Cylinder Force Calculator | Pneumatic & Hydraulic Push and Pull Quote Check

Drive area, net theoretical force, usable force, margin, load ratio, needed pressure and comparable price by quote and direction
Quote	Direction	Drive area (mm²)	Theoretical (N)	Usable (N)	Required (N)	Margin	Load ratio	Needed pressure (MPa)	Comparable price
Supplier A · 25 mm rod, same pull figure Does not meet requirement	Push (extend)	3,117.2	1,558.62	—	1,558.62	0.00%	—	0.500	168,000
Supplier A · 25 mm rod, same pull figure Does not meet requirement	Pull (retract)	2,626.4	1,313.19	—	1,401.54	-6.30%	—	0.534
Supplier B · 63 mm bore, 20 mm rod Checks passed	Push (extend)	3,117.2	1,558.62	—	1,558.62	0.00%	—	0.500	215,000
Supplier B · 63 mm bore, 20 mm rod Checks passed	Pull (retract)	2,803.1	1,401.54	—	1,401.54	0.00%	—	0.500
Supplier C · 2.5 in bore, psi rating Needs review	Push (extend)	3,166.9	1,583.46	—	1,558.62	+1.59%	—	0.492	189,000
Supplier C · 2.5 in bore, psi rating Needs review	Pull (retract)	2,969.0	1,484.49	—	1,401.54	+5.92%	—	0.472

Rating pressure, stated force, theoretical value at the same pressure, gap and implied pressure by quote and direction
Quote	Direction	Rating pressure	Stated (N)	Theoretical at rating (N)	Gap	Implied pressure
Supplier A · 25 mm rod, same pull figure	Push (extend)	0.500 MPa	1,560.00	1,558.62	+0.09%	0.500 MPa
Supplier A · 25 mm rod, same pull figure	Pull (retract)	0.500 MPa	1,560.00	1,313.19	+18.80%	0.594 MPa
Supplier B · 63 mm bore, 20 mm rod	Push (extend)	0.500 MPa	1,560.00	1,558.62	+0.09%	0.500 MPa
Supplier B · 63 mm bore, 20 mm rod	Pull (retract)	0.500 MPa	1,400.00	1,401.54	-0.11%	0.499 MPa
Supplier C · 2.5 in bore, psi rating	Push (extend)	80.00 psi	1,748.15	1,746.81	+0.08%	80.06 psi
Supplier C · 2.5 in bore, psi rating	Pull (retract)	80.00 psi	1,636.95	1,637.64	-0.04%	79.97 psi

Confirmed or unconfirmed supplier checklist items by quote
Quote	Stroke, mounting style (foot, flange, clevis, trunnion) and dimensions	Rod-end thread and coupling	Port size, thread type (Rc, G, NPT) and piping	Medium (non-lube air, hydraulic oil), seals, temperature and cushioning	Side load, buckling at long stroke and speed
Supplier A · 25 mm rod, same pull figure	Confirmed	Confirmed	Confirmed	Confirmed	Confirmed
Supplier B · 63 mm bore, 20 mm rod	Confirmed	Confirmed	Confirmed	Confirmed	Confirmed
Supplier C · 2.5 in bore, psi rating	Confirmed	Unconfirmed	Unconfirmed	Confirmed	Confirmed

The cost of trusting only the push force in a cylinder quote

When a press jig, clamp, lift table or transfer pusher driven by a pneumatic or hydraulic cylinder fails, the first step is usually a replacement quote matched on bore and stroke.
Many quotes, however, list only one push (extend) force, or copy the same number into the pull (retract) column.
On a single-rod cylinder the retract side loses the rod cross-section, so the pull force is smaller at the same pressure; a replacement with a thicker rod can run out of force when pulling, leading to a second order and machine downtime.

This pneumatic and hydraulic cylinder push and pull force quote check calculator works out the net theoretical force in both directions from bore, rod diameter, site supply pressure and back pressure.
It compares them with the force back-calculated from the failed cylinder or with a load confirmed by an engineer, and checks in one pass whether the supplier figures for both directions agree at the same pressure basis and whether the rod area was forgotten or units were mixed.
The result can be saved as a TXT checklist for the supplier, and no input is sent to a server.

The force formulas are physics and apply anywhere.
The VAT conversion and the legal-unit guidance are based on Korean rules (2026): the Korean Value-Added Tax Act rate of 10% and the Korean legal metrology units of newtons and pascals.

