In short: multiply flow rate by head by water density and gravity to get hydraulic power, then divide by pump efficiency for the brake horsepower the motor must supply. Moving 50 US gpm against 100 ft of head at 70% pump efficiency needs about 1.26 hydraulic HP (0.94 kW) and, after losses, about 1.80 brake HP (1.34 kW) at the shaft — use the calculator above for your own numbers.
These figures are planning aids based on published engineering formulas. For a final motor or pump purchase, confirm the selection against the manufacturer's curve and a licensed engineer.
How to calculate pump power
Pumping water takes power because you are lifting and pushing mass against gravity and friction. The starting point is hydraulic power — the power actually delivered to the water — which depends only on how much water you move, how high and how forcefully you move it, and how dense the water is:
No real pump is perfectly efficient — friction, turbulence and internal leakage all consume some of the shaft's work before it reaches the water. So the motor must actually supply more than the hydraulic figure: the brake horsepower, found by dividing hydraulic power by pump efficiency. If you also want the electrical power drawn from the wall, divide brake horsepower again by the motor's own efficiency.
Worked example. Take 50 US gpm against 100 ft of head, with a 70% efficient pump. First convert: 50 gpm is 0.0031545 m³/s, and 100 ft is 30.48 m. Fresh water at 20 °C has a density of 998.2 kg/m³. Hydraulic power = 998.2 × 9.80665 × 0.0031545 × 30.48 ≈ 941 W, or 1.26 HP. Divide by 70% efficiency: 941 ÷ 0.70 ≈ 1,345 W, or about 1.80 brake horsepower — the number your motor nameplate needs to meet or exceed.
The classic US shortcut. In the water-supply trade, the same result is often found with WHP = (GPM × ft of head) ÷ 3,960 for hydraulic horsepower, then BHP = WHP ÷ efficiency. The constant 3,960 bakes in water's standard density and the definition of a horsepower, so it gives the same answer as the density-based formula above for fresh water near room temperature.
Why pump and motor efficiency change the answer
Efficiency sits in the denominator of the power equation, so it has an outsized effect. A pump at 50% efficiency needs nearly twice the brake horsepower of one at 100% efficiency moving the identical flow and head — because half the shaft's work is lost to internal friction and recirculation rather than reaching the water. Small, single-stage jet pumps typically run 40–55% efficient; well-selected centrifugal pumps run 65–80%; large, well-matched industrial pumps can reach 85% or more.
Motor efficiency is a separate loss stage, downstream of the pump. It only affects the electrical power drawn from the wall — the mechanical brake horsepower the pump shaft needs is unchanged by what kind of motor drives it. Standard motors run 80–88% efficient; NEMA Premium and IE3/IE4-class motors reach 90–96%. Multiplying pump efficiency by motor efficiency gives the overall "wire-to-water" efficiency, shown in the results above, which is the figure utilities and energy audits care about most.
Brake horsepower by flow and head
Required brake horsepower for common combinations of flow and head, assuming fresh water at 20 °C and 70% pump efficiency. Every value matches the calculator above at these inputs.
| Flow (US GPM) | 50 ft head | 100 ft head | 200 ft head |
|---|---|---|---|
| 25 gpm | 0.45 HP | 0.90 HP | 1.80 HP |
| 50 gpm | 0.90 HP | 1.80 HP | 3.61 HP |
| 100 gpm | 1.80 HP | 3.61 HP | 7.22 HP |
| 200 gpm | 3.61 HP | 7.22 HP | 14.43 HP |
Worked examples
Sizing a deep-well pump
1.24 HP
15 gpm against 180 ft of head with a 55%-efficient submersible pump needs about 1.24 brake HP — round up to a standard 1.5 HP motor with margin to spare.
A home hydronic circulator
85 W
12 gpm against only 15 ft of head, at a typical 40% circulator efficiency, needs just 0.11 HP — about 85 watts, in line with common small circulator pumps.
An irrigation booster pump
4.66 HP
100 gpm against 120 ft of head with a 65%-efficient centrifugal pump needs about 4.66 brake HP — this would typically be rounded up to a 5 HP motor.
What else affects the result
Service factor and standard motor sizes. Motors come in discrete standard sizes (1, 1.5, 2, 3, 5, 7.5, 10 HP and so on). Add a 10–15% margin above the calculated brake horsepower before rounding up, to cover operating-point shifts, voltage sag and periodic overload.
Fluid viscosity and specific gravity. This calculator assumes water. Thicker or denser fluids need proportionally more power — use the density override in the advanced options if you are pumping brine, a sugar solution or another liquid with a known density.
Variable-speed operation. If the pump runs on a variable-frequency drive rather than at a fixed speed, power scales with the cube of speed. See the Pump Affinity Laws Calculator to estimate power at a different speed, and the Pump Energy Cost Calculator to turn input power into an electricity bill.
Available net positive suction head (NPSH). Power sizing assumes the pump can actually achieve the flow and head you entered. If suction conditions are marginal, check the NPSH Calculator to confirm the pump won't cavitate.
Frequently asked questions
How do I calculate the horsepower needed for a water pump?
Multiply the flow rate by the total head by the density of water and gravity to get hydraulic power, then divide by the pump's efficiency to get brake horsepower — the power the motor must deliver at the shaft. In US units, a shortcut is horsepower = (GPM × feet of head) / (3,960 × pump efficiency).
What is the difference between hydraulic power and brake horsepower?
Hydraulic power (also called water horsepower) is the power actually transferred to the water. Brake horsepower is the power the motor shaft must supply to the pump, which is always higher because no pump is 100% efficient — some energy is lost to friction, turbulence and internal leakage.
How does pump efficiency affect the motor size I need?
Lower efficiency means more brake horsepower is needed to move the same amount of water. A pump that is only 50% efficient needs almost twice the shaft power of one that is 100% efficient for the identical flow and head, so efficiency has a direct, proportional effect on motor size.
Do I need to size the motor exactly to the calculated brake horsepower?
No. It is standard practice to add a service factor, typically 10 to 15 percent, above the calculated brake horsepower before rounding up to the next standard motor size (such as 1, 1.5, 2, 3, 5 or 7.5 HP). This protects the motor against operating-point shifts and periodic overload.
Does water temperature change the power a pump needs?
Slightly. Warmer water is a little less dense, so it takes marginally less power to move the same volume. Between 4 °C and 100 °C the difference is only about 4%, which rarely changes a motor size selection but matters for precise engineering calculations.
What is the difference between brake horsepower and motor input power?
Brake horsepower is the mechanical power delivered to the pump shaft. Motor input power is the electrical power drawn from the wall, which is higher still because electric motors also have losses. Motor input power equals brake horsepower divided by the motor's own efficiency.
Sources & references
- Hydraulic Institute. ANSI/HI Standards for Rotodynamic (Centrifugal) Pumps — Nomenclature, Definitions, Application, and Test Standards.
- Karassik, I. J., Messina, J. P., Cooper, P., & Heald, C. C. (2008). Pump Handbook (4th ed.). McGraw-Hill.
- Kell, G. S. (1975). Density, thermal expansivity, and compressibility of liquid water from 0° to 150 °C. Journal of Chemical & Engineering Data, 20(1), 97–105.
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)