Hydraulic Horsepower Calculator

Calculate hydraulic horsepower from flow (GPM or L/min) and pressure (PSI or bar), plus pump shaft power in hp and kW at a typical 85% efficiency.

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Calculator Functions

Function	What it does	What it requires
Hydraulic power	Finds the hydraulic horsepower a pump delivers to the fluid, and the shaft power needed to drive it	Requires the delivered flow rate and the pump pressure rise
Available flow	Finds the flow a pump can deliver from a known shaft power at a required pressure	Requires the available pump shaft power and the pump pressure rise
Available pressure	Finds the pressure a pump can reach from a known shaft power at a required flow	Requires the available pump shaft power and the delivered flow rate

Flow goes in as US gpm, L/min or m³/s, pressure as psi, bar, kPa or MPa, and shaft power as hp or kW. Optional settings holds the overall pump efficiency, which is 85% unless changed, and Hydraulic power also takes a sizing margin. Every result lists hydraulic power in kW, pump shaft power and the estimated pump loss as heat.

Hydraulic Horsepower Formulas

The 1714 is a unit conversion, not a property of the pump. One US gallon is 231 cubic inches and one horsepower is 33,000 ft·lbf per minute [2], which makes the exact divisor 12,000 ÷ 7, or 1,714.2857. The calculator uses the exact value. In metric units the same relationship is kW = bar × L/min ÷ 600.

Hydraulic power

A pump delivering 10 US gpm at a 2,000 psi rise puts 2,000 × 10 ÷ 1,714.2857 = 11.67 hp into the fluid, and 32 US gpm at 71 psi is 1.33 hp. The shaft has to supply more than that, because the pump is not perfectly efficient:

η is the overall pump efficiency as a decimal. At the 85% default, 11.67 hp of hydraulic power needs 13.73 hp at the shaft, and the 2.06 hp difference is the estimated pump loss. A sizing margin multiplies the shaft power, so 20% raises 13.73 hp to 16.47 hp, and the result names the next size up in a list of common motor ratings.

Available flow

This is the main formula solved for flow, with the shaft power first reduced by the pump efficiency. A 10 hp shaft at 85% and 2,000 psi supports 1,714.2857 × 10 × 0.85 ÷ 2,000 = 7.29 US gpm.

Available pressure

The same rearrangement gives pressure. A 10 hp shaft at 85% moving 5 US gpm can reach 1,714.2857 × 10 × 0.85 ÷ 5 = 2,914 psi.

Limits of This Estimate

• The 85% efficiency is a typical figure, not a rating. Real pumps vary with type, speed, pressure, fluid viscosity and wear, so use the maker’s figure when it is known.
• Shaft power is what the pump needs from its driver. Losses inside an electric motor or engine are not included, and neither are losses in valves, hoses and actuators.
• Pressure means the rise across the pump and flow means the delivered flow. Both must stay inside the pump’s ratings.
• The motor size shown is the next value in an example list. It is not a motor selection, which also depends on starting torque, duty and service conditions.

Sources