Who this is for

Owners of small manufacturing and maintenance shops comparing two or three replacement quotes for a failed pneumatic or hydraulic cylinder
Maintenance staff evaluating inch, psi and lbf catalog cylinders for an existing metric machine
Operators who want to do the cylinder force calculation themselves and verify the supplier’s rating pressure and units

Key features from two-way force to the supplier checklist

Requirement from the old cylinder

Enter the failed cylinder’s bore, rod diameter and rod type, and its theoretical push and pull force at the same site pressure becomes the requirement.
If an engineer has defined the load, enter the required push and pull force directly and choose a load factor.

Net force at the site pressure

For every quote it calculates the cap-side area and rod-side annulus, the net theoretical push and pull force, the margin against the requirement and the supply pressure that the requirement would need.
Back pressure, double-rod cylinders and a separate retract pressure are included.

Supplier figures at the same pressure

Stated forces are compared with the theoretical value at their own rating pressure, and the implied pressure is back-calculated from each figure.
If a direction that pushes on the rod-side annulus states pressure × full bore area, it is flagged as a rod area that was not subtracted.

Pressure rating, checklist and lowest price

If the site pressure exceeds the quoted maximum operating pressure, the quote does not meet the requirement.
Mounting, rod-end thread, port thread, medium and seals, and side load are tracked per quote, and the lowest VAT-exclusive price among fully passing quotes is shown.

Match the meaning and units of each input first

Bore D and rod diameter d: The bore is the tube inner diameter (piston diameter) and the rod is the piston rod outer diameter.
A rod equal to or larger than the bore leaves no annulus, so it is reported as an input error instead of being calculated.
Extend and retract supply pressure: The gauge pressure set by the regulator or relief valve.
Pneumatics usually run at 0.4 to 0.6 MPa and hydraulics at several to tens of MPa; enter a separate retract pressure if only the retract stroke is reduced.
Back pressure: Pressure left in the chamber on the other side of the piston.
Use 0 for pneumatic exhaust to atmosphere, and the confirmed value for meter-out speed control or a hydraulic return line.
Rating pressure of the stated forces: The pressure the supplier used, such as the 0.5 in “theoretical output at 0.5 MPa”.
If it is blank, the site extend pressure is used and the basis is listed as not stated.
Maximum operating pressure: The pressure the cylinder is rated for.
If the site supply exceeds it, the quote does not meet the requirement even when the force is enough.
Units: Pick length (mm, in), pressure (MPa, bar, kPa, kgf/cm², psi) and force (N, kN, kgf, tf, lbf) per quote as printed in the catalog.
Choose the unit before typing; changing it afterwards converts the value to the same quantity.

Cylinder force formulas

Pressure areas and net theoretical force

Cap-side area A = π × D² ÷ 4
Rod-side annulus Ar = π × (D² − d²) ÷ 4
Single rod: extend drive A, exhaust Ar / retract drive Ar, exhaust A
Double rod: both strokes drive Ar, exhaust Ar
Net theoretical force F = supply pressure × drive area − back pressure × exhaust area (MPa × mm² = N)
Usable force = F × load factor λ

SMC technical data writes the double-acting cylinder force as F1 = η × A1 × P for extension and F2 = η × A2 × P for retraction, and explains that the retract-side area of a single-rod cylinder is reduced by the piston rod cross-section.
Here η is the load factor, and the force from pressure × area alone, assuming no internal resistance, is called the theoretical output.
The calculator uses the general form that subtracts exhaust pressure × area for back pressure; with zero back pressure it equals the SMC formula.

Specification check metrics

Theoretical at rating = rating pressure × drive area (no back pressure, catalog convention)
Specification gap = (stated force − theoretical at rating) ÷ theoretical at rating × 100
Implied pressure = stated force ÷ drive area
Margin = (usable force ÷ required force − 1) × 100
Needed pressure = (required force ÷ λ + back pressure × exhaust area) ÷ drive area

Pressure areas and theoretical output at 0.5 MPa from the SMC theoretical output table
Bore and rod	Push area (mm²)	Push at 0.5 MPa (N)	Pull area (mm²)	Pull at 0.5 MPa (N)
50 mm bore · 20 mm rod	1,960	980	1,650	825
63 mm bore · 20 mm rod	3,120	1,560	2,800	1,400

The SMC table rounds areas to three significant figures, so it differs from the exact 1,963.5 mm² and 1,649.3 mm² by less than 0.5%.
That is why the default specification tolerance is 3%: on ordinary cylinders whose rod is at least a quarter of the bore, a forgotten rod area (an area gap of 6.25% or more) still exceeds the tolerance and is caught.

