Torque calculator
A force of 10 N on a 0.5 m lever arm at 90° gives a torque of 5 N·m. Enter force, arm length and angle to get the turning effect for bolts, doors or statics homework. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Applied force F
- 10
- Length
- 0.5
- Angle
- 90
- Angle rad
- 1.5707963268 N·m
- Sin theta
- 1
- Torque
- 5
Torque is the rotational effect of a force about a pivot: for a single force applied at a fixed lever-arm distance, the magnitude is the product of the arm length, the force, and the sine of the angle between them. Workshop fasteners, wrench sizing, statics homework, door hinges, and machine design sketches all need that number in newton-metres when the three inputs are known. Negative lever-arm length, missing fields, and non-finite values fail with invalid input before any result is returned.
What torque means and which three quantities you need to send
In classical mechanics, the magnitude of the moment of a force about a point is the product of the force magnitude, the perpendicular distance from the line of action to the pivot, or equivalently the product of the force, the lever-arm length to the application point, and the sine of the angle between the force vector and the arm. When force is in newtons and length in metres, torque comes out in newton-metres, the SI unit used on bolt tables, motor nameplates, and textbook statics answers.
Search intent clusters around phrases such as torque calculator, lever arm force angle, tau equals r F sin theta, newton metres from force and distance, wrench torque, and moment of force. People want a numeric answer they can check against a worksheet, embed in a simulation, or feed into a larger pipeline—not only a reminder that the formula exists. Units stay consistent with whatever force and length basis you chose: newtons with metres yield true SI newton-metres; any coherent pair yields a coherent moment in the same system.
Ninety degrees maximises torque for a given force and arm; zero degrees aligns the force with the arm and produces zero torque.
What you can do with it
Homework and statics drills
Students and graders confirm torque in newton-metres for given force, lever arm, and angle, with clear rejection when length is negative or a field is missing.
Wrench and machine sizing checks
Quick structured numbers for moment from known force, arm length, and application angle without standing up a full multi-body dynamics stack.
FAQ
How do I calculate torque with this tool?
The response includes torque = length × force × sin(angle) in N·m.
What happens if the lever-arm length is negative?
Length must be non-negative; a negative arm is not accepted. Zero length is valid and yields zero torque.
Is the torque calculator free?
The browser tool runs free on your device.
When is torque zero for a non-zero force?
When the angle is 0° or 180° (force along the arm, sin θ = 0) or when length is zero. At 90°, sin θ = 1 and torque is maximised for the given force and arm.
Which unit does the torque come out in?
In newton-metres when the force is in newtons and the arm in metres, the unit used on bolt tables and motor nameplates. Other consistent force and length units work the same way.
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/torque \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"force":10,"length":0.5,"angle":90}'const res = await fetch("https://api.kit.forhosting.com/mech/torque", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"force": 10,
"length": 0.5,
"angle": 90
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/torque",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"force": 10,
"length": 0.5,
"angle": 90
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/torque", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"force":10,"length":0.5,"angle":90}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"force":10,"length":0.5,"angle":90}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/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
{
"force": 10,
"length": 0.5,
"angle": 90
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.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
This capability takes finite force, non-negative length, and an angle in degrees, evaluates τ equals r F sin of theta with a pure arithmetic path, and returns structured JSON including torque, sin theta, the angle in radians, formula, and method.
What torque means and which three quantities you need to send
Delivering force, length, angle, angle in radians, sin theta, torque, unit, formula, and method as JSON makes the result easy to paste into notes, diff in automated tests, or reuse across languages without reimplementing the arithmetic.
How this calculator validates input and applies τ = r F sin(θ)
Numeric strings that parse to finite numbers are accepted so forms and CSV-style pipelines can pass values without an extra cast. Length must be non-negative; a negative lever-arm length is rejected with a clear message because a physical arm length cannot be negative in this product model, while zero length simply yields zero torque. Force may be signed: a negative value reverses the sense of rotation encoded in the signed torque result. There is no multi-force netting, no friction model, and no unit auto-conversion; this is ideal single-force lever torque from the three known quantities. Send a JSON body with force, length, and angle. All three fields are required and must be finite: missing any field, empty strings, non-numeric text, NaN, and Infinity all fail immediately with invalid_input before any result is returned, and failed validation is not charged. Aliases are recognized for convenience: force also accepts F and f; length also accepts r, lever_arm, and arm; angle also accepts theta and degrees. Angle is interpreted in degrees, matching classroom problems and everyday wrench diagrams; the engine converts to radians only for the sine evaluation and echoes both the original angle and angle_rad. After validation, sin_theta is computed as the sine of the angle in radians and torque as length times force times sin_theta. Results are rounded to a stable decimal precision so the same input always yields the same JSON across JavaScript engines. The same pure function powers the free in-browser tool and the API path.
Practical use, limits, pricing, and delivery channels
Use the browser tool when you want an immediate newton-metre check while grading statics homework, verifying a lab moment measurement, sizing a wrench load from known force and arm, or comparing lever geometries on a shared torque basis. Choose units consistently—if force is in newtons and length is in metres, torque is true SI newton-metres. There is no language model, no external physics service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible lesson materials. Each successful request is one billable item at $0.002; failed validation does not consume balance. Results are fully deterministic: the same force, length, and angle always yield the same torque and the same sin_theta. Wire the endpoint into mechanics drills, contest answer checkers, fastener worksheets, or preprocessing steps where you already prefer explicit domain errors—such as rejecting negative length—over opaque black-box widgets that cannot explain why a bad input was refused.
Integration use cases
Deterministic fixtures for physics tests
Pipelines that seed unit tests or interactive lever demos can call a pure τ=rF sin(θ) oracle instead of reimplementing torque arithmetic in every language.
Technical questions
Is the angle in degrees or radians?
Angle is in degrees. The engine converts internally for sine and also returns angle_rad and sin_theta so you can verify the conversion.