| Gravitational Acceleration | g | m/s² | g ≈ 9.81 m/s² |
| Efficiency | η | – (decimal) | Range: 0.5 – 0.9 (50%–90%) |
| Conversion Factor (US) | 3960 | – | Relates gpm × ft × SG → horsepower |
| Power | P | hp / kW | 1 hp = 0.746 kW |
FAQs
What is pump power?
Pump power is the amount of energy a pump needs to move liquid against a certain head.
Why is pump efficiency important?
Efficiency tells you how much of the input power is actually used for pumping. A higher efficiency means less wasted energy.
What is the difference between US and SI formulas?
Both give the same result but use different unit systems. US uses a conversion constant (3960), while SI uses density and gravity directly.
Can I use this calculator for any liquid?
Yes! Just enter the right density or specific gravity for the fluid, and the calculator works for water, oil, chemicals, or any liquid.