Hydraulic cylinders can lose half their force on the pull stroke

Hydraulic cylinders use thick rods, so the area ratio φ = A ÷ Ar is large.
A 100 mm bore with a 70 mm rod at 16 MPa (160 bar) has A of 7,853.98 mm² and Ar of 4,005.53 mm², an area ratio of 1.96, giving 125.66 kN push and 64.09 kN pull.
Unlike the 1.11 ratio of a pneumatic 63 mm bore with a 20 mm rod, the pull is about half the push, so hydraulic cylinder quotes especially need both figures.

Conversion factors for pressure, force and length units
Quantity	Unit	1 unit = MPa or stated unit
Pressure	MPa (N/mm²)	1
Pressure	bar	0.1
Pressure	kgf/cm²	0.0980665
Pressure	psi (lbf/in²)	0.006894757
Force	kgf	9.80665 N
Force	lbf	4.4482216 N
Length	in	25.4 mm

Step-by-step use

Check the site regulator or relief valve setting and enter the extend supply pressure and back pressure.
If only the retract stroke is reduced, choose a separate retract pressure.
Find the failed cylinder’s bore, rod diameter and rod type on its nameplate or drawing to back-calculate the requirement.
If an engineer has defined the load, switch to direct entry and choose the SMC load factor or the supplier’s value.
Enter up to four supplier quotes.
Pick the length, pressure and force units as printed, then enter bore, rod, rating pressure, maximum operating pressure, both stated forces and price.
Tick the items confirmed with the supplier.
Leave stroke and mounting, rod-end thread, port thread, medium and seals, and side load or buckling unticked if not yet confirmed.
Read the status and items to check, then save the supplier checklist as TXT.
Send it to obtain the missing figures and rating pressures, and confirm the replacement only after engineer approval.

A fictional example checked by hand

Three quotes for a clamp cylinder replacement

The site runs pneumatics at 0.5 MPa with zero back pressure.
The old cylinder is a single-rod 63 mm bore with a 20 mm rod, so A = 3,117.2 mm², Ar = 2,803.1 mm² and the requirement is 1,558.62 N push (158.94 kgf) and 1,401.54 N pull.

Supplier A uses the same bore with a 25 mm rod and states 1,560 N for both directions.
The push force is the same 1,558.62 N, but the pull force is 1,313.19 N, a margin of −6.30%, and the stated pull force is +18.80% above the theoretical value at the same pressure, implying 0.594 MPa.
Because that figure matches full bore area × 0.5 MPa within +0.09%, the calculator flags a rod area that was not subtracted and shows that 0.534 MPa would be needed for the required pull.

Supplier B states the SMC table values of 1,560 N and 1,400 N, a specification gap of +0.09% and −0.11%, with a 0.00% margin both ways, so it passes.
Supplier C quotes a US catalog 2.5 in bore with a 0.625 in rod as 393 lbf and 368 lbf at 80 psi.
393 lbf is 1,748.15 N and looks 12% stronger than B’s 1,560 N, but only because the rating pressure is a higher 0.552 MPa; at the 0.5 MPa site it delivers 1,583.46 N push (+1.59%) and 1,484.49 N pull (+5.92%).
C’s figures match the theoretical values at their pressure within +0.08% and −0.04%, but the rod-end and port threads (NPT or not) are unconfirmed, so it needs review and its price of 189,000 is not shown as the lowest even though it is below B’s 215,000.

Push and pull force at the site pressure, pull margin, pull specification gap and verdict for each fictional quote
Quote	Push (N)	Pull (N)	Pull margin	Pull specification gap	Verdict
Supplier A · 25 mm rod, same pull figure	1,558.62	1,313.19	−6.30%	+18.80%	Does not meet requirement
Supplier B · 63 mm bore, 20 mm rod	1,558.62	1,401.54	0.00%	−0.11%	Checks passed
Supplier C · 2.5 in bore, psi rating	1,583.46	1,484.49	+5.92%	−0.04%	Needs review

Direct requirement with a load factor

An engineer has set a clamp force of 1,000 N push and 800 N pull and chosen the stationary load factor of 0.7.
At 0.5 MPa, a 63 mm bore with a 20 mm rod gives usable forces of 1,091.04 N and 981.08 N, margins of +9.10% and +22.64% and load ratios of 64.16% and 57.08%.
A 50 mm bore with a 20 mm rod gives 687.22 N and 577.27 N, margins of −31.28% and −27.84%, and would need 0.728 MPa and 0.693 MPa to reach the requirement.

