Bore size is the single number that sets how much force a hydraulic cylinder can produce, and it is the first calculation in any cylinder selection. The relationship is simple — force equals pressure times piston area — but the two places engineers most often go wrong are using the pump’s nominal pressure instead of the pressure actually available at the cylinder, and rounding the result down to a convenient number instead of up to the next standard bore.
This guide works through the calculation in the order it should be applied: establish the real available pressure, compute the required area, convert to bore, round up to the ISO 3320 standard series, and then verify that the cylinder you have chosen actually holds pressure and pulls the load it needs on the return stroke.
The bore calculation in one line
Cylinder force comes from pressure acting on piston area. Rearranging that relationship gives the bore directly:
D = √(4F / πP)
Where D is bore diameter in metres, F is force in newtons, and P is pressure in pascals. In the units used on the shop floor — force in kN, pressure in bar, diameter in mm — the same relationship becomes:
D (mm) = √(F (kN) × 10,000 / (π × P (bar)))
And the intermediate step, piston area, is simply A = πD²/4. Work in whichever form your datasheets use, but keep the units consistent throughout — the most common arithmetic error in this calculation is mixing newtons with bar.
Step 1: Establish the pressure available at the cylinder
The pump’s rated pressure is not the pressure available at the cylinder. Between the pump and the cylinder there are losses that reduce it: the relief valve setting, valve pressure drop, hose and pipe friction, filter restriction, pump wear, oil temperature, and any simultaneous actuator operation.
For sizing, use the pressure you can expect at the cylinder port while the machine is doing the work, not the maximum the system can produce. If the relief valve is set at 180 bar but the pump delivers only 150 bar at the required flow, calculate at 150 bar. Where practical, measure pressure at both cylinder ports during a loaded cycle — measuring both chambers also reveals whether return-side back pressure is reducing the net force.
| Pressure term | What it means for sizing |
|---|---|
| Normal working pressure | Use this for the routine bore calculation |
| Relief valve setting | The ceiling, not the working value |
| Maximum allowable cylinder pressure | A component limit, not a design target |
| Transient pressure peak | Sets the test pressure, not the bore |
| Test pressure | Typically 1.5 × working pressure |
Step 2: Compute the required piston area
Divide the required force by the available pressure to get the minimum piston area. Expressed in the metric shop-floor form:
A (mm²) = F (kN) × 10,000 / P (bar)
Remember to add a safety factor before this step, not after. The margin depends on how well the load is known, how severe the shock is, the duty cycle, and the consequences of failure — there is no single safety factor correct for every application, and the range below is a reasonable starting guide.
| Application | Typical safety factor |
|---|---|
| Static or light shock | 1.1 – 1.25 |
| Mobile equipment with real shock loading | 1.3 – 1.5 |
| Industrial presses and forming | 1.25 – 1.5 |
| Personnel-carrying or overhead lifting | 2.0 and above |
Do not stack several overlapping allowances for friction, shock and safety on top of each other without checking what each one covers. A 20% margin for shock and another 20% for safety is not automatically a 44% margin — and it may leave the rod undersized for buckling, which is a separate check entirely.
Step 3: Convert area to bore, then round up
Take the square root of 4A/π to get the minimum bore in millimetres. This gives a theoretical figure, not a purchasable one.
Standard bores follow the ISO 3320 preferred series. Always select the next standard bore above the calculated minimum. Rounding down leaves the cylinder unable to produce the required force at any pressure, and rounding to a nearby non-standard size restricts your sourcing of pistons, seals and barrels for the life of the machine.
