Cylinder Force Calculator Hydraulic

Hydraulic Cylinder Force Calculator

Find the extend (push) force of a hydraulic cylinder from the full bore area with F = pressure x bore area x efficiency. Enter bore and system pressure in Imperial or Metric, read the force in pounds, US tons, Newtons, and kN, or flip to back-solve the pressure you need to hit a target force with any number of cylinders in parallel.

šŸ”§Choose a Mode

šŸŽÆReal Cylinder Presets

šŸ“Cylinder Inputs

Sets bore and pressure units; both systems are always shown.

Inside diameter of the barrel; drives the full piston area.

Working pressure applied to the cap (blind) end on extend.

Seal and friction losses; drops usable force below the ideal.

Identical cylinders sharing the load; multiplies total force.

Force you must reach; the tool solves the pressure needed.

Controls rounding on every result card and row.

Extend force 0 lbf push force in pounds
Force in US tons 0 tons short tons, lbf / 2000
Force in Newtons 0 N SI force / kN
Piston bore area 0 in² full bore area / cm²

šŸ”¢Formula Snapshot

A0.7854 x D²
FP x A x eff
Tonslbf / 2000
PF / (A x eff)

šŸ“Bore Area Chart

Bore (in)Area (in²)Bore (mm)Area (cm²)
1.51.76738.111.40
23.14250.820.27
2.54.90963.531.67
37.06976.245.60
3.59.62188.962.07
412.566101.681.07
519.635127.0126.68
628.274152.4182.41
850.265203.2324.29
1078.540254.0506.71

šŸ“ŠPressure and Force Unit Conversions

ConvertMultiply ByTo GetExample
psi0.06895bar3000 psi = 206.8 bar
bar14.5038psi200 bar = 2901 psi
psi6894.76Pascal1 psi = 6895 Pa
lbf4.44822Newton1000 lbf = 4448 N
Newton0.224809lbf10000 N = 2248 lbf
lbf0.0005US ton2000 lbf = 1 ton

āš™Typical System Pressures by Application

ApplicationTypical PressureCommon BoreNote
Bottle jack7000-10000 psi1.5-2 inSmall ram, very high pressure
Log splitter2500-3000 psi4-4.5 inHigh force, moderate speed
Dump trailer2500-3000 psi3-4 inTelescopic or single stage
Farm loader2200-2800 psi2.5-3.5 inTractor open-center system
Skid steer3000-3500 psi2.5-3 inLift and tilt circuits
Excavator4500-5500 psi4-8 inBoom, arm, and bucket
Shop press2500-3000 psi4-6 inBench or H-frame press
Industrial press2000-3000 psi8-12 inLarge tonnage forming

šŸ—ƒExtend Force Comparison Grid (lbf, 100% eff)

Bore1500 psi2000 psi2500 psi3000 psi3500 psi
2 in471262837854942510996
2.5 in73639817122721472617181
3 in1060314137176712120624740
3.5 in1443119242240522886333673
4 in1885025133314163769943982
5 in2945239270490875890568722
6 in4241256549706868482398960

āš™Formula Breakdown

Bore area A = (Ļ€/4) D²The full piston area is a circle of the bore diameter. A 4 in bore gives A = 0.7854 x 4 x 4 = 12.566 in².
Extend force F = P x A x effPush force equals pressure times bore area times efficiency. At 2500 psi and 100%, F = 2500 x 12.566 = 31416 lbf.
US tons = lbf / 2000Convert pounds of force to US short tons. 31416 lbf / 2000 = 15.7 tons of clamping or pushing force.
Metric F = P(Pa) x A(m²)In SI, bar x 100000 gives Pascal and mm/1000 squared gives m², so force comes out in Newtons, then kN = N / 1000.
Parallel force = F x nIdentical cylinders sharing a load add up. Two 4 in cylinders at 2500 psi give 2 x 31416 = 62832 lbf total.
Pressure P = F / (A x eff)Back-solve the pressure to hit a target. To reach 20000 lbf with 12.566 in², P = 20000 / 12.566 = 1592 psi.
Extend uses full boreThe rod is on the retract side, so extend uses the whole bore area and always makes more force than retract.

