Actual flow
-Hydraulic power
-Input shaft power
-Input shaft torque
-All results
| Theoretical flow (no leakage) | - |
| Internal leakage flow | - |
| Theoretical torque (no friction loss) | - |
| Mechanical-hydraulic efficiency (overall / volumetric) | - |
| Power lost as heat in the pump | - |
| Displacement needed for the required flow | - |
Method and formulas
Standard positive-displacement pump relations, so every figure can be checked by hand.
| Quantity | Metric (cm³/rev, rpm, bar) | US (in³/rev, rpm, psi) |
|---|---|---|
| Theoretical flow | Qth = D n / 1000 (L/min) | Qth = D n / 231 (gpm) |
| Actual flow | Q = Qth ηv | same |
| Hydraulic power | Ph = Q p / 600 (kW) | Ph = Q p / 1714 (hp) |
| Input shaft power | Pin = Ph / ηo | same |
| Input torque | T = 9549 Pin / n (N·m) | T = 5252 Pin / n (lbf·ft) |
| Theoretical torque | Tth = D p / (20π) (N·m) | Tth = D p / (24π) (lbf·ft) |
| Displacement for a flow | D = 1000 Q / (n ηv) | D = 231 Q / (n ηv) |
The calculator works in SI internally and converts: 1 in³ = 16.387 cm³, 1 gpm = 3.7854 L/min, 1 psi = 0.068948 bar, 1 hp = 0.7457 kW. Efficiencies are for the stated operating point: they change with speed, pressure and oil temperature.
Worked example: 45 cm³/rev at 1500 rpm and 200 bar
With ηv = 95 % and ηo = 87 %: Qth = 45 × 1500 / 1000 = 67.5 L/min, so Q = 67.5 × 0.95 = 64.125 L/min. Ph = 64.125 × 200 / 600 = 21.375 kW and Pin = 21.375 / 0.87 = 24.57 kW. T = 9549 × 24.57 / 1500 = 156.4 N·m, against a theoretical 143.2 N·m. About 3.19 kW of the input power ends up as heat. A required flow of 60 L/min at this speed needs a displacement of 42.1 cm³/rev.
Questions
How do you calculate hydraulic pump flow?
Theoretical flow is displacement times speed: Q = D n / 1000 in L/min with D in cm3/rev and n in rpm (or Q = D n / 231 in gpm with D in in3/rev). Actual flow is lower by the volumetric efficiency, Q = D n eta_v / 1000, because some oil leaks internally from the high-pressure side to the low-pressure side.
How do you calculate hydraulic power?
Hydraulic power is flow times pressure: P = Q p / 600 in kW with Q in L/min and p in bar, or P = Q p / 1714 in hp with Q in gpm and p in psi. This is the power delivered to the fluid, so the motor must supply more by the overall efficiency: P_in = P_hyd / eta_o.
How do you find the motor torque needed for a hydraulic pump?
Shaft torque is T = P_in x 9549 / n in N-m with P_in in kW and n in rpm (T = hp x 5252 / n in lbf-ft). The theoretical torque is T = D p / (20 pi) in N-m with D in cm3/rev and p in bar, and the actual torque is larger by the mechanical-hydraulic efficiency.
What are typical pump efficiencies?
Gear pumps usually reach 80 to 90 percent overall, vane pumps 75 to 90 percent, and axial piston pumps 85 to 95 percent at rated conditions, falling at low speed, very high pressure, hot thin oil or worn clearances. The overall efficiency equals volumetric efficiency times mechanical-hydraulic efficiency, so it can never exceed the volumetric figure. Use your manufacturer's data.
What displacement do I need for a given flow?
Rearrange the flow equation: D = 1000 Q / (n eta_v) in cm3/rev. For 60 L/min at 1500 rpm and 95 percent volumetric efficiency that is 42.1 cm3/rev, so you would choose the next standard size up and check the pressure rating.
Where does the lost power go?
Into heat in the oil: P_loss = P_in - P_hyd. At 87 percent overall efficiency, 13 percent of the input power heats the fluid, which sets the cooler and reservoir size together with the losses in valves and pipework. This page covers the pump only.
What does this calculator not cover?
Pump variable-displacement control, relief and pressure-compensator losses, pipework and valve pressure drops, fluid viscosity effects, cavitation and suction limits, and pump noise. It is a first-pass sizing aid: verify against the manufacturer's data.
Engineering aid for guidance. It uses constant efficiencies and ignores control, pipework, cavitation and thermal effects. Hydraulic systems store dangerous energy: verify critical designs against manufacturer data and applicable safety rules.