Hydraulic Motor Torque Calculator

Reviewed By: Patrick Myers (BSME)

Enter the pressure (psi) and the displacement (in^3) into the calculator to determine the Hydraulic Motor Torque.

Hydraulic Motor Torque Formula

Hydraulic motor torque is the twisting force generated when hydraulic pressure acts through a motor’s displacement. This calculator estimates the theoretical torque produced by a hydraulic motor from the pressure applied across the motor and the motor displacement.

T = \frac{P \times D}{2\pi}

T = hydraulic motor torque
P = pressure differential across the motor
D = motor displacement per revolution

This relationship is linear, which means torque increases directly as either pressure or displacement increases. If the pressure doubles, torque doubles. If the displacement doubles, torque also doubles.

Variable Definitions

Input / Output	Description	Common Units	Important Note
Pressure	The effective pressure acting across the motor	psi, bar, kPa, atm	Use operating pressure difference, not just pump nameplate pressure
Displacement	Fluid volume required for one revolution of the motor	in³/rev, cm³/rev, m³/rev	Use motor displacement, not system flow rate
Torque	Rotational output force	lb-in, N·m	lb-in can be converted to lb-ft when needed

How the Calculation Works

A hydraulic motor converts fluid energy into rotational mechanical energy. Pressure provides the force potential, and displacement determines how much fluid is converted into motion during each revolution. The formula divides the work done per revolution by the angular distance of one full turn to obtain torque.

In practical terms:

Higher pressure produces more torque from the same motor.
Larger displacement produces more torque at the same pressure.
For a given flow rate, larger displacement motors generally produce more torque and rotate more slowly.

Rearranged Forms

If you know any two values, the same relationship can be rearranged to solve for the third:

P = \frac{2\pi T}{D}

D = \frac{2\pi T}{P}

This is useful when sizing a motor for a required torque or estimating the pressure needed to achieve a target output.

Ideal Torque vs. Actual Shaft Torque

The formula above gives theoretical torque. Real hydraulic motors experience losses from friction, internal leakage, fluid shear, and seal drag. Because of that, actual output torque is usually lower than the theoretical value.

T_{actual} = T_{theoretical} \times \eta_m

Here, η_m is the motor’s mechanical efficiency expressed as a decimal. If efficiency is known, this adjustment gives a better estimate of real shaft torque under load.

How to Use the Calculator Correctly

Enter the motor pressure differential under operating load.
Enter the motor displacement per revolution.
Select the correct units for each field.
Calculate the missing value and verify the output unit.

Be careful not to confuse:

motor displacement with pump flow,
system maximum pressure with actual running pressure,
lb-in with lb-ft.

Torque Unit Conversion

If you need the result in pound-feet instead of pound-inches, convert using:

T_{lb-ft} = \frac{T_{lb-in}}{12}

Example 1

If the pressure is 500 psi and the motor displacement is 0.36 in³/rev, the theoretical torque is:

T = \frac{500 \times 0.36}{2\pi} = 28.65 \text{ lb-in}

Example 2

If the pressure is 1250 psi and the displacement is 0.75 in³/rev, the theoretical torque becomes:

T = \frac{1250 \times 0.75}{2\pi} = 149.21 \text{ lb-in}

Practical Notes

Use this calculator for motor selection, torque checks, and system performance estimates.
The result is best treated as a theoretical baseline unless efficiency and operating losses are accounted for.
Actual output can vary with fluid temperature, viscosity, internal wear, and motor design.
When comparing motors, displacement and continuous pressure rating should always be evaluated together.