Hydraulic lift calculator
Pistons of 2 and 10 cm turn a 100 N push into 2,500 N, because the force grows with the square of the diameter ratio. Enter both diameters in the same unit and the input force to get the ideal mechanical advantage and output force. Free in your browser.
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Worked example
- Input diameter
- 2
- Output diameter
- 10
- Input force
- 100
- Diameter ratio
- 5
- Mechanical advantage
- 25
- Output force
- 2,500
- Model
- ideal
A hydraulic lift uses pressure transmitted through a confined fluid to turn a modest force on a small piston into a larger force on a larger piston. This calculator takes the input-piston diameter, output-piston diameter, and applied input force, then returns the ideal mechanical advantage and output force. Both diameters may use millimetres, centimetres, inches, or another length unit as long as they use the same unit. The force result uses the same unit as the input force. The calculation follows Pascal's law, assumes ideal pressure transfer, and clearly rejects a zero input diameter instead of producing an undefined result.
How piston diameter determines mechanical advantage
Pascal's law states that pressure applied to a confined fluid is transmitted throughout that fluid. Pressure is force divided by piston area, so an ideal hydraulic lift satisfies input force divided by input area equals output force divided by output area. Circular piston area is proportional to diameter squared: area equals pi times diameter squared divided by four.
When the output-to-input area ratio is formed, pi and four cancel, leaving mechanical advantage equal to the square of output diameter divided by input diameter. That square is important. If the output piston is twice the input diameter, its area is four times as large and the ideal output force is four times the input force.
If it is five times the diameter, the ideal force multiplier is twenty-five.
Entering compatible values and interpreting the result
The two diameters must be expressed in the same length unit, but that unit is your choice. A pair of 20 millimetres and 100 millimetres gives the same ratio as 2 centimetres and 10 centimetres because only their ratio enters the formula. All three values must be finite numbers.
Diameters must be greater than zero, while input force may be zero but cannot be negative. Negative diameters are also rejected rather than silently converted to magnitudes. For example, diameters of two and ten give a diameter ratio of five and a mechanical advantage of twenty-five; an input force of one hundred therefore gives an ideal output force of two thousand five hundred in the same force unit.
Ideal predictions, real equipment, and safe use
The returned output is a theoretical benchmark, not a rated lifting capacity. Real hydraulic systems lose useful force through seal friction, fluid viscosity, pressure drops in hoses and valves, leakage, piston misalignment, and deformation of components. Pump limits, cylinder stroke, reservoir volume, temperature, duty cycle, mounting geometry, side loads, and mechanical linkage ratios can also control whether a lift performs safely.
Manufacturers specify working pressure, proof pressure, load ratings, safety factors, inspection intervals, and compatible fluids; those limits take precedence over a result from this calculator. Use the ideal value to check classroom exercises, compare cylinder sizes, establish an upper bound for preliminary design, or identify suspicious measurements in a lab. For engineering selection, apply documented efficiency and safety factors, verify the cylinder areas from actual bore diameters, and have the complete system reviewed under the standards that govern the application.
Conservation of volume also means force multiplication trades against travel: when the output piston has twenty-five times the area, it ideally moves one twenty-fifth as far as the input piston for equal displaced fluid volume. The capability intentionally does not calculate stroke, pressure, efficiency, or safe working load because those require additional inputs and assumptions. Its deterministic scope is the diameter-based ideal mechanical advantage and corresponding ideal output force, with no network calls, random values, or time-dependent behavior.
What you can do with it
Check a physics exercise
Turn two piston diameters and an applied force into the ideal area ratio and output force for a Pascal's-law problem.
Compare cylinder sizes
See how changing the output bore changes theoretical force multiplication before adding efficiency and safety factors.
Prepare a hydraulic lab
Create an ideal reference value to compare with measured output force and discuss losses in real apparatus.
FAQ
What formula does the hydraulic lift calculator use?
It uses MA = (D_out / D_in)^2 and F_out = F_in × MA, derived from equal pressure and circular piston areas.
Do both piston diameters need the same unit?
Yes. They may both be millimetres, inches, or another length unit, but mixing units produces an incorrect ratio.
Does output force include hydraulic losses?
No. It is an ideal theoretical force. Real output is lower because of friction, leakage, pressure drops, and other losses.
Why does doubling the piston diameter quadruple the force?
Because the force follows the piston area, and area grows with the square of the diameter. An output piston twice as wide as the input one has four times the area, so the ideal output force is four times larger.
Does the calculator tell me how far the big piston moves?
No. It is an ideal static model of force multiplication only: it does not estimate piston travel, lifting speed or energy lost. The result is a theoretical benchmark, not the rated capacity of a real lift.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/mech/hydraulic-lift-advantage \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"input_diameter":2,"output_diameter":10,"input_force":100}'const res = await fetch("https://api.kit.forhosting.com/mech/hydraulic-lift-advantage", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"input_diameter": 2,
"output_diameter": 10,
"input_force": 100
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/hydraulic-lift-advantage",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"input_diameter": 2,
"output_diameter": 10,
"input_force": 100
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/hydraulic-lift-advantage", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"input_diameter":2,"output_diameter":10,"input_force":100}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"input_diameter":2,"output_diameter":10,"input_force":100}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/hydraulic-lift-advantage", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"input_diameter": 2,
"output_diameter": 10,
"input_force": 100
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.hydraulic_lift_advantage",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How piston diameter determines mechanical advantage
The calculator reports this dimensionless area ratio as mechanical_advantage, then multiplies it by input_force to obtain output_force. It also reports the unsquared diameter_ratio to make the intermediate relationship easy to inspect. This is an ideal static model: it describes force multiplication through equal fluid pressure and does not estimate how far either piston travels, how quickly it moves, or how much energy is lost.
Entering compatible values and interpreting the result
Provide input_diameter for the smaller driving piston, output_diameter for the driven piston, and input_force for the applied effort. Input force can be in newtons, pounds-force, kilonewtons, or another force unit; output_force remains in that same unit because mechanical advantage has no unit. A zero input diameter receives an invalid_input error with a specific explanation because the formula would divide by the square of zero. On success, check mechanical_advantage for the ideal force multiplier and output_force for the theoretical force available at the output piston. API requests cost $0.002 per successful item.
Technical questions
What happens when the input diameter is zero?
The request fails with invalid_input because the area ratio would require division by the squared input diameter.
What does an API calculation cost?
A successful API request costs $0.002 per item. The browser calculator is free to run.