How it works
Each revolution of a fixed-displacement pump moves its displacement of oil. Multiply by RPM and divide by 231, the cubic inches in a gallon, to get gallons per minute. Internal leakage reduces the delivered flow by the volumetric efficiency.
Hydraulic power out is flow times pressure; with flow in gpm and pressure in psi the constant is 1,714. The engine or motor must supply that power divided by the overall efficiency of the pump.
Worked example
A 0.6 in³/rev pump at 3,400 RPM working at 2,000 psi:
- Theoretical flow = 3,400 RPM × 0.6 in³ ÷ 231 = 8.83 gpm
- Delivered flow = 8.83 × 90% = 7.95 gpm
- Hydraulic power = 7.95 gpm × 2,000 psi ÷ 1,714 = 9.27 hp
- Input power = 9.27 ÷ 85% = 10.91 hp
| Input | Value |
|---|---|
| Pump speed | 3400 RPM |
| Displacement per revolution | 0.6 in³ |
| Working pressure | 2000 psi |
| Volumetric efficiency | 90 % |
| Overall efficiency | 85 % |
| Result | Value |
|---|---|
| Delivered flow | 7.95 gpm |
| Theoretical flow | 8.83 gpm |
| Hydraulic (output) power | 9.27 hp |
| Input power needed at the shaft | 10.91 hp |
Assumptions and limits
- Fixed-displacement pump at steady speed and pressure. Variable pumps and load-sensing systems differ.
- Efficiencies are your inputs; the calculator does not know your pump’s data sheet values.
- Ignores line losses and relief-valve flow. Pressure is the working pressure at the pump.
Common questions
How do I calculate pump flow?
Multiply RPM by displacement per revolution in cubic inches and divide by 231 for gpm.
How much horsepower does a hydraulic pump need?
Multiply gpm by psi and divide by 1,714 for hydraulic horsepower, then divide by overall efficiency for the input power.
Why is the real flow less than the theoretical?
Internal leakage, which rises with pressure and oil temperature. It is described by the volumetric efficiency.
How does this relate to cylinder speed?
Cylinder speed equals flow divided by piston area; see the hydraulic cylinder calculator.
Sources
- Hydraulic horsepower = gpm × psi ÷ 1,714 (Engineering ToolBox, Engineers Edge).
- Pump flow = RPM × displacement ÷ 231 gpm; 231 in³ per US gallon.
- Read them: Engineering ToolBox: Hydraulic pump horsepower
Updated 2026-09-30