Hydraulic jack calculator (bottle jack)
This free hydraulic jack calculator gives the lifting capacity of a bottle jack from the force on the handle, or the hand force needed for a given load, together with the pump pressure, lift per stroke, number of strokes, oil volume and heights. The method reproduces two published textbook solutions, and a pumping simulation shows how the jack works stroke by stroke.
Key parameters at a glance
| Parameter | Definition | Main effect | Trade-off |
|---|---|---|---|
| Handle length l | Pivot to the point where the hand acts | Longer handle, lower hand force | Larger swing and handle travel |
| Plunger arm l₁ | Pivot to the plunger pin | Shorter arm, lower hand force | More strokes, larger swing angle |
| Plunger diameter d | Pump plunger | Smaller d, lower hand force | Less oil per stroke, more strokes |
| Ram bore D | Cylinder bore under the ram seal | Larger D, lower pressure | Bigger jack, more oil |
| Efficiency η | Friction in pins, seals and valves | Lower η, higher hand force | Pressure at load does not change |
| Extension screw C | Screw in the ram, turned by hand | Extra height without pumping | Slender part under load |
How to use the calculator
- Pick an example (typical 10 t jack or the textbook example) or enter your own dimensions.
- Choose the task: capacity from hand force, or hand force for a load.
- Read the result tiles and the table: pressure at load, force ratio, strokes and heights, with checks against the pressure and hand-force limits.
- Start the pumping simulation and drag the round grip at the handle end, or press Pump one stroke. Open the release valve to lower the ram; unscrew the extension screw for the remaining height.
- Print the result (Print / PDF, 3 pages A4) or check the formulas and sources in Method and data sources.
[Screenshot: fig4-calculator-screenshot]
How does a bottle jack work
A bottle jack is a small hydraulic press with a hand pump built into its base. On the down stroke the pump plunger pushes oil through the delivery check valve into the ram cylinder and the ram rises. On the up stroke the delivery valve closes, the load stays put, and the suction check valve lets oil flow from the reservoir into the pump. The reservoir is the space between the cylinder and the outer shell, a formed tube shaped like a bottle. Opening the release valve returns the oil to the reservoir and lowers the load.
[Figure: fig1-section-pumping]
[Figure: fig3-details-valve-plunger]
Hydraulic jack formula
The lever turns the hand force F into the plunger force F₁ = F · l / l₁. The plunger creates the pressure p = F₁ / (π · d² / 4), and by Pascal’s law the same pressure lifts the ram of bore D:
Q = η · F · (l / l₁) · (D / d)²
The product (l / l₁) · (D / d)² is the force ratio of the jack, typically 300 to 500 for a 10 t bottle jack. The price is travel: each plunger stroke s lifts the ram by only s · (d / D)².
Hydraulic jack lifting capacity: a worked example
Typical 10 t bottle jack (dimensions estimated, “Typical 10 t” in the example list), hand force 350 N:
| Quantity | Value |
|---|---|
| Handle l / plunger arm l₁ | 550 / 26 mm |
| Plunger d / stroke s, ram bore D | 11 / 20 mm, 50 mm |
| Force ratio | 437 |
| Lifting capacity Q (η = 0.65) | 99.4 kN (10.1 t) |
| Pressure at load | 506 bar |
| Lift per stroke / strokes for 145 mm | 0.97 mm / 150 |
| Oil for the full stroke | 285 cm³ |
| Height min / with ram / with screw | 220 / 365 / 445 mm |
Result: a 350 N push lifts 10 t. Cost: about 150 strokes and 500 bar in the cylinder. The pressure is the load divided by the ram area and does not depend on friction; friction only raises the hand force.
Hydraulic jack design: what to watch
- Hand force. A few hundred newtons is comfortable for continuous pumping. The calculator shows the handle travel and swing angle that come with a longer handle or a shorter arm.
- Pressure. Bottle jacks work at roughly 400 to 600 bar at rated load; the cylinder wall, seals and overload valve are sized for it.
- Fast approach. Many jacks use a two-stage pump: a large plunger lifts the ram quickly to the load, then a small one takes over under pressure.
The Pro version adds sizing of bore and plunger for an allowable hand force, a comparison of variants from standard bore and rod series, buckling of the ram and extension screw, a thick-wall check of the cylinder tube, the two-stage pump with its simulation, and a full calculation report.
[Figure: fig2-isometric-cutaway]
Limitations of the model
- Steady pumping: no oil compressibility, no leakage through the check valves (the stroke count is theoretical).
- One overall efficiency for the lever, seals and valves.
- No strength checks in the free version: ram buckling, cylinder wall and screw are in Pro.
- Allowable pressure and hand force are editable estimates, not values from a standard.
- The drawing is to scale for the entered dimensions; body, base, valves and handle proportions are typical.
Validation
The method follows Zieliński, Dźwignice i urządzenia transportowe, chapter 6.4, and reproduces the book’s example 6.2 exactly: 112.5 kN without losses and 73.1 kN with η = 0.65. It also matches problems VI-16 to VI-20 in Górecki, Zbiór zadań z dźwignic i urządzeń transportowych: hand force 185 N, plunger 36 mm, ram bore 39 cm (38 cm in the book, rounded down), capacity 80 kN and lifting time 94 s. A hand-pump check at 700 bar gives the published plunger diameter of 9.5 mm. Drawing proportions were checked against a published, fully dimensioned jack drawing set.
FAQ
How much force does a bottle jack need?
For a typical 10 t bottle jack, about 350 N on the handle at full load, with a force ratio near 440 and an overall efficiency of 0.65. Enter your own handle, plunger and ram dimensions to check your jack.
Why does a bottle jack need so many strokes?
The lift per stroke equals the plunger stroke times (d / D)². With an 11 mm plunger and a 50 mm ram it is under 1 mm, so a 145 mm ram stroke takes about 150 strokes. A two-stage pump shortens the empty approach.
What pressure is inside a bottle jack?
The load divided by the ram area. A 10 t load on a 50 mm ram gives about 500 bar. Friction does not change this pressure; it only increases the hand force.
What efficiency should I use for a hydraulic jack?
The textbook average is 0.65. It covers friction in the lever pins, the plunger and ram seals and the valves. A well-kept jack can be better; a worn one worse.
Can I use the calculator for a hydraulic press with a hand pump?
Yes. The same relations apply: pump plunger, lever and cylinder bore. Enter the cylinder bore as D.
A short history
Joseph Bramah patented the hydraulic press in 1795, applying Pascal’s principle. The portable version came from Richard Dudgeon in New York: his US patent 8,203 of 8 July 1851, titled “Portable Hydraulic Press”, describes a hollow ram that holds the liquid, a force pump inside it, and a handle that, pushed further down, opens the valves to lower the load. Today’s bottle jack moves the reservoir into an outer shell and the pump into the base, but works the same way.
Hydraulic presses, workshop cranes and lifting equipment as complete CAD projects: [Link: CAD projects]. Need a jack, press or cylinder designed for your application? [Link: contact]