ISO 3320 standard bore series
| Bore (mm) | Piston area (mm²) | Piston area (cm²) | Push force @160 bar | Push force @250 bar |
|---|---|---|---|---|
| 25 | 491 | 4.91 | 7.9 kN (0.8 t) | 12.3 kN (1.3 t) |
| 32 | 804 | 8.04 | 12.9 kN (1.3 t) | 20.1 kN (2.1 t) |
| 40 | 1,257 | 12.57 | 20.1 kN (2.1 t) | 31.4 kN (3.2 t) |
| 50 | 1,964 | 19.63 | 31.4 kN (3.2 t) | 49.1 kN (5.0 t) |
| 63 | 3,117 | 31.17 | 49.9 kN (5.1 t) | 77.9 kN (7.9 t) |
| 80 | 5,027 | 50.27 | 80.4 kN (8.2 t) | 125.7 kN (12.8 t) |
| 100 | 7,854 | 78.54 | 125.7 kN (12.8 t) | 196.3 kN (20.0 t) |
| 125 | 12,272 | 122.72 | 196.3 kN (20.0 t) | 306.8 kN (31.3 t) |
| 160 | 20,106 | 201.06 | 321.7 kN (32.8 t) | 502.7 kN (51.3 t) |
| 200 | 31,416 | 314.16 | 502.7 kN (51.3 t) | 785.4 kN (80.1 t) |
| 250 | 49,087 | 490.87 | 785.4 kN (80.1 t) | 1,227.2 kN (125.1 t) |
| 320 | 80,425 | 804.25 | 1,286.8 kN (131.2 t) | 2,010.6 kN (205.0 t) |
Tonnes shown are metric tonne-force (1 t = 9.81 kN) and are theoretical values at the stated pressure. Confirm against the manufacturer’s published ratings, which account for allowable working pressure and the specific cylinder series.
Step 4: Check the retract stroke separately
On a single-rod double-acting cylinder, the rod occupies part of the piston area. During retraction, pressure acts on the annulus only — piston area minus rod area:
Aannulus = π/4 × (D² − d²)
This means retract force is always lower than extend force, sometimes by half. Sizing on extend force alone is a classic error: the cylinder lifts the load but cannot lower it under control. If the critical load is carried on the return stroke — a pull, a hold-down, or a return under load — size for retract force.
Common bore and rod combinations at 200 bar
| Bore / rod (mm) | Extend force | Retract force | Retract as % of extend |
|---|---|---|---|
| 63 / 36 | 62.3 kN | 42.0 kN | 67% |
| 63 / 45 | 62.3 kN | 30.5 kN | 49% |
| 80 / 45 | 100.5 kN | 68.7 kN | 68% |
| 80 / 56 | 100.5 kN | 51.3 kN | 51% |
| 100 / 56 | 157.1 kN | 107.8 kN | 69% |
| 100 / 70 | 157.1 kN | 80.1 kN | 51% |
| 125 / 70 | 245.4 kN | 168.5 kN | 69% |
Choosing between two rod options for the same bore is a genuine trade-off: the smaller rod gives faster retraction and higher retract force, the larger rod gives more stability against buckling. Decide which of those the machine actually needs before specifying the rod.
Worked example: why rounding up matters
A machine must lift 10 tonnes at a system pressure of 160 bar at the cylinder. 10 tonnes is 98.1 kN.
- Required area: A = 98.1 × 10,000 / 160 = 6,131 mm²
- Minimum bore: D = √(4 × 6,131 / π) = 88.3 mm
- Next standard bore above 88.3 mm: 100 mm
- Verify: a 100 mm bore at 160 bar produces 125.7 kN, which is 28% above the 98.1 kN requirement
Now note what happens with the 80 mm bore, which is not the next size up but a tempting choice because it is closer to the calculated figure: at 160 bar it produces only 80.4 kN — 18% short of the load it is supposed to lift. An 80 mm bore would be the wrong cylinder even though it appears in the same part of the table.
This is why the rounding direction matters. Never round down, and never round to the nearest size: round up to the next standard bore, then verify the margin is acceptable.
Worked example: applying a safety factor
A lifting function must raise 6 tonnes at 200 bar, with shock loading present so a safety factor of 1.3 applies.
- Design force: 6 t = 58.9 kN; with a 1.3 factor, 76.5 kN
- Required area: A = 76.5 × 10,000 / 200 = 3,825 mm²
- Minimum bore: D = √(4 × 3,825 / π) = 69.8 mm
- Next standard bore: 80 mm
- Verify: an 80 mm bore at 200 bar produces 100.5 kN against the 76.5 kN design requirement — a 31% margin above the factored load
Note that a 63 mm bore produces 62.3 kN, which is less than the 76.5 kN factored requirement. Rounding 69.8 mm down to 63 mm would produce a cylinder that fails under the shock loading the safety factor was added to protect against.