Margins and load ratios by bore for the direct requirement example
Bore and rod	Push margin	Pull margin	Load ratio (push / pull)	Verdict
63 mm bore · 20 mm rod	+9.10%	+22.64%	64.16% / 57.08%	Within requirement
50 mm bore · 20 mm rod	−31.28%	−27.84%	101.86% / 97.01%	Does not meet requirement

These values come from the calculator’s pure functions for a fictional example and are not product specifications or market prices.

How to read the results

Does not meet requirement

The usable push or pull force is below the requirement, back pressure leaves zero or negative net force, or the site pressure exceeds the maximum operating pressure.
Use the needed pressure and margin to ask the supplier for a different bore or rod combination.

Needs review

The force is enough, but a stated force, rating pressure, maximum pressure or checklist item is missing, or a figure disagrees with the calculation.
The items to check are the questions to send the supplier; re-enter the answers once you have them.

Rod area not subtracted

Shown when a direction that pushes on the annulus, such as single-rod pull or both strokes of a double rod, states pressure × full bore area.
The quote probably copied the push figure, so ask for the real pull force.

Checks passed

Both forces meet the requirement, the figures agree at the same pressure basis and every checklist item is confirmed.
Friction, acceleration, impact, buckling and side load are still not calculated, so get engineer approval before the final choice.

Korean legal units and VAT on quotes

Article 4 of the Korean Measures Act (MST 280029, effective 2026-03-03) divides legal units into base, derived and special units, and derives them from Article 11 of the Framework Act on National Standards (MST 283385).
Article 9 and Annex 2 of its Enforcement Decree (MST 283771, effective 2026-03-03) set the newton (N) as the unit of force and the pascal (Pa) as the unit of pressure and stress.
Article 6 of the same Act bars non-legal units in measurement and advertising, while allowing them to be shown together with legal units when the ministerial labelling requirements are met.
The calculator therefore works internally in MPa and N, and suggests asking for MPa and N alongside quotes written only in kgf/cm² or kgf.

The Korean Value-Added Tax Act Article 30 (MST 276117, effective 2026-01-02) sets a 10% rate, so VAT-inclusive quotes are divided by 1.1 to compare on the same basis.
The calculator does not judge pressure-vessel or machine safety compliance or certification; the statutes were checked through the Korean National Law Information open API on 2026-10-25.

Three practical situations

Replacing a failed cylinder with another maker’s model

When discontinuation or lead time forces a different series, build the requirement from the old bore and rod and enter the quotes side by side.
A quote with the same bore but a thicker rod shows a negative pull margin straight away, preventing a pulling motion that stalls after installation.

Evaluating inch and psi catalog cylinders

Overseas catalogs list the bore in inches, pressure in psi and force in lbf, and often rate forces at 80 psi or 100 psi, above many metric sites.
Choosing units per quote compares everything in newtons, while the stated figures are checked at their rating pressure and the requirement at the site pressure.

Hydraulic cylinder replacement or modification

Hydraulic cylinders have thick rods, so the pull can fall to about half the push, and the return line adds back pressure.
Enter back pressure and the retract pressure to confirm the net force, and check that the pump relief setting is within the quoted maximum operating pressure.

Limits of the calculation and quote-checking tips

This is an arithmetic check under static conditions.
Seal and guide friction, load acceleration and inertia, end-of-stroke impact, rod buckling at long stroke, side load, cushion capacity, air consumption and speed are not calculated.
It does not select cylinders, recommend raising pressure or judge the safety of lifting or press machines with fall or pinch hazards.

Check whether the quoted force is a theoretical output or a recommended load already multiplied by a load factor.
An implied pressure well below the site pressure can mean the factor was already applied.
Check whether the rod-end thread is metric or an inch thread such as UNF, and whether the ports are Rc, G or NPT.
Even with the right force, different connections need adapters and extra work.
Machines that push over a long stroke need a rod buckling check.
Give the supplier the mounting style and stroke and ask for the permissible load.
Seal materials differ for non-lube or lubricated air and for the hydraulic oil type and temperature.
Confirm in the checklist that the conditions match the old cylinder.

