Gear output torque calculator
An input torque of 50 N·m through a 4:1 reduction becomes 200 N·m at the driven shaft, while speed drops to 0.25 of the input. Enter input torque and gear ratio to get the ideal output, with losses left out. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Input torque
- 50
- Gear ratio
- 4
- Output torque
- 200
- Speed ratio
- 0.25
- Torque multiplication
- 4
- Transmission
- reduction
When two gears mesh, the pair is a torque transformer as well as a speed changer. Power conservation on an ideal shaft-to-shaft mesh says the product of torque and angular speed is the same on both sides, so driven-shaft torque equals driver-shaft torque multiplied by the gear ratio, with mesh friction, bearing drag, and windage set aside. Students checking a machine-elements problem, designers sizing a reducer output shaft, and automation scripts that already know the catalogue ratio all need that one product without standing up a full drivetrain model or inventing an efficiency they were not given. This gear output torque calculator takes input torque and a strictly positive gear ratio and returns the ideal output torque, the complementary speed ratio, and whether the mesh is a reduction, an overdrive, or one-to-one. Invalid input is not billed.
Why T_out equals T_in times the gear ratio on an ideal pair
A single external or internal gear pair connects two shafts through a fixed ratio of teeth. If N2 is the tooth count on the driven gear and N1 the count on the driver, the classical gear ratio GR equals N2 over N1, which is also the inverse speed ratio ω_in over ω_out. Instantaneous power at a shaft is torque times angular speed.
When losses are neglected, power in equals power out, so T_in times ω_in equals T_out times ω_out. Rearrangement immediately gives T_out equals T_in times GR. That identity is the first number a machine-elements course asks for after the ratio is known: a 4:1 reduction multiplies torque by four and cuts speed to one quarter; a 0.5 overdrive halves torque and doubles speed; a one-to-one mesh copies torque and speed.
The same product applies to spur, helical, and simple bevel pairs when you already have GR from teeth, from a measured speed drop, or from a catalogue page—you do not re-count teeth here. Efficiency is taken as one, so the result is the ideal geometric multiplication used in textbooks before anyone applies a mesh-efficiency factor. Negative input torque is accepted as reverse or braking torque and is scaled by the same positive ratio; zero input correctly yields zero output.
A non-positive gear ratio is rejected because it would not describe a physical mesh. This calculator does not fold in a final-drive axle, a multi-stage gearbox, or vehicle wheel radius; it answers the single-pair question only.
What to enter and what you get back
Numeric results are rounded to twelve decimal places for stable goldens and automation. Example: input torque fifty and gear ratio four yields output torque two hundred and speed ratio one quarter, because a four-to-one reduction multiplies torque by four. Keep torque units consistent: if T_in is in N·m then T_out is in N·m; if you work in lbf·ft the product is still in lbf·ft.
Pair the result with your own shaft diameter and allowable shear stress if you need a strength check; this capability solves ideal kinematics only and does not size keys, hubs, or bearings.
Who needs gear output torque
Machine-design courses and exam generators routinely ask for driven-shaft torque from a given pinion torque and a stated ratio; a deterministic oracle marks a zero or inverted ratio and never invents a mesh efficiency the problem did not supply. Reducer and gearbox vendors convert catalogue GR and a known motor torque into the ideal output the customer should see before applying a service factor. Plant maintenance scripts can log expected output torque from a measured motor current-to-torque map and a nameplate ratio without embedding ad-hoc spreadsheets that disagree on rounding.
Content sites that rank for gear output torque calculator, output torque from gear ratio, or ideal gear pair torque benefit from a live free tool whose arithmetic matches the paid automation path byte-for-byte. This landing is not a tooth-count gear-ratio tool and not a vehicle wheel-torque tool that also multiplies a final drive: it is the single-pair T_out equals T_in times GR page. Invalid input is not billed.
What you can do with it
Reducer and gearbox output checks
Convert a known motor or pinion torque and a catalogue gear ratio into the ideal driven-shaft torque before applying a service factor.
FAQ
What does gear ratio mean here?
GR is ω_in/ω_out, equal to N_driven/N_driver for a simple pair. Values greater than one are reductions (more output torque); values less than one are overdrives.
What units should I use?
The ratio is dimensionless. Stay consistent; this tool does not convert units.
Does the output torque include gear losses?
No. Efficiency is taken as one, so the result is the ideal textbook multiplication. If you know the mesh efficiency, apply it to the result afterwards.
What happens to torque with an overdrive ratio?
It drops. A ratio of 0.5 halves the torque and doubles the speed, while a one-to-one mesh passes both through unchanged.
Can the input torque be negative?
Yes. A negative value stands for reverse or braking torque and is scaled by the same ratio, and zero gives zero. The gear ratio itself must always be positive.
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/gear-output-torque \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"input_torque":50,"gear_ratio":4}'const res = await fetch("https://api.kit.forhosting.com/eng/gear-output-torque", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"input_torque": 50,
"gear_ratio": 4
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/eng/gear-output-torque",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"input_torque": 50,
"gear_ratio": 4
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/eng/gear-output-torque", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"input_torque":50,"gear_ratio":4}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"input_torque":50,"gear_ratio":4}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/eng/gear-output-torque", 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_torque": 50,
"gear_ratio": 4
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "eng.gear_output_torque",
"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
Input contract, units, response shape, and error behaviour
POST a JSON body with two required finite numbers: input_torque (aliases torque_in, t_in, T_in, tin, driver_torque), the driver-shaft torque in any coherent unit such as newton-metres; and gear_ratio (aliases ratio, GR, gr, i, transmission_ratio), the strictly positive dimensionless ratio of the pair. Fields may arrive as JSON numbers or numeric strings. Missing fields, non-finite values, or a non-positive gear_ratio fail with invalid_input naming the problem; those failures are not billed. On success the body echoes rounded input_torque and gear_ratio; returns output_torque as their product; reports speed_ratio as one over GR and torque_multiplication as GR; labels transmission as reduction when GR is greater than one, overdrive when GR is less than one, or 1:1 when GR equals one; sets efficiency to one and losses_model to none; and includes formula T_out = T_in × GR (losses neglected), method ideal_gear_pair, and a short human-readable message.
Where a gear-pair output torque API earns its keep
Laboratory benches that instrument a two-gear rig can pin output_torque in continuous integration against the same pure module students use in the browser. Keep requests small, pin the rounded output_torque field in tests, and you get reproducible ideal mesh moments for LMS plugins, edge workers, and design notebooks without standing up a full multi-body contact model.
Integration use cases
Machine-elements homework and exams
Compute T_out=T_in×GR from a textbook pinion torque and stated ratio; reject a non-positive GR so graders get a clear invalid_input signal.
Lab and automation scripts
Pin output_torque from measured input torque and a nameplate ratio in CI using the same pure module as the free browser widget.
Technical questions
How do I calculate the output torque of a gear pair?
Send finite input_torque T_in and a strictly positive gear_ratio GR. The API returns T_out = T_in × GR as output_torque, plus speed_ratio = 1/GR, with losses neglected.
Does this include gearbox efficiency or mesh losses?
No. Efficiency is taken as one and losses_model is none. Multiply the returned output_torque by your own efficiency if you need a lossy estimate.
What does the gear output torque calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.