July 2025 8 min read
Hydraulic Motor Torque Calculator
Calculate the theoretical and actual torque output of a hydraulic motor from displacement, pressure drop, and mechanical efficiency. Essential for rotary actuator sizing and drive system design.
Enter Your Values
Displacement
cm³/rev
Pressure Drop (Δp)
bar
Mechanical Efficiency
%
Hydraulic Motor Torque Formulas
Torque is proportional to displacement and pressure differential, reduced by mechanical efficiency.
T (Nm) = V × Δp × η_m / (20π)
Alternative Form
T (lb-ft) = V × Δp × η_m / (24π)
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| T | Torque | Nm | Output torque at the motor shaft |
| V | Displacement | cm³/rev | Volume displaced per revolution of the motor |
| Δp | Pressure Differential | bar | Pressure drop across the motor (inlet minus outlet) |
| η_m | Mechanical Efficiency | % | Efficiency of converting hydraulic pressure to torque |
Explanation
The 20π constant: 1 bar = 100,000 Pa, V in cm³/rev = V×10^-6 m³/rev, T = Δp×V/(2π) in Nm. T = 100000 × V×10^-6 / (2π) = V/(20π) Nm per bar.
Derivation
T(Nm) = Δp(Pa) × V(m³/rev) / (2π). Δp(bar) = Δp × 100000 Pa. V(cm³/rev) = V × 10^-6 m³/rev. T = (Δp×100000) × (V×10^-6) / (2π) × η_m = V × Δp × η_m / (20π).
Step-by-Step Calculation
Follow each step to understand how the result is calculated from your inputs.
Step 1
Calculate theoretical torque.
T_th = V × Δp / (20π)
Displacement:50 cm³/rev
Δp:200 bar
Intermediate: 50 × 200 / (20π)
Result: 159.15 Nm
Step 2
Apply mechanical efficiency for actual torque.
T_act = T_th × η_m / 100
Theoretical Torque:159.15 Nm
Efficiency:92%
Intermediate: 159.15 × 0.92
Result: 146.42 Nm
Final Answer
146.42 Nm (108.0 lb-ft)
Worked Examples
See how the calculator works with different scenarios.
Scenario
Orbital motor: 50 cm³/rev, 200 bar Δp, 92% mechanical efficiency.
Inputs
Displacement:50 cm³/rev
Δp:200 bar
Efficiency:92%
Calculation
T_th = 50×200/(20π) = 159.15 Nm. T_act = 159.15×0.92 = 146.42 Nm
Result
146.4 Nm
Interpretation
Suitable for medium-duty applications like conveyor drives.
Understanding Hydraulic Motor Torque
Hydraulic motors convert fluid power into rotary mechanical power. Torque is the rotational force available at the output shaft. Unlike electric motors, hydraulic motors can deliver maximum torque at zero speed — a key advantage for starting heavy loads.
Torque vs Speed Trade-off
For a fixed hydraulic power input, torque and speed are inversely related. A large-displacement motor delivers high torque at low speed. A small-displacement motor delivers low torque at high speed. Variable displacement motors allow adjusting this trade-off during operation.
Practical Tips
- •Hydraulic motors deliver maximum torque at zero speed (starting torque), typically 85-95% of running torque.
- •Motor displacement determines torque: larger displacement = higher torque at the same pressure.
- •Back pressure on the motor outlet reduces effective Δp. Account for it: Δp = Inlet_pressure - Outlet_pressure.
- •For variable displacement motors, torque is proportional to displacement setting. Reduce displacement for higher speed, lower torque.
- •Use pressure drop across the motor (not system pressure) for accurate torque calculation.
Common Mistakes
Using system pressure instead of pressure drop across the motor
Δp = Motor_Inlet_Pressure - Motor_Outlet_Pressure. Return line back pressure can be 5-30 bar. Using system pressure overestimates torque by 10-20%.
Confusing mechanical and overall efficiency
Mechanical efficiency relates to torque. Overall efficiency = η_mech × η_vol. Use η_mech for torque calculations and η_overall for power calculations.
Ignoring starting torque limitations
Motors produce less torque at start (typically 85-95% of running torque). If the load requires high breakaway torque, oversize the motor by 10-20%.
Assumptions
This calculator makes the following assumptions to provide estimates:
Constant Δp: Assumes constant pressure drop during operation. In reality, Δp varies with load and speed. Use the maximum expected Δp for conservative sizing.
No Internal Leakage Effect: Internal leakage (slip) does not affect steady-state torque but reduces speed. Very high leakage can reduce effective pressure drop at the motor.
Limitations
Be aware of these limitations when using this calculator:
No Dynamic Torque: Acceleration torque requirements during speed changes are not modeled. Inertial loads may require 1.5-2× the steady-state torque.
No Speed-Torque Curve: Motor torque typically decreases at very high speeds due to pressure drop in internal passages. Not modeled in this calculator.
Related Calculators
Educational Guides
Glossary
Technical terms used in mortgage calculations explained in plain language.
- Displacement
- Volume of fluid required for one revolution of the motor output shaft, typically in cm³/rev or in³/rev.
- Starting Torque
- Torque available at zero speed. Lower than running torque due to static friction and internal leakage.
- Pressure Drop (Δp)
- The difference between inlet and outlet pressure of the motor. Determines the actual torque-producing pressure.
- Gerotor
- A type of hydraulic motor using an inner and outer rotor, common in low-speed high-torque applications.
Authoritative References
Frequently Asked Questions
Answers to common questions about this calculator.
How do you calculate hydraulic motor torque?