šŸ’”Cylinder Sizing Tips

Bore beats pressure: Force scales with the square of the bore diameter, so doubling the bore quadruples the force while doubling the pressure only doubles it. Going from a 2 in to a 4 in cylinder gives four times the push at the same psi. When you need more tonnage, a bigger bore is almost always cheaper and safer than cranking the relief valve higher.
Extend versus retract: This calculator sizes the extend (push) stroke using the full bore area. Retract force is always lower because the rod removes area from the annulus side. Never exceed the cylinder barrel, rod, or hose rated pressure to chase force, and derate for seal friction by running the efficiency at 85 to 95 percent for real, worn hardware.

When you look at cylinder, there comes one such moment of uncertainty. There’s three-thousand psi on the pressure gauge, but what does that equate to in terms of meat? Is that enough oomph to heave loader bucket into air, or is it going to give out halfway to full power?

It’s a matter of relationship, something that sounds easy until you try to perform the mathematical equation in your brain. The solution: Let this tool does the work. Force are calculated by multiplying pressure, piston area, and efficiency. That’s one clean equation for extension force. And it makes sense: Force equals pressure times piston area times efficiency.

How to Calculate Cylinder Force

But it’s the geometry that trips folks up all the time. Remember, since the piston face is a circle, the area increases as the square of bore diameter. So strength doesn’t just double when you double the bore; it quadruples. You can hold a two inch cylinder and think ā€œhefty,ā€ then swap out that cylinder for a four inch cylinder, use the same pressure and now you have four times the pushing power! The calculator takes care of the squaring for you so you don’t need to remember your geometric formulas.

The biggest error I see with most operators is they chase pressure without verifying their bore size. They believe that if they crank their relief valve up, then they will increase their tonnage. In reality, going with a bigger cylinder is generaly cheaper in the long term and safer. Every time your relief valve opens you are putting stress on all of the seals, fittings and hoses in system. A larger bore will allow you to achieve the load capacity you desire while keeping everything in a safe operating range. This may seem like a little design decision, but it will matter when it comes to longevity of the whole system.

In real world, nothing runs at one hundred percent efficiency. Back pressure from return line fights against the stroke. Seals drag against the rod and bushing friction increases as time goes by. That’s why tuning the efficiency isn’t simply a matter of technicalities, it’s necessary to plan accurately. While new equipment may run at ninety-five percent, heavy side loads or worn out seals can decrease that number to eighty-five percent or less. Dialing in this loss allows you to predict the actual force you’ll experience on job site using the tool.

Rather than starting with the pump, sometimes you start with the load. For instance, let’s say that you have a concrete slab to bust out, and you know it will take twenty thousand pounds. Rather than guessing, you flip the equation and ask how much pressure is needed for your cylinder. It will save hours of trial and error in fitting rams to available power units. The user inputs the desired amount of force and the calculator informs them whether they are good to go or need to upgrade their component.

It also cleans up well with parallel cylinders… Something common in many machines where multiple ram share a load. (For example, an excavator boom has two arms.) As long as they’re properly synchronized and rated to handle pressure, two equal cylinders will have double the output of one cylinder; the force simply adds up linearally. In the breakdown view, it lets you see not just the combined but also individual forces. That’s how you can check that nothing’s getting overworked.

Before committing to a design, I like a quick sanity check and that’s what the built-in reference tables on the page do for you. From lower pressure farm loader applications to higher psi bottle jacks, you can get a sense of what is normal operating pressure so your calculations are grounded in reality different than theory. Remember, there’s always more force in extend than retract because the rod occupies space on the pull side of system. Because typically the maximum effort occurs during the push stroke, that’s what the calculator concentrates on. If you keep this in mind, you won’t get frustrated by how much weaker the machine appears to be while pulling a load compared with pushing one.

You should of used this earlier! The bottom line on sizing a hydraulics system has more to do with matching pressure to surface area than it does to raw horsepower. That’s where this tool gets rid of the guesswork and allows you to concentrate on getting the heavy stuff done rather than arguing over the math.

Cylinder Force Calculator Hydraulic