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Linear actuator force calculator

A motor torque of 1 N·m on a screw with a 5 mm lead at 0.9 efficiency pushes with more than 1000 N. Enter torque, lead and efficiency to get the axial force of a lead-screw or ball-screw actuator. Free in your browser.

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Worked example

If you enter

Torque: 1
Screw lead: 0.005
Efficiency: 0.9

You get

Force: 1,130.97335529 N

This linear actuator force calculator returns the axial output force of a lead-screw or ball-screw actuator in newtons from three drivetrain numbers: motor torque in newton-metres, screw lead in metres per revolution, and drivetrain efficiency as a dimensionless fraction. It applies the work-balance identity that one revolution of the screw converts two-pi times torque into force times lead, then scales by efficiency so friction, gearing, and nut losses are not ignored.

How a turning screw becomes a straight push

A rotary motor turns a screw; a nut on that screw converts rotation into a straight push or pull. Over one full revolution the motor delivers work equal to torque times two pi radians, while the nut advances one lead and the axial force does work equal to force times that lead. Efficiency is the ratio of useful axial work to motor work, so rearranging gives the closed form used here: force equals two pi times efficiency times torque, divided by lead.

Lead is the axial travel per revolution, not the pitch of a multi-start thread counted the wrong way and not a millimetre figure still wearing a millimetre label: five millimetres per turn is 0.005 metres, and sending 5 would understate the force by a factor of a thousand. Efficiency is a fraction, typically 0.3 to 0.5 for a sliding Acme or trapezoidal screw and 0.85 to 0.95 for a ball screw with a modest gearbox; ninety percent is 0.9, not 90.

Force grows linearly with torque and with efficiency, and it falls as the lead gets coarser: doubling torque doubles thrust, doubling lead halves thrust for the same motor. A vanishing or reversed lead would send force to infinity or reverse the geometry of the screw, and a zero or negative efficiency would claim the drivetrain creates energy or dumps more than it receives, so those cases fail instead of emitting infinity.

What to enter and what comes back

Screw lead must be strictly positive: zero or negative lead is not a physical helix advance in this model. Efficiency must be strictly positive and at most one: zero or negative efficiency is rejected, and a value above one is almost always a percent sent by mistake, which this calculator refuses rather than multiplying thrust by ninety. Torque may be zero, which yields zero force, or negative, which models reverse or retracting torque and yields a signed force of the same sign.

Magnitude ceilings keep pathological teranewton-metre motors and kilometre leads from overflowing isolate arithmetic while still covering classroom millimetre screws and ordinary industrial jacks. Failed validation does not consume balance. Keep requests in SI end to end, convert millimetre drawings and percent datasheets before calling, and pin the newton value in tests so homework checks, LMS plugins, and edge workers stay reproducible.

Who needs a linear actuator force figure

Machine-design classrooms and tutoring platforms use a linear actuator force calculator so learners can check newton results for arbitrary torque, lead, and efficiency without mixing millimetres with metres and without forgetting the two-pi conversion from rotation to translation. Exam-prep generators need a deterministic oracle that marks wrong a zero lead or a negative efficiency instead of silently returning infinity that a buggy grader might treat as success. Automation engineers size electric cylinders, scissor-lift screws, and press actuators with this analytic baseline before buying a motor or opening a vendor spreadsheet.

Failed validation does not consume balance. Keep torque in newton-metres, convert millimetre leads to metres, send efficiency as a fraction, and you get reproducible newtons for homework, CAD plugins, and edge workers without standing up a multi-body dynamics solver of your own. Holding brakes, column buckling, and reflected inertia remain outside this identity, so treat the number as the classic work-balance thrust rather than a full actuator selection report.

What you can do with it

Electric-cylinder and jackscrew sizing

Estimate axial thrust of a ball-screw or Acme actuator from catalogue torque, lead, and drivetrain efficiency before buying a motor or opening a vendor spreadsheet.

FAQ

How do I compute the force of a linear actuator?

Send finite torque T in N·m, a positive screw lead L in metres per revolution, and a positive efficiency η no greater than 1.

What happens if screw lead or efficiency is zero or negative?

A zero or negative lead is not a physical advance per turn, and a zero or negative efficiency is not a physical drivetrain; those failures are not billed.

Is screw lead in millimetres or metres?

Inputs are SI metres per revolution. Convert a 5 mm lead to 0.005 before calling; sending 5 would understate the force by a factor of one thousand.

Should efficiency be a percent or a fraction?

Send a dimensionless fraction in (0, 1]. Ninety percent is 0.9. Values above 1 are rejected so a percent is not silently treated as a 90× multiplier.

What efficiency should I use for an Acme screw or a ball screw?

A sliding Acme or trapezoidal screw is typically 0.3 to 0.5, and a ball screw with a modest gearbox 0.85 to 0.95. Enter it as a fraction: the force grows in direct proportion to the efficiency.

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

POSThttps://api.kit.forhosting.com/phys/linear-actuator-force

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/phys/linear-actuator-force \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"torque":1,"screw_lead":0.005,"efficiency":0.9}'

const res = await fetch("https://api.kit.forhosting.com/phys/linear-actuator-force", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "torque": 1,
    "screw_lead": 0.005,
    "efficiency": 0.9
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/phys/linear-actuator-force",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "torque": 1,
    "screw_lead": 0.005,
    "efficiency": 0.9
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/linear-actuator-force", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"torque":1,"screw_lead":0.005,"efficiency":0.9}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"torque":1,"screw_lead":0.005,"efficiency":0.9}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/linear-actuator-force", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "torque": 1,
  "screw_lead": 0.005,
  "efficiency": 0.9
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "phys.linear_actuator_force",
  "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

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Limits

`max_abs_torque`	1000000000000
`max_abs_screw_lead`	1000

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

The engine is fully deterministic: it insists that screw lead and efficiency are strictly positive, rejects zero or negative values as invalid_input, and never calls a network, a clock, or a random generator.

What F = 2π η T / L means for a lead-screw actuator

The payload echoes the three inputs, reports force in newtons, and tags the method as lead-screw work so a notebook can cite the identity next to the number. Pair the response with your own column-buckling or duty-cycle checks if the next question is whether the screw will buckle or overheat; this endpoint computes axial force only.

Input contract, response shape, and error behaviour

POST a JSON body with three required fields: torque, the motor torque T in newton-metres; screw_lead, the axial travel L in metres per revolution; and efficiency, the drivetrain fraction η. Each field may arrive as a JSON number or as a numeric string. Aliases T, motor_torque and input_torque, lead, L and lead_m, and eta, η and drivetrain_efficiency are accepted so lab notebooks and CAD exports map without renaming columns. Missing fields, empty strings, and non-finite values fail with invalid_input naming the field. On success the body echoes torque, screw_lead, and efficiency, reports force in newtons, and includes formula F = 2π·η·T / L, method lead_screw_work, and unit N.

Integration use cases

Homework and exam checks

Enter motor torque, screw lead in metres per revolution, and efficiency, compare newton results with hand work, and get a clear invalid_input when lead or efficiency is zero or negative.

Notebooks and CAD fixtures

Pin a reproducible force in newtons from T, L, and η in calibration scripts without importing a multi-body dynamics library.

Technical questions

What does the linear actuator force calculator cost?

The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.

Read the full KIT documentation →

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