Power screw efficiency calculator
See how much of your effort a square-thread screw turns into lift: a 5° lead angle with a friction coefficient of 0.15 gives an efficiency of just over a third, and the screw holds its load by itself. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Lead angle
- 5
- Friction coefficient
- 0.15
- Efficiency
- 0.3635564002 fraction
- Efficiency percent
- 36.3556400155
- Lead angle deg
- 5
- Lead angle rad
- 0.0872664626
This power screw efficiency calculator finds the square-thread raising efficiency of a power screw when you already know the lead angle and the thread friction coefficient. The closed form is eta equals the tangent of the lead angle over the tangent of that angle plus the friction angle, and the friction angle is simply the arctangent of mu. That identity is the machine-design standard for a square thread with collar friction neglected, the first number a designer or student wants before choosing a jack, vise, C-clamp, or linear actuator. Enter the lead angle in degrees or radians and a non-negative friction coefficient; the tool returns efficiency as a fraction and as a percent, both angle conversions, the friction angle, and whether the screw is self-locking or overhauling.
What screw efficiency means and what you get
A power screw converts rotary effort into axial force along a helix. Square-thread raising efficiency is the ratio of ideal torque without friction to the actual torque needed to raise a load, and for a square thread with no collar that ratio collapses to a function of two angles only. If alpha is the lead angle of the helix and phi is the friction angle whose tangent is the thread coefficient mu, then eta equals tan of alpha over tan of alpha plus phi.
The same number can be written without naming phi as tan of alpha times one minus mu times tan of alpha, all over tan of alpha plus mu. Efficiency is a dimensionless fraction between zero and one; one hundred percent would require a frictionless thread, which this calculator reports when mu is exactly zero and the lead angle is valid. Search intent clusters around power screw efficiency calculator, lead angle and friction coefficient, square thread jack efficiency, and whether a power screw is self-locking.
Where this efficiency belongs in study, design, and software
Students meet eta equals tan of alpha over tan of alpha plus phi when a machine-elements textbook introduces jackscrews, when a problem gives a lead angle and a dry or lubricated steel coefficient and asks whether the screw will hold a load by itself, or when a contest problem insists on the square-thread formula before anyone mentions Acme or collar washers.
Teachers can pre-generate answer keys for modest angle and mu pairs without trusting opaque calculator apps that silently treat the lead as a pitch in millimetres or forget that self-locking is tan of alpha at most mu, not a magic four-degree rule. Developers call the same contract from scripts to seed deterministic test vectors for mechanism simulators, to normalize user-entered helix data before a torque sketch, or to satisfy programming-challenge statements that demand a fraction rather than a hand-waved percent.
First-order design checks use this bound when only the geometry angle and a handbook friction coefficient are known, before mean diameter, lead, collar radius, or thread angle are modeled. Pair it with a thread-pitch converter when you still need to turn lead and diameter into an angle, and with a torque helper when the next question is how large a wrench the jack needs. This landing will not invent an Acme secant correction or a collar term: those are different searches and different contracts.
What you can do with it
Homework and machine-design checks
Compute square-thread raising efficiency from a textbook lead angle and friction coefficient before grading jackscrew worksheets.
Self-locking screening for jacks and clamps
See whether tan(α) ≤ μ so a jack, vise, or C-clamp holds the load when the input torque is removed.
FAQ
What does the power screw efficiency calculator cost?
It is free in your browser on this page.
How is square-thread power screw efficiency defined?
Raising efficiency with collar friction neglected is η = tan(α) / tan(α + φ), where α is the lead angle and φ = arctan(μ) is the friction angle from the thread coefficient μ. The result is returned as a fraction and as a percent.
When is a power screw self-locking?
The screw is reported self-locking when tan(α) ≤ μ, equivalently when the lead angle does not exceed the friction angle. Otherwise it is flagged overhauling: the load can lower itself if the input torque is removed.
Can I enter the lead angle in radians?
The default is deg, matching typical machine-design tables.
Does this include Acme thread angle or collar friction?
No. This landing evaluates the square-thread identity from lead angle and thread μ only. An Acme correction replaces μ with μ / cos(β), and a collar adds a second friction radius; both are different models and out of scope here.
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/power-screw-efficiency \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"lead_angle":5,"friction_coefficient":0.15}'const res = await fetch("https://api.kit.forhosting.com/eng/power-screw-efficiency", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"lead_angle": 5,
"friction_coefficient": 0.15
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/eng/power-screw-efficiency",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"lead_angle": 5,
"friction_coefficient": 0.15
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/eng/power-screw-efficiency", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"lead_angle":5,"friction_coefficient":0.15}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"lead_angle":5,"friction_coefficient":0.15}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/eng/power-screw-efficiency", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"lead_angle": 5,
"friction_coefficient": 0.15
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "eng.power_screw_efficiency",
"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.
Limits
max_lead_angle_deg | 90 |
max_friction_coefficient | 10 |
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
Zero or right-angle lead, a negative friction coefficient, and combinations where the lead angle plus the friction angle reaches ninety degrees are rejected with invalid_input. Successful API calls cost $0.002; failed validation is not charged.
What power screw efficiency means and what the response contains
People who already have alpha and mu want that textbook eta as structured JSON, not a torque from load and mean diameter, not an Acme correction that replaces mu with mu over cosine of the thread half-angle, and not a collar-friction add-on. The response echoes the validated lead angle in the unit you sent, repeats it in degrees and in radians, echoes mu, reports the friction angle in both units, flags self_locking when tan of alpha is at most mu, flags overhauling otherwise, and labels the method square_thread_power_screw. There is no look-up of steel-on-steel handbook values, no automatic conversion from lead and mean diameter into alpha, and no Monte Carlo sampling of surface finish: the engine either evaluates the closed form inside the supported range or rejects the input with invalid_input naming the field that failed.
How lead angle and friction are read and how the result stays reproducible
In degrees the lead angle must be strictly between zero and ninety; in radians it must be strictly between zero and pi over two. A zero lead is not a helix, and a right angle makes the tangent blow up, so both ends of the interval are rejected rather than returning a silent nonsense efficiency. Friction coefficient must be at least zero and at most ten; a negative mu is not a Coulomb thread model. Floating fields are rounded to twelve decimal places with negative zero collapsed, so the same pair always serializes the same way across JavaScript engines. The preferred field for the helix is lead_angle, but aliases alpha, helix_angle, lead, and lambda are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. The preferred field for thread friction is friction_coefficient, with aliases mu, mu_thread, friction, and coefficient. Both must be finite numbers or numeric strings that parse as finite decimals, including optional scientific notation; missing fields, empty strings, letters, mixed tokens, NaN, and Infinity fail immediately with invalid_input and are not billed. Optional angle_unit is a closed pair deg or rad and defaults to deg, so a classroom example written as five degrees does not have to name the unit. When the sum of the lead angle and the friction angle reaches or exceeds ninety degrees, tan of alpha plus phi is undefined or the algebraic form goes non-positive, and the request fails instead of inventing a negative efficiency. After those checks the engine evaluates tan of alpha over tan of alpha plus arctan of mu and cross-checks the algebraic twin; disagreement beyond a tight tolerance is treated as invalid_input rather than published.
Where this efficiency belongs in study, design, and software
Product and education tools use the endpoint when a learner types five degrees and zero point one five and the interface must show both the efficiency and the self-locking flag. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns.
Integration use cases
Deterministic fixtures for mechanism software
Generate reproducible η, friction-angle, and self-locking flags for unit tests and teaching demos that must not invent the tangent identity.