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Hydraulic Cylinder Sizing Worksheet

Machine builders usually have several cylinders on one power unit and need force, speed and cycle time for each. This worksheet computes all of it per row and totals the flow demand so you can size the pump.

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Cap area (sq in)	Annulus area (sq in)	Extend force (lbf)	Retract force (lbf)	Extend speed (in/s)	Retract speed (in/s)	Cycle time (s)
9.6211	7.2158	19,242	14,432	3.2013	4.2684	4.3732
28.2743	21.2058	70,686	53,014	4.085	5.4466	10.2816
4.9087	3.4238	7,363	5,136	3.9216	5.6223	7.7915
3.1416	2.3562	5,655	4,241	4.902	6.536	2.142
12.5664	9.4248	22,619	16,965	3.6765	4.902	14.28

Largest extend force check (sum)

70,686

Total flow if all move at once

Total sequential cycle time

38.8683

Average cylinder cycle time (s)

7.7737

Peak flow hydraulic hp at 2500 psi

86.056

Upper bound if every cylinder runs at the same time at 2500 psi.

Formulas: area = pi x d squared / 4; force = pressure x area; speed in in/s = GPM x 3.85 / area (231 cu in per gallon divided by 60 seconds); cycle time sums extend and retract stroke times. Ignores seal friction (typically 3 to 10 percent), back pressure, acceleration and dwell time. Check long-stroke compression loads for rod buckling using Euler column rules and the maker's stop-tube chart. Rod-side speed is faster than cap-side speed at equal flow in a regenerative-free circuit.

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How to use it

List each cylinder with bore, rod diameter, stroke, working pressure and the flow you plan to give it. The sheet returns cap and annulus areas, extend and retract force in pounds-force, extend and retract speed in inches per second and full cycle time. The totals show the largest extend force, the total flow if everything moves at once and the sequential cycle time. Replace the example rows with your own, add or delete rows, then export the sheet to Excel for a design package.

Use actual bore and rod sizes from the catalog
Use the pressure at the cylinder, not at the pump
Enter the flow available during that motion
Add dwell and acceleration time separately

Formulas and assumptions

Cap area is pi times bore squared over four. Annulus area subtracts the rod area. Force is pressure times area, which is why retract force is always lower on a single-rod cylinder. Speed equals flow divided by area, with 231 cubic inches per gallon and 60 seconds per minute giving the 3.85 constant. Cycle time is stroke over extend speed plus stroke over retract speed. These are the idealized fluid power relationships. Real force is reduced by seal friction and back pressure, so allow a margin when the load is close to the limit.

Reading the results

In the example, the 6 inch press ram produces about 70,700 lbf at 2500 psi and travels at roughly 4.1 in/s on extend with 30 GPM, so its 24 inch stroke takes about 5.9 seconds. Its retract is faster because the annulus is smaller, about 5.5 in/s. If the cycle is too slow, increase flow, reduce bore, or add a regenerative circuit. If force is too low, increase bore or pressure, and check that the rod and mounting can take the load.

Common mistakes

Common errors are using rod diameter in the extend area, assuming the pump delivers full flow during a pressure peak, and ignoring pressure intensification on the rod side when the cap side is fed through a restrictor. Another is sizing for force only and skipping the cycle time check, which can make the machine miss its takt. Long stroke cylinders also need buckling and side-load checks that this worksheet does not do.

Frequently Asked Questions

Why is retract force lower than extend force?

On a single-rod cylinder the rod takes up part of the piston area on the rod side. Retract force is pressure times the annular area, so it is lower by the rod area times pressure.

What does 3.85 mean in the speed formula?

One US gallon is 231 cubic inches and a minute is 60 seconds, so 231 divided by 60 is 3.85. Speed in inches per second equals GPM times 3.85 divided by area in square inches.

Should I include seal friction?

For quick estimates, derate force by 5 to 10 percent for friction, more for low pressure and small bores. The manufacturer's data gives the breakaway pressure of your seal package.

How do I add more cylinders?

Use the add row control, fill in tag, bore, rod, stroke, pressure and flow, and the computed columns update. Delete unused rows before export so the totals match your machine.

Netray can pull equipment and engineering change data into a private assistant so cylinder specifications stay linked to your machine records.

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