Frequently asked questions

If the push force is the same, is the pull force the same too?

No.
On a single-rod cylinder the retract side loses the rod cross-section, so the pull force is always smaller at the same pressure.
A 63 mm bore with a 20 mm rod pulls about 90% of its push, but the same bore with a 25 mm rod pulls 6.30% less again, which can leave a pulling motion short of force.

What if the quote only lists the push force?

Leave the stated pull force blank and the calculator works out the theoretical pull force from the bore and rod and marks the figure as missing.
Save the supplier checklist and ask for the pull force together with its rating pressure.
On machines that pull a load, ordering without checking the pull force is the most common reason for a second purchase.

What if the supplier rated the forces at a different pressure from my site?

Catalog theoretical output tables are written at a given pressure such as 0.5 MPa, 0.7 MPa or 80 psi.
The calculator checks the supplier figures at that rating pressure and judges the requirement separately at the site pressure.
In the example the inch quote looks larger at 393 lbf (1,748.15 N) at 80 psi, but delivers 1,583.46 N at the 0.5 MPa site supply.

Where do the load factors 0.7 and 0.5 come from?

SMC pneumatic cylinder technical data recommends sizing above theoretical output because of seal and bearing resistance and exhaust back-pressure during motion: 0.7 or below when stationary, 0.5 or below when moving a load and 1.0 or below for horizontal motion on a guide.
These are pneumatic values; for hydraulics, high speed or impact, enter the value set by the supplier or an engineer.
By default no load factor is applied; the calculator multiplies one only when you choose it.

Why enter back pressure?

Pressure left in the chamber on the other side of the piston subtracts from the force.
Pneumatic exhaust to atmosphere is close to zero, but meter-out speed control or a hydraulic return line creates back pressure.
Net force is supply × drive area − back pressure × exhaust area, so if back pressure reaches the supply the net force drops to zero or below and the quote is marked as not meeting the requirement.

Can I enter quotes in kgf/cm² or psi as written?

Yes. Each quote has its own pressure unit (MPa, bar, kPa, kgf/cm² or psi) and force unit (N, kN, kgf, tf or lbf).
Exact definitions are used, 1 kgf/cm² = 0.0980665 MPa and 1 psi = 0.006894757 MPa, so everything is normalised to MPa and N internally.
Changing a unit after typing converts the value to the same quantity, so if you picked the wrong unit, change it and then re-enter the number.

How is a double-rod cylinder calculated?

A double (through) rod cylinder has a rod on both faces of the piston, so both strokes push on the annulus.
Choose double rod and both directions use the same area; a stated push force based on the full bore is also caught as an error.
The push force is lower than on a single-rod cylinder, so check the push margin when replacing a single-rod cylinder with a double-rod one.

Is the lowest price among passing quotes a recommendation?

No.
It only shows the cheapest quote whose figures meet the required force and pressure rating and whose checklist is complete.
Under the Korean Value-Added Tax Act Article 30 rate of 10%, VAT-inclusive prices are divided by 1.1 before comparing, and the final choice needs engineer approval of mounting and load conditions.

Sources and next steps

Sources were checked on 2026-10-25.
The definition of theoretical output follows the SMC theoretical output FAQ, and the push and pull formulas, load factors and theoretical output table follow the SMC cylinder technical data (Data 1 and Data 3).
The Korean Measures Act, the Framework Act on National Standards and Annex 2 of its decree, and the Value-Added Tax Act Article 30 were confirmed as current through the Korean National Law Information open API.
Re-enter cylinder specifications, maximum operating pressure and prices from each supplier for every quote.

Enter the quotes you received above and save the supplier checklist as TXT to confirm the rating pressure of both forces, the maximum operating pressure and the load conditions.
Once the missing data is filled in and an engineer approves, the replacement quote can be confirmed.

Pneumatic and Hydraulic Cylinder Push and Pull Force Quote Check Calculator

1. Site pressure and required force

2. Supplier quotes (up to 4)

Check results

Required force · from the old cylinder

Push and pull force at the site pressure

Supplier figures at their rating pressure

Supplier checklist

Supplier A · 25 mm rod, same pull figure · Items to check

Supplier C · 2.5 in bore, psi rating · Items to check