Hydraulic Motor Torque Calculator – Theoretical & Actual Torque

Hydraulic Motor Torque Calculator

Calculate hydraulic motor theoretical torque and estimated actual shaft torque from pressure difference, displacement and mechanical efficiency. Free Metric and Imperial calculator with formulas and examples.

T_actual depends on pressure difference Δp, motor displacement V_g and mechanical efficiency η_m.

1. Online Hydraulic Motor Torque Calculator

Select a unit system, enter the pressure difference across the motor, displacement per revolution and mechanical efficiency, then calculate.

Unit systemMetric (bar, cm³/rev, N·m)Imperial (psi, in³/rev, lbf·ft)

Mechanical efficiency η_m (%)

Enter a value greater than 0 and up to 100.

Pressure difference Δp (bar)

Use inlet pressure minus outlet pressure at the motor ports, not pump setting alone.

Motor displacement V_g (cm³/rev)

Theoretical fluid volume per shaft revolution.

Enter the operating values and select Calculate torque.

Theoretical torque T_theoretical

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Estimated actual shaft torque T_actual

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Mechanical efficiency η_m used

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Pressure difference used

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2. What Is Hydraulic Motor Torque?

A hydraulic motor converts hydraulic energy into rotary mechanical output. Torque is the turning moment available at the motor shaft. In a simplified calculation, torque increases when the pressure difference or motor displacement increases.

Mechanical efficiency accounts for internal mechanical losses. This calculator reports theoretical torque T_theoretical and estimated actual shaft torque T_actual after applying the mechanical efficiency η_m entered by the user.

3. Hydraulic Motor Torque Formula

Theoretical torque

T_theoretical = (Δp × V_g) / (2π)

For Metric inputs in MPa and cm³/rev, matching the featured infographic:

T_theoretical (N·m) = Δp (MPa) × V_g (cm³/rev) / (2π)

If pressure is entered in bar, use the equivalent form:

T_theoretical (N·m) = Δp (bar) × V_g (cm³/rev) / 62.8319

Estimated actual shaft torque

T_actual ≈ T_theoretical × η_m

Here, η_m is the mechanical efficiency expressed as a decimal; for example, 90% = 0.90. For Imperial inputs, Δp is in psi and V_g is in in³/rev. The theoretical equation gives torque in lbf·in; the calculator converts the displayed result to lbf·ft.

4. Worked Example — Metric Units

Parameter	Value
Pressure difference, Δp	160 bar
Motor displacement, Vg	100 cm³/rev
Mechanical efficiency, ηm	90% (0.90)

Step 1 — Theoretical torque

T_theoretical = (160 × 100) / 62.8319 = 254.65 N·m

Step 2 — Estimated actual torque

T_actual ≈ 254.65 × 0.90 = 229.18 N·m

This is an estimate under the assumed conditions. Actual performance depends on motor design, speed, temperature, wear and manufacturer data.

5. Worked Example — Imperial Units

Using approximately equivalent values: 2,320.6 psi, 6.1024 in³/rev and 90% mechanical efficiency.

T_theoretical ≈ 187.82 lbf·ft

T_actual ≈ 187.82 × 0.90 ≈ 169.04 lbf·ft

6. How to Interpret the Result

• Higher pressure difference: increases torque if displacement and efficiency stay unchanged.
• Larger displacement: increases torque per revolution, but typically reduces speed for the same flow.
• Lower mechanical efficiency: reduces estimated shaft torque.
• Pressure difference matters: use inlet pressure minus outlet pressure. Do not automatically use the pump pressure setting.

7. Important Engineering Limitations

Engineering note: This calculator gives a theoretical estimate and an efficiency-adjusted estimate. It does not select a motor model or verify continuous, intermittent, peak or starting-torque limits.

Before selecting or operating a motor, check manufacturer data for pressure ratings, speed range, starting torque, case-drain requirements, temperature, duty cycle, shaft and mounting limits, and service life. Dynamic loads, shock loads and return-line back pressure can affect actual performance.

For critical applications, verify calculations against manufacturer data and measurements.

8. Frequently Asked Questions

Does higher pressure always mean more torque?

For the same displacement and efficiency, a higher pressure difference generally produces more torque. The motor's rated limits must still be respected.

What is the difference between theoretical and actual torque?

Theoretical torque assumes ideal conversion. Estimated actual shaft torque applies the entered mechanical efficiency to the theoretical value.

Should I enter pump pressure or motor pressure?

Enter the pressure difference across the motor: inlet pressure minus outlet pressure. It may differ from the pump setting.

Can this result select a commercial motor?

Use it as an initial estimate only. Confirm torque, speed, pressure, flow and duty cycle against the manufacturer's data.

9. Related Hydraulic Calculators

• Hydraulic Cylinder Force Calculator – Push & Pull Force — calculate linear cylinder force.
• Hydraulic Cylinder Bore Size Calculator — estimate the required cylinder bore.
• Hydraulic Cylinder Flow & Speed Calculator — calculate cylinder speed or required flow.

10. Technical Reference

The torque relationship and notation used here follow hydraulic motor sizing equations published in technical catalogues, including Parker's Basic formulas for hydraulic motors. Consult the documentation for the motor being evaluated because efficiency definitions and operating limits can vary by design.

11. Summary

Hydraulic motor torque is primarily determined by pressure difference and displacement per revolution. Mechanical efficiency reduces theoretical torque to an estimated shaft output. Use this calculator for preliminary checks, then verify the result against the motor manufacturer's ratings and real operating conditions.

Scope note: V1 focuses on theoretical torque T_theoretical and estimated actual shaft torque T_actual using mechanical efficiency η_m. It does not automatically recommend standard motor sizes or select a commercial product.