T (Nm) = V (cm³/rev) × Δp (bar) × η_m / (20π). The theoretical torque is V × Δp / (20π), then multiply by mechanical efficiency.
What is the difference between theoretical and actual motor torque?
Theoretical torque assumes 100% mechanical efficiency. Actual torque is lower due to friction in bearings, seals, and internal contacts.
Why is starting torque lower than running torque?
Static friction (stiction) is higher than dynamic friction. Internal leakage at low speed also reduces effective pressure. Typical starting torque: 85-95% of running torque.
How does motor displacement affect torque?
Torque is directly proportional to displacement. Doubling displacement doubles torque at the same pressure. This is the primary method for increasing motor torque.
How does pressure affect torque?
Torque is linearly proportional to pressure differential (Δp). Doubling Δp doubles torque, within the motor's maximum pressure rating.
What is a typical mechanical efficiency for hydraulic motors?
Gerotor/geroller: 80-90%. Axial piston: 92-97%. Radial piston: 90-95%. Vane: 85-92%. Gear: 80-88%.
What is the formula for torque in US customary units?
T (lb-in) = V (in³/rev) × Δp (psi) × η_m / (2π). Or T (lb-ft) = V × Δp × η_m / (24π).
How do I calculate the required motor displacement for a given torque?
V = T_act × 20π / (Δp × η_m). Select the next standard displacement above the calculated value for safety margin.
What is the effect of back pressure on motor torque?
Back pressure reduces effective Δp. If inlet = 250 bar and outlet = 20 bar, Δp = 230 bar — a 8% torque reduction from ignoring back pressure.
How does motor speed affect torque?
Ideal constant-torque behavior: torque is independent of speed. In practice, torque drops 5-10% at maximum speed due to internal flow restrictions.
What is the torque output range for common hydraulic motors?
Small gerotors: 10-100 Nm. Medium axial piston: 100-800 Nm. Large radial piston: 1000-10000+ Nm. The largest can develop over 50,000 Nm.
How do I account for gearbox losses when using a motor?
Output torque = Motor_torque × gear_ratio × gearbox_efficiency. Gearbox efficiency: planetary 95-98%, worm 70-90%, helical 94-97%.
What is the relationship between torque and hydraulic power?
Power (kW) = T (Nm) × RPM / 9550. Hydraulic power = Δp × Q / 600. These must match (accounting for losses) for consistent system design.
Can a hydraulic motor produce more torque than its rating?
Briefly, yes — at the risk of damage. Continuous operation above rated torque causes overheating and accelerated wear. Use pressure relief to protect the motor.
How do parallel motors affect total torque?
Two identical motors on the same shaft double torque at the same pressure. In independent circuits, each motor contributes its own torque to separate loads.
What is the difference between high-speed and low-speed high-torque motors?
High-speed (axial piston): 500-4000 RPM, lower torque. Low-speed high-torque (radial piston): 0-500 RPM, very high torque. Choose based on speed requirement without a gearbox.
How does oil viscosity affect motor torque?
Thicker oil increases viscous friction, slightly reducing mechanical efficiency and torque. Thinner oil increases internal leakage, reducing effective pressure at low speeds.
What is the torque ripple of a hydraulic motor?
Torque ripple is the variation in instantaneous torque during rotation. Piston motors have ripple of 2-5%. Gerotors: 5-10%. Gear motors: 10-15%. Lower is smoother.
How do I measure actual motor torque?
Use a torque transducer (strain gauge or rotary transformer) on the motor shaft. Alternatively, measure motor power and speed: T = P × 9550 / RPM.
What is the effect of motor wear on torque?
Wear increases internal clearances, increasing leakage and reducing effective Δp at the motor. Torque output decreases by 5-15% over the motor lifetime.
How do I select a motor for a winch application?
Calculate required torque from load and drum radius: T = Load × Drum_radius. Add 25% safety factor for acceleration and friction. Select motor displacement accordingly.
What is the stall torque of a hydraulic motor?
Stall torque is the torque at zero RPM at rated Δp. It is typically 85-95% of running torque at the same pressure. Critical for starting heavy loads.
How does inlet pressure affect motor torque?
Higher inlet pressure increases Δp (assuming constant outlet pressure), proportionally increasing torque. Ensure inlet pressure does not exceed the motor's maximum rating.
What is the role of case drain in motor torque?
Case drain returns internal leakage to the reservoir. A blocked case drain causes pressure buildup in the housing, reducing torque and potentially damaging shaft seals.
How do cross-port relief valves protect motor torque?
Cross-port reliefs limit peak pressure during overrunning load conditions. They protect the motor from torque spikes that could damage the shaft or mounting.
What is the effect of speed on volumetric efficiency in motors?
Volumetric efficiency improves at higher speeds (less time for internal leakage). A motor with 90% η_v at 100 RPM might achieve 97% at 1000 RPM.
How do I calculate the torque for a brake motor?
Brake torque = spring-applied brake force × friction radius × number of friction surfaces. Ensure brake holding torque exceeds maximum load torque by 1.5× safety factor.
What is the torque output of a typical wheel motor?
Wheel motors for mobile equipment: 500-3000 Nm for skid-steer loaders, 3000-8000 Nm for large wheel loaders. Torque depends on vehicle weight and gradeability requirement.
How does temperature affect motor torque?
Cold oil (high viscosity): increases friction, reducing mechanical efficiency by 5-10% until warm. Hot oil (low viscosity): increases internal leakage, reducing low-speed torque.
What is the efficiency of a motor at partial displacement?
Variable motors at reduced displacement have lower efficiency. At 50% displacement, mechanical efficiency drops 10-15% because friction losses remain nearly constant.