Pump & liquid
Running cost (optional)
Load factor is the average share of full load the pump runs at over the hours given.
How it's calculated
P_h = ρ × g × Q × HP_h = Q × ΔpH = Δp / (ρ × g)P_shaft = P_h / η_pumpP_in = P_shaft / η_motorP_motor ≥ P_shaft × (1 + margin)E = P_in × hours × load factorhp = H(ft) × Q(gpm) × s.g. / 3960ρ is the density of the liquid in kg/m³, g is 9.80665 m/s², Q is the flow in m³/s and H is the total head in metres of liquid. The result is in watts. The hydraulic power is the useful power the liquid receives. The pump needs more at its shaft, because its efficiency is below 100%, and the motor draws more again from the supply, because it too is not perfectly efficient. The total head is the head the pump has to produce: the height the liquid is lifted, the pressure it has to be delivered at, the friction losses in the pipes and fittings, and the velocity head. If you know the pressure rise across the pump instead, the calculator turns it into a head with the density you chose, and the power comes out the same. For the motor, the shaft power is increased by the margin and the next size up in the list is suggested. In imperial units, with water, the same calculation is hp = H × Q × s.g. / 3960, with H in feet and Q in US gallons per minute.
Worked examples
| Case | Working | Result |
|---|---|---|
| 10 L/s of fresh water lifted to 20 m total head | 998.2 × 9.80665 × 0.010 × 20 | 1.958 kW hydraulic |
| Pump efficiency 70% | 1.958 / 0.70 | 2.797 kW at the shaft |
| Motor efficiency 90% | 2.797 / 0.90 | 3.108 kW from the supply |
| Motor to fit, with a 10% margin | 2.797 × 1.10 = 3.077 kW | 4 kW, the next common size |
| The same flow given as 196 kPa across the pump | H = 196 000 / (998.2 × 9.80665) | 20.02 m, 1.96 kW hydraulic |
| Running 4000 h a year at 0.15 per kWh | 3.108 kW × 4000 h = 12 430 kWh | about 1865 a year |
| 100 gpm at 100 ft of head, water | 100 × 100 / 3960 | 2.52 hp hydraulic |
Assumptions
- The head you enter is the total dynamic head, with the pipe friction already included. This calculator does not work out friction losses.
- The liquid is incompressible at the density you choose. Fresh water is taken as 998.2 kg/m³ at 20 °C, and seawater as 1025 kg/m³, a typical value: it varies with temperature and salinity. Use the custom option for anything else.
- The efficiencies are typical starting values and are editable. Pump efficiencies range widely, from about 35% to over 90% depending on the design and on where on its curve the pump runs. For real work, read it from the pump curve.
- The efficiency of a pump changes with flow, so one figure is an estimate of the duty point only.
- The margin is an allowance you choose. It is not a standard. Check what your specification or supplier requires.
- Motor sizes in kW are common sizes, not taken from a standard, so check your supplier's range. The hp list is the set of ratings in the US motor efficiency regulation (10 CFR 431.25).
- Viscous liquids, slurries, NPSH, system and pump curves, variable speed drives and several pumps working together are not covered.
- The running cost uses a single price per kWh and ignores demand charges. The cost is in whatever currency you used for the price.
Frequently asked questions
How do I calculate pump power?
Multiply the density of the liquid, g (9.80665), the flow in m³/s and the total head in metres. That gives the hydraulic power in watts. Divide by the pump efficiency to get the power at the shaft, and by the motor efficiency to get what the motor draws from the supply.
What is the difference between hydraulic, shaft and motor power?
Hydraulic power is the useful power delivered to the liquid. Shaft power is what the pump takes from the motor shaft, which is more because the pump is not perfectly efficient. Motor input power is what the motor takes from the electrical supply, which is more again because the motor loses some as heat. Your electricity bill follows the motor input. To turn the motor input into a supply current, use the power calculator.
How much power does it take to pump water to a height?
For fresh water, lifting 1 m³ each hour through 10 m needs about 27 W of hydraulic power (998.2 × 9.80665 × (1/3600) × 10). Divide by the efficiencies of the pump and motor to get the electrical power. A long pipe adds friction head to the lift, which raises the figure.
How do I convert kW to hp for a pump?
One mechanical horsepower is 745.7 W, so divide kW by 0.7457 to get hp. The results show both. In US units, the hydraulic horsepower of a water pump is the head in feet times the flow in gpm divided by 3960.
What is total dynamic head?
The total head the pump must add to the liquid. It is the sum of the static lift between the suction and the discharge levels, any pressure difference between the two ends, the friction loss in the pipes and fittings, and the velocity head. A pump curve plots the head a pump gives at each flow.
What is a typical pump efficiency?
It depends on the pump type and size. Efficiencies run from about 35% to over 90%, with large pumps running at their best efficiency point at the high end and small pumps at the low end. The default here is 70%, and a pump curve gives a better figure for your pump.
How do I estimate the running cost of a pump?
Multiply the motor input power in kW by the hours it runs in a year, by the load factor if it does not run at full load, and by the price per kWh. Open "Running cost" and enter the hours and the price to see it.
Standards and references
- Free to read: Improving Pumping System Performance: A Sourcebook for Industry (US Department of Energy), for the fluid power equation, efficiency and running cost method.
- Free to read: standard acceleration of gravity (NIST), exactly 9.80665 m/s².
- Free to read: 10 CFR 431.25, the US electric motor efficiency tables, for the list of motor horsepower ratings.
- Pump performance tests are defined in standards such as ISO 9906, which this calculator does not use. Check pump data against the supplier's tested curve.
This calculator estimates pump and motor power. It does not size a pumping system, check suction conditions or select a pump. Have the design checked by a qualified engineer.