Hydraulic Motor Selection Calculator
Calculate hydraulic motor displacement, flow, torque, and power from speed and load requirements.
About this calculator
Given the torque and speed you need at the motor shaft, this calculator works backward through the standard hydraulic motor equations to find the smallest catalog-standard displacement that will do the job, then reports what that real motor will actually deliver. It first solves torque (ft·lb) = displacement (in³/rev) × ΔP × mechanical efficiency / (2π × 12) for displacement, using the pressure differential across the motor (supply pressure minus your specified back pressure) and your assumed mechanical efficiency — the fraction of theoretical torque a real motor's internal friction actually delivers. That exact number is then rounded up to the next size in a list of common gear/gerotor motor displacements (0.5 through 40 in³/rev), because you buy motors in fixed sizes, not exact-fit custom ones. With a real displacement selected, the calculator recomputes actual torque and — using the GPM = RPM × displacement / (231 × volumetric efficiency) relationship — the flow needed to hit your target speed, accounting for the leakage losses volumetric efficiency represents.
If you tell it your pump's available flow is less than that, it recalculates the actual achievable RPM instead of overstating performance. Output and input horsepower (from torque×RPM/5252 and PSI×GPM/1714 respectively) combine into an overall efficiency figure, and drain (case leakage) flow is reported separately. Because mechanical and volumetric efficiency are user-supplied estimates rather than measured values, results are only as accurate as the efficiency figures you enter — real motors vary meaningfully by manufacturer and wear state.
Inputs
Results
Motor displacement (in³/rev)
5
How to Use This Calculator
- Enter Required torque (ft·lb), Required speed (RPM), and System pressure (PSI).
- Set Back pressure (PSI), Mechanical efficiency, and Volumetric efficiency.
- Adjust Available flow (GPM, 0=unlimited) as needed.
- Review the Motor displacement (in³/rev) result.
- Use Calculated displacement (in³/rev) and Required flow (GPM) to inform your decision.
How the result changes with Required torque (ft·lb)
| Required torque (ft·lb) | Motor displacement (in³/rev) |
|---|---|
| 75 | 3 |
| 113 | 4 |
| 225 | 8 |
| 375 | 12 |
What each input means
- Required torque (ft·lb)
- Continuous output torque needed at the motor shaft.
- Required speed (RPM)
- Desired motor output shaft speed.
- System pressure (PSI)
- Pump supply pressure available at the motor inlet.
- Back pressure (PSI)
- Pressure at the motor outlet (return line back pressure).
- Mechanical efficiency
- Motor mechanical (torque) efficiency (85-95% typical).
- Volumetric efficiency
- Motor volumetric (speed) efficiency (88-97% typical).
- Available flow (GPM, 0=unlimited)
- If pump flow is limited, enter available GPM (0 = no limit).
What each result means
- Motor displacement (in³/rev)
- Next standard motor displacement meeting torque requirement.
- Calculated displacement (in³/rev)
- Exact displacement needed from torque and pressure.
- Required flow (GPM)
- Flow needed to achieve desired RPM with the selected motor.
- Actual torque (ft·lb)
- Output torque with the selected motor displacement.
- Actual speed (RPM)
- Shaft speed (may be lower if flow is limited).
- Output power (HP)
- Mechanical power at the motor shaft.
- Input power (HP)
- Hydraulic power consumed (PSI × GPM / 1714).
- Overall efficiency (%)
- Mechanical × volumetric efficiency.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersRequired torque (ft·lb) = 150, Required speed (RPM) = 500, System pressure (PSI) = 3000, Back pressure (PSI) = 100 = 7 input(s) provided
- Calculate Motor displacementMotor displacement5 = 5
- Calculate Calculated displacementCalculated displacement = (requiredTorqueFtLb * 2 * π * 12) / (deltaPsi * mechEff)4.33 = 4.33
- Calculate Required flowRequired flow = (requiredRpm * selectedDisplacement) / (231 * volEff)11.76 = 11.76
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does the calculator round displacement up to a standard size instead of using the exact value?
The exact displacement solved from torque = displacement × ΔP × mechanical efficiency / (2π × 12) is almost never a size a manufacturer actually stocks, so the calculator picks the next value at or above that exact figure from a list of common gear/gerotor displacements (0.5 through 40 in³/rev). Rounding up rather than down guarantees the selected motor can meet or exceed your torque requirement, never fall short of it.
What happens if I enter an available flow that's lower than the flow the motor needs?
When available flow is set above zero and is less than the required flow for your target RPM, the calculator switches from reporting your requested speed to computing the actual RPM the motor will turn using RPM = (available GPM × 231 × volumetric efficiency) / selected displacement. This keeps the output honest about a flow-starved circuit instead of showing a speed the pump can't actually supply.
Why do I need to enter both mechanical and volumetric efficiency separately?
Mechanical efficiency governs how much of the theoretical torque from pressure and displacement is actually delivered at the shaft, since internal friction eats some of it — it's used in the torque equation. Volumetric efficiency governs how much of the theoretical flow-based speed you actually get, since internal leakage (case drain) reduces effective displacement — it's used in the speed and drain-flow equations. A motor can be strong on one axis and weak on the other, so the calculator keeps them independent.
What is drain flow and why does it matter for motor selection?
Drain flow is the portion of flow that leaks internally past the motor's rotating group instead of doing work — the calculator computes it as actual flow × (1 − volumetric efficiency). It has to be routed back to the reservoir through a case drain line, and its magnitude tells you how much of your pump's output is being lost to internal slippage rather than converted into shaft speed.
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