Screw jack mechanical advantage calculator
A 0.5 m handle on a screw with a 0.005 m pitch gives an ideal mechanical advantage of 2π × 100: your hand travels a whole circle while the load rises one pitch. Enter both lengths in the same unit to size a jack or leadscrew. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- 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 multiplies force by turning a long operating lever while the threaded shaft advances only 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 mechanical advantage MA equals two pi times lever arm length divided by thread pitch. Students use this closed form for machine-design homework; teachers need a deterministic oracle for answer keys; shop and plant staff size a jack or leadscrew before applying friction deratings and safety factors. This calculator accepts a positive lever arm and a positive pitch in matching length units and returns ideal MA, effort path per revolution, and load path per revolution. Zero pitch is rejected so callers never divide by zero or invent infinite advantage.
How screw mechanical advantage is defined from arm and pitch
Begin with a screw or screw jack whose load platform rises by the thread pitch p for every full revolution of the operating handle. The effort is applied at a radial distance equal to the lever arm from the screw axis, so over one revolution the effort force travels a circular path of circumference two pi times the arm length. 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 times arm to load times pitch yields MA equals load over effort equals two pi times arm over pitch. 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 screws 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.
Where screw mechanical advantage calculators show up in real work
Secondary-school and introductory university machine-design and statics courses assign screw free-body and work-energy problems, ask for ideal effort before efficiency problems, and expect MA from lever arm and pitch 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 force multiplication so students can compare prediction with a spring scale on a classroom jack model. Mechanical design notes often state ideal MA next to measured actual mechanical advantage 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 with friction tables or multi-machine compound machines that would dilute the closed-form arm-and-pitch contract.
What you can do with it
Jack and leadscrew lab prep
Predict ideal force multiplication 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 mechanical advantage of a screw?
In the ideal (frictionless) model, MA equals 2π·arm/pitch where arm is the operating lever arm length and pitch is the thread pitch (axial advance per revolution).
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 MA 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.
Should I enter the pitch or the lead for a multi-start screw?
Enter the lead. A multi-start screw advances one lead per turn, and that is the distance the formula needs. For an ordinary single-start screw the pitch and the lead are the same.
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/screw-mechanical-advantage \
-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/mech/screw-mechanical-advantage", {
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/mech/screw-mechanical-advantage",
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/mech/screw-mechanical-advantage", 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/mech/screw-mechanical-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
{
"lever_arm": 0.5,
"pitch": 0.005
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.screw_mechanical_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 screw mechanical advantage is defined from arm and pitch
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 MA and is rejected with invalid_input so automation never silently invents unbounded force multiplication.
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 MA is dimensionless and the engine performs no unit conversion. Zero pitch is called out explicitly because MA equals two pi times arm over pitch would become infinite. Classic checks include arm equals zero point five and pitch equals zero point zero zero five for MA equal to two pi times one hundred, or arm equals four hundred millimetres and pitch equals five millimetres for the same dimensionless ratio when units match. 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 between millimetres and metres mid-calculation. Send two required finite numbers under the fields lever_arm and pitch. Lever_arm is the operating handle length from the screw centreline to the effort point; aliases include arm, L, effort_arm, lever, and handle_length. Pitch is the axial advance per revolution; aliases include p, screw_pitch, lead, and thread_pitch. Missing fields, non-numeric strings, NaN, Infinity, zero or negative lever_arm, and zero or negative pitch 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 times arm over pitch, effort_path_per_rev as two pi times arm, load_path_per_rev as pitch, model set to ideal, a units hint object, method screw_ma_2pi_arm_over_pitch, and the formula string MA equals two pi times arm over pitch. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where screw mechanical advantage 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 MA = 2π·arm/pitch from lever arm and thread 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; MA is dimensionless.