This post involves something people either love or love to hate: MATH! Sometimes, it’s handy to be able to calculate things like speed, torque, and flow rate for your hydraulic motor. In this Shop Talk Blog post, we are going to show you some common hydraulic motor calculations and provide examples on how to use them. Impress your mechanic or sales contact with your newfound technical knowledge! Let's start!

First Things First

Let’s use these symbols and units in our calculations:

• ⍵ is hydraulic motor speed in rpm
• D is motor displacement per rotation in cubic inches
• F is flow rate in gpm
• HP is horsepower
• P is pressure in psi
• T is torque in inch-pounds

Fortunately, you can do the calculations with a simple calculator (including the one on your smartphone).  Just keep in mind that ℼ = 3.14.

Calculating Hydraulic Motor Speed

You can calculate the speed in ⍵ in rpm if you know the fluid motor displacement D in cubic inches and the flow rate F in gallons per minute. Here's the equation:

⍵ = F x 231 / D

For example, a flow rate F of 75 gpm and a displacement D of 11.3 cubic inches, the hydraulic motor speed would be …

⍵ = 75 x 231 / 11.3 = 1,533 rpm

Calculating Hydraulic Motor Torque

There are different ways to calculate the torque of a hydraulic motor depending on what values you know.  What follows are the most commonly used formulas.

Flow Rate, Pressure, and Speed

If you have the flow rate F in gpm, the pressure P in psi, and speed in ⍵ in rpm, you can find the torque T in inch-pounds using this formula:

T = F x P x 36.77 / ⍵

If you have a flow rate F of 75 gpm, a pressure P of 5,076 psi, and a speed ⍵ of 1,558 rpm, then the resulting torque T in inch-pounds would be …

T = 76.1 x 5000 x 36.77 / 1500 = 9,193 inch-pounds

Horsepower and Speed

If you have the horsepower HP and the hydraulic motor speed in ⍵ in rpm, you can find the torque T in inch-pounds using this formula:

T = HP x 63025 / ⍵

If you a hydraulic motor with 225 hp and a speed ⍵ of 1,500 rpm, then the resulting torque would be …

T =  225 * 63025 / 1500 = 9,454 inch-pounds

Pressure and Displacement

If you have the pressure P in psi and the motor displacement D in cubic inches, then you can find the torque T in inch-pounds using this formula:

T = P x D / (2 x ℼ)

If you have a pressure P of 5,000 psi and a displacement D of 11.3 cubic inches, then the resulting torque T would be …

T =  5000 x 11.3 / (2 x ℼ) = 8,989 in-pounds

Calculating Hydraulic Motor Flow Rate

You can determine the flow rate F in gallons per minute needed to achieve a certain speed in ⍵ in rpm if you also know the motor displacement D in cubic inches:

F = D x ⍵ / 231

If you have a displacement of 11.3 cubic inches and need a speed of 1,500 rpm, the flow rate would need to be …

F = 11.3 x 1500 / 231 = 73.38 gpm

Conclusion

Hydraulic motor calculations may seem a bit daunting at first, but once you've seen examples and you've got the right data, these calculations are fairly straightforward. There are also many different hydraulic motor formula resources available on the web, like those at like those at The Engineering Toolbox.

Texas Final Drive is your partner in providing new or remanufactured final drive hydraulic motors from a single mini-excavator to a fleet of heavy equipment. Call today so we can find the right final drive or hydraulic component for you, or check out our online store to find your O.E.M. manufacturer brand motor now.