What to verify after the bore is chosen
Rounding up to a standard bore does not complete the selection. Confirm each of the following before ordering.
- Net extension force after back pressure, friction and system losses
- Net retraction force, if the return stroke carries load
- Required operating pressure against the cylinder’s allowable pressure
- Oil flow demand — a larger bore consumes more oil for the same stroke, which changes speed at a fixed pump flow
- Rod buckling capacity — a separate check from bore, governed by stroke, rod diameter and mounting end fixity
- Installation envelope — the physical bore size the machine can accept
A standard bore does not mean a standard pressure rating
A 63 mm bore is available in several cylinder families, but bore size alone does not define pressure capability. ISO 6020 covers dimensional series for 16 MPa (160 bar) single-rod cylinders; ISO 6022 covers the 25 MPa (250 bar) series. These standards fix mounting dimensions and interchangeability — they do not mean every cylinder listed with a given bore is rated for the same pressure, mounting load or duty cycle. Always confirm the rated operating pressure, pressure peaks, test pressure, bore and rod combination, mounting limits and seal temperature range for the specific product.
Common bore sizing errors
| Error | Consequence |
|---|---|
| Using pump nominal pressure instead of delivered pressure | Cylinder oversized or, worse, undersized on a machine that never reaches its rating |
| Rounding the calculated bore down | Cannot produce the required force at any pressure |
| Rounding to the nearest size instead of the next size up | Force falls short of the load |
| Sizing only on extend force | Cylinder lifts but will not lower the load under control |
| Stacking several margins without checking overlap | Unnecessary cost, or a rod left undersized for buckling |
| Oversizing the bore for extra confidence | Higher oil consumption, slower cycle, bigger pump, higher cost |
The calculation in summary
Establish the real pressure available at the cylinder, add the safety factor to the required load, compute A = F/P, take D = √(4A/π), and round up to the next ISO 3320 standard bore. Then verify the retract force, the rod buckling capacity, the flow demand and the pressure rating before treating the selection as final.
That sequence takes a few minutes and prevents the two failures that account for most premature cylinder problems: a cylinder that cannot produce the force it was calculated for, and a cylinder that lifts but will not control the load on the way back.
Send the numbers and we will check them
If you have a load in tonnes or kN, a system pressure, and a stroke, send them with the machine type and whether the load is carried on the push or the return stroke. We will return a bore and rod recommendation, and flag which parameters still need confirming before production.
Frequently asked questions
How do I calculate hydraulic cylinder bore size?
Divide the required force by the available pressure to get the minimum piston area, convert that area to a diameter with D = √(4A/π), then round up to the next ISO 3320 standard bore. Add your safety factor to the load before starting, not after.
Why must the bore be rounded up to the next standard size?
Standard bores exist so pistons, seals and barrels stay available across suppliers. Rounding down produces a cylinder that cannot reach the required force; rounding to the nearest size rather than up can also fall short. Always round up and then verify the margin.
Does a larger bore always give more force?
At the same pressure, yes — piston area scales with the square of the bore. But a larger bore also requires more oil for each millimetre of stroke, so at a fixed pump flow it moves more slowly and may overload the pump. More force is not free; it comes from a larger cylinder, a bigger pump, and a higher cost.
How much safety factor should I use?
Between 1.1 and 1.25 for static loads, 1.3 to 1.5 with shock loading such as mobile equipment, and 2.0 or more for personnel-carrying or overhead lifting. The right margin depends on load accuracy, shock severity, duty cycle and the consequences of failure.
Can I use the theoretical force in a quotation?
Theoretical values are the starting point for comparison. A firm specification must confirm rated working pressure, allowable peaks, test pressure, rod and bore combination, mounting limitations, seal temperature range and cushioning capability against the manufacturer’s published data for the specific product.
Why is my calculated bore different from the cylinder already on the machine?
Most often because the existing cylinder was chosen for a lower safety margin, a different available pressure, or a different load geometry such as a lever or linkage that multiplies the required force. If you are replacing an existing cylinder and the calculated bore comes out smaller, the original was likely specified on extend force alone or at a lower margin. Match the original if you are replacing like for like, and size on retract force if the return stroke carries the load.