Pump Horsepower Calculator
The pump horsepower calculator is used to estimate the pump power, i.e., the power transmitted to the shaft. A pump is one of the most common pieces of hydraulic machinery and is used to move fluid by means of the mechanical action of its impeller. Some of its applications include maintaining the water supply across a city, heating, ventilation and air conditioning (HVAC) systems, hydraulics and pneumatics, and electricity generation.
The pump power is a function of the hydraulic power and the efficiency. Given the importance of this component, it is imperative to understand the basic characteristics of a pump to ensure greater efficiency of the larger processes. You can find more information about pump efficiency and pump power calculations in the paragraphs below.
Types of pump power – shaft and hydraulic power
A pump is a device used to move fluid using mechanical action. The most common components of a pump are the impeller, casing, suction pipe and delivery pipe. The pumping action involves drawing fluid in via the suction end of the pipe and moving it across the body of the pump over to the delivery end of the pipe. To do so, the impeller, which is housed inside the casing, moves either by a rotating or a reciprocating motion, depending on the type of pump. The impeller is connected to the shaft, which is driven by an electric motor.
The pump shaft power (also called brake power) is defined as the power applied to achieve the head and the volumetric flow rate. It is a function of the volumetric flow rate Q, the differential head H, the density of the fluid ρ, the efficiency η, and the gravitational constant g. Mathematically:
Ps = (Q · H · ρ · g) / η
Similarly, the hydraulic power (also called water power) can be estimated as:
Ph = Q · H · ρ · g
The efficiency, therefore, can be rewritten as the ratio of hydraulic power to shaft power:
η = Ph / Ps
where:
- Ps — Shaft (brake) power transmitted to the pump shaft;
- Ph — Hydraulic (water) power imparted to the fluid;
- Q — Volumetric flow rate of the fluid;
- H — Differential (total) head developed by the pump;
- ρ — Density of the pumped fluid (1000 kg/m³ for water);
- g — Gravitational acceleration (9.80665 m/s²); and
- η — Pump efficiency (a value between 0 and 1, or 0–100 %).
How to calculate shaft power?
To calculate the pump shaft power, follow these steps:
- Determine the volumetric flow rate Q of the fluid being pumped.
- Determine the differential head H that the pump must develop.
- Look up the density ρ of the fluid (use 1000 kg/m³ for water, or the specific gravity in the imperial system).
- Estimate the pump efficiency η. Typical centrifugal pumps range between 50 % and 85 %.
- Calculate the hydraulic power: Ph = Q · H · ρ · g.
- Divide by the efficiency to obtain the shaft power: Ps = Ph / η.
Example of using the pump horsepower calculator
Let's calculate the power of a pump that delivers a flow rate of Q = 50 m³/h of water against a head of H = 30 m, with an efficiency of η = 70 %.
- First convert the flow rate to SI units: Q = 50 / 3600 = 0.01389 m³/s.
- Hydraulic power: Ph = 0.01389 · 30 · 1000 · 9.80665 ≈ 4086 W ≈ 4.09 kW (about 5.48 hp).
- Shaft power: Ps = 4086 / 0.70 ≈ 5837 W ≈ 5.84 kW (about 7.83 hp).
So the pump needs a shaft (brake) power of roughly 5.84 kW, while only about 4.09 kW is actually transferred to the water — the rest is lost to inefficiency.
Units & currency
This calculator supports both the metric system (flow rate in m³/h, head in metres, density in kg/m³) and the American / imperial system (flow rate in US gallons per minute, head in feet, density as specific gravity). Whatever system you choose, the results are reported in both kilowatts (kW) and horsepower (hp).
You can also estimate the annual operating cost of running the pump. Just enter the running hours per day, the working days per year and your electricity price, and pick your currency — US dollar, Russian ruble, euro, British pound, Chinese yuan, Indian rupee, Japanese yen or Brazilian real.
FAQs
What is the difference between shaft power and hydraulic power?
Hydraulic power is the useful power actually delivered to the fluid, while shaft power is the (larger) power that must be supplied to the pump shaft by the motor. Their ratio is the pump efficiency.
What is a typical pump efficiency?
Most centrifugal pumps operate between 50 % and 85 % efficiency, depending on size, design and operating point. Larger, well-matched pumps tend to be more efficient.
Why is the motor power higher than the shaft power?
The electric motor itself has its own efficiency and losses, so the electrical power drawn from the grid is always somewhat higher than the mechanical shaft power. A service factor is usually added when selecting the motor.