Hydraulic Motor Torque from Displacement
A hydraulic motor turns pressure and displacement into torque: T = dP x D / (2*pi), derated by mechanical efficiency - and its speed is flow over displacement, N = Q/D. The working calculator runs torque, required flow and both powers.
Torque from pressure
Each revolution sweeps one displacement against the pressure difference:
T = dP * D / (2*pi) (x eta_m)
Speed from flow
The same displacement sets speed: N = Q/D - more flow or a smaller motor spins faster, trading away torque.
N = Q / D
Pick by corner power
Choose displacement so the worst simultaneous torque and speed stay inside the pump flow and relief pressure - the working calculator shows all four numbers.
Frequently asked questions
Why divide by 2 pi?
Work per revolution is dP x D; torque is work per radian, and there are 2 pi radians per revolution.
What efficiency should I use?
Mechanical efficiency commonly runs 0.85-0.95 for piston and gear motors at rated conditions; manufacturer curves govern at low speed where starting torque sags.
Related pages
- Hydraulic motor torque calculator - torque, flow, speed and power with efficiencies.
- Pump flow & HP calculator - the supply side of the same circuit.
- Hydraulic pressure calculator - pressure from force and area.