Screw jack MA calculator
See how much a screw jack multiplies your effort: a 0.5 m handle on a 0.005 m pitch gives an ideal advantage of 2π times 100, so each newton of effort lifts over six hundred. Friction is left out on purpose. Free in your browser.
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- Your data stays on your device
Run — free
Worked example
- Lever arm
- 0.5
- Pitch
- 0.005
- Mechanical advantage
- 628.318530718
- Ideal mechanical advantage
- 628.318530718
- Effort path per rev
- 3.1415926536
- Load path per rev
- 0.005
A screw jack multiplies force by turning a long operating lever while a threaded screw advances a small pitch per revolution. In the ideal textbook model the work done by effort around the lever circle equals the work done on the load over one turn, which rearranges to ideal mechanical advantage IMA equals two pi times lever arm L divided by screw pitch p. Students use this closed form for machine-design homework; teachers need a deterministic oracle for answer keys; shop and plant staff size a jack before applying friction deratings and safety factors. This calculator accepts a positive lever arm and a positive pitch in matching length units, optionally a non-negative load, and returns ideal IMA, effort path per revolution, load path per revolution, and ideal effort force when load is supplied. Zero or negative pitch and lever arm are rejected so callers never divide by zero or invent infinite advantage.
How ideal screw jack mechanical advantage is defined
Begin with a screw jack whose nut or load platform rises by the pitch p of the screw for every full revolution of the operating handle. The effort is applied at a radial distance L from the screw axis, so over one revolution the effort force travels a circular path of circumference two pi L. In the ideal model there is no friction on the threads or collar, the screw and lever are rigid, and work input equals work output.
Equating effort times two pi L to load times p yields IMA equals load over effort equals two pi L over p. Larger lever arms and finer pitches increase ideal advantage; coarser pitches and shorter handles decrease it. For single-start screws the pitch equals the lead; multi-start screws advance one lead per turn, and if you know lead rather than pitch you should pass lead as the pitch field for this kinematic formula.
Real jacks have actual mechanical advantage below the ideal value because of thread friction, collar friction, and efficiency losses; those effects need measured effort or a friction-angle model and are intentionally outside this page. Load, when provided, must be finite and non-negative so weight is never silently negated.
Where screw jack MA calculators show up in real work
Secondary-school and introductory university machine-design and statics courses assign screw jack free-body and work-energy problems, ask for ideal effort before efficiency problems, and expect IMA from L and p on a single page of notes. Vehicle recovery and plant maintenance training staff size a bottle jack or floor-jack style screw from handle length and thread pitch as a first filter before applying safety factors and real friction deratings.
Maker spaces and STEM outreach programs convert a measured pitch and lever length into expected pull force so students can compare prediction with a spring scale on a classroom jack model. Mechanical design notes often state ideal IMA next to measured AMA when documenting jack or leadscrew tests. If you later need actual mechanical advantage from measured effort, screw efficiency with friction angle, inclined-plane force reduction, or pulley strand IMA, treat those as separate search intents and landings rather than overloading this ideal screw jack mechanical advantage calculator page.
What you can do with it
Jack and leadscrew lab prep
Predict ideal effort for a measured pitch and handle length before measuring real effort and efficiency with a spring scale.
Plant and shop sizing drafts
Convert operating lever length and thread pitch into ideal mechanical advantage as a first filter before safety factors and friction deratings.
FAQ
What is the ideal mechanical advantage of a screw jack?
In the ideal (frictionless) model, IMA equals 2πL/p where L is the operating lever arm length and p is the screw pitch (axial advance per revolution). Effort force is load divided by IMA when load is known.
What happens if pitch is zero?
Zero pitch would imply infinite mechanical advantage and is physically meaningless for this formula.
Does this include friction or efficiency?
No. This page returns ideal IMA only from kinematics. Actual mechanical advantage and efficiency with thread friction are separate problems and landings.
What does it cost?
The browser tool is free and runs locally.
How much effort do I need to lift a load with a screw jack?
Divide the load by the ideal mechanical advantage; enter the load and the tool does it for you. That is the frictionless minimum, so a real jack needs more effort once thread and collar friction are counted.
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/eng/screw-jack-ma \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"lever_arm":0.5,"pitch":0.005}'const res = await fetch("https://api.kit.forhosting.com/eng/screw-jack-ma", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"lever_arm": 0.5,
"pitch": 0.005
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/eng/screw-jack-ma",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"lever_arm": 0.5,
"pitch": 0.005
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/eng/screw-jack-ma", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"lever_arm":0.5,"pitch":0.005}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"lever_arm":0.5,"pitch":0.005}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/eng/screw-jack-ma", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"lever_arm": 0.5,
"pitch": 0.005
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "eng.screw_jack_ma",
"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 ideal screw jack mechanical advantage is defined
The pipeline is deterministic floating-point arithmetic: no random seeds, no wall-clock timestamps, no network calls, and no model drift, so identical inputs always produce identical JSON. Lever arm and pitch must be finite and strictly positive; zero pitch would imply infinite IMA and is rejected with invalid_input.
What you send and what you get back
Both lengths must use the same unit—metres with metres, millimetres with millimetres, inches with inches—because IMA is dimensionless and the engine performs no unit conversion. Classic checks include L equals zero point five and p equals zero point zero zero five for IMA equal to two pi times one hundred, or L equals four hundred millimetres and p equals five millimetres with a two thousand unit load for effort equal to load over that same IMA. Wire the free browser form for homework and quick sanity checks, then call the identical contract from scripts when you need bulk answer keys, lab prep sheets, or grading oracles. Keep length units consistent across a multi-step lab so reports stay coherent without hidden conversions. Send two required finite numbers under the fields lever_arm and pitch. Lever_arm is the operating handle length L from the screw centreline to the effort point; aliases include arm, L, effort_arm, lever, and handle_length. Pitch is the axial advance p per revolution; aliases include p, screw_pitch, lead, and thread_pitch. Optional load (aliases W, weight, force) is the weight or force to lift or hold; when present and non-negative the response includes effort_force as load divided by IMA in the same force unit. Missing fields, non-numeric strings, NaN, Infinity, zero or negative lever_arm or pitch, and negative load fail with invalid_input and are not charged. On success the response echoes cleaned lever_arm and pitch, mechanical_advantage and ideal_mechanical_advantage both equal to two pi L over p, effort_path_per_rev as two pi L, load_path_per_rev as p, model set to ideal, a units hint object, method screw_jack_ideal_ma, and the formula string IMA equals two pi L over p. When load is supplied, load and effort_force appear and the formula string also states F_e equals W over IMA. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where screw jack MA calculators show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Integration use cases
Homework and exam answer keys
Compute ideal IMA = 2πL/p from lever arm and screw pitch so students and auto-graders share one closed-form ground truth.
Technical questions
Must lever_arm and pitch use the same units?
Yes. Both must be positive finite lengths in the same unit (m, mm, in, …). The engine does not convert units; IMA is dimensionless.