Convert mass moment of inertia
Convert mass moment of inertia between kg·m², g·cm² and lb·ft²: 1 kg·m² is 10000000 g·cm². Line up a European motor datasheet, a micro-gear catalogue and a US flywheel table in one unit. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Value
- 1
- From
- kg_m2
- To
- g_cm2
- Value
- 10,000,000
- From
- kg·m²
- To
- g·cm²
- Kg m2
- 1
Mass moment of inertia measures how mass is distributed about an axis, and datasheets rarely agree on the unit. SI machine design uses kilogram square metres, small-component catalogues often quote gram square centimetres, and many North American rotor or flywheel tables still list pound square feet. This converter accepts a numeric value plus a source unit and a target unit, then returns the converted figure through one deterministic path based on exact SI definitions.
One property, three very different numbers
Mass moment of inertia describes how mass is spread around an axis, and datasheets rarely agree on the unit. European machine design works in kilogram square metres, small-component catalogues quote gram square centimetres, and many North American rotor and flywheel tables still list pound square feet. The same physical property can therefore appear with numbers that differ by many orders of magnitude: 1 kg·m² is 10000000 g·cm². You enter the value with its source and target units, and the converter returns the figure in the unit your sizing sheet, simulation or report expects.
How the conversion works and where it goes wrong
Every conversion passes through kilogram square metres. A gram square centimetre is exactly one ten-millionth of a kilogram square metre, because a gram is a thousandth of a kilogram and a centimetre a hundredth of a metre. A pound square foot uses the international avoirdupois pound of 0.45359237 kg and the exact foot of 0.3048 m, squared. Two slips are common when people convert by hand: treating the pound as a force instead of a mass, and using a rounded 0.042 factor for lb·ft². They look small, but an undersized servo chosen from a wrong inertia can overshoot, and an oversized one wastes cost and energy.
Why mass moment of inertia units keep colliding
A motor inertia on a European datasheet in kilogram square metres, a micro-gear catalogue line in gram square centimetres, and a US flywheel table in pound square feet can describe the same physical property with numbers that differ by many orders of magnitude.
Teams that glue those sources together usually paste a one-line formula into a notebook or a helper function, then discover months later that one service treated pound as force rather than mass, or that someone used a rounded 0.042 factor for lb·ft² instead of the international avoirdupois definition. Small slips matter: an undersized servo selected from a wrong inertia conversion can overshoot, and an oversized one wastes cost and energy.
What you can do with it
Motor and gearbox datasheet normalization
Map supplier inertia from mixed kg·m², g·cm², and lb·ft² listings into one SI column before sizing, matching, and simulation steps run.
Flywheel and rotating machinery tables
Convert North American pound-square-foot tables into kilogram square metres so European plant models stay dimensionally consistent.
CAD exports and product configurators
Show the unit a local engineer expects while storing a single kg·m² value in the backend for audit and calculation.
FAQ
How is the conversion calculated?
Every value is converted to kilogram square metres with fixed SI factors, then to the target unit.
Is lb·ft² mass moment of inertia or torque?
This tool treats pound square feet as mass × length² (mass moment of inertia), not as a torque unit. Torque conversion is out of scope.
What happens if I send an unknown unit?
No silent fallback and no charge for the failed call.
How many g·cm² are in 1 kg·m²?
Ten million: 1 kg·m² is 10000000 g·cm², because a gram is a thousandth of a kilogram and a square centimetre is a ten-thousandth of a square metre. That is why catalogue and datasheet figures look so different.
Why not use 0.042 to convert lb·ft² to kg·m²?
Because it is a rounded shortcut. The converter uses the international avoirdupois pound of 0.45359237 kg and the exact foot of 0.3048 m, squared, so motor and flywheel figures stay consistent across sources.
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/conv/moment-of-inertia \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"value":1,"from":"kg_m2","to":"g_cm2"}'const res = await fetch("https://api.kit.forhosting.com/conv/moment-of-inertia", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"value": 1,
"from": "kg_m2",
"to": "g_cm2"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/conv/moment-of-inertia",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"value": 1,
"from": "kg_m2",
"to": "g_cm2"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/conv/moment-of-inertia", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"value":1,"from":"kg_m2","to":"g_cm2"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"value":1,"from":"kg_m2","to":"g_cm2"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/conv/moment-of-inertia", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"value": 1,
"from": "kg_m2",
"to": "g_cm2"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "conv.moment_of_inertia",
"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
No spreadsheet scrap, no mixed factors from forum posts, and the same number whether you run it free in the browser or call the API at $0.002 per successful request.
Why mass moment of inertia units keep colliding
Centralizing conversion behind one tested endpoint means every CAD export, sizing spreadsheet, and mobile field form applies the same chain.
Units covered and how the conversion is defined
Every conversion goes through kilogram square metres as the SI base: the input is multiplied by a fixed factor to kg·m², then divided by the factor for the target unit. Factors are exact engineering constants—one kilogram square metre is the identity, one gram square centimetre equals 1×10⁻⁷ kg·m² because one gram is 10⁻³ kg and one centimetre is 10⁻² m, and one pound square foot uses the international avoirdupois pound (0.45359237 kg) times the exact foot squared (0.3048 m). The converter supports the three units most often requested for mass moment of inertia work: kg_m2 (kilogram square metres, kg·m²), g_cm2 (gram square centimetres, g·cm²), and lb_ft2 (pound square feet, lb·ft²). Unit strings are normalized case-insensitively for common aliases such as kgm2, gcm2, and lbft2, and the response echoes the canonical symbols kg·m², g·cm², and lb·ft². Unknown unit names fail fast with an invalid_input error that names the bad field and lists the supported set, so a typo never becomes a silently wrong number charged to your balance.
Where to run it: browser tool or paid API calls
For a one-off check—reading a hobby motor in g·cm² and wanting kg·m², or translating a flywheel listing from lb·ft² into SI before a simulation—use the free in-browser tool. Responses are deterministic: the same inputs always yield the same outputs, with floating-point noise cleaned to conversion-grade precision. The same pure function powers the API path when you need to normalize supplier catalogues, product configurators, or batch imports without embedding conversion tables in every service. Each successful API call costs $0.002; failed validation is not billed, so probing an unknown unit or forgetting the value field does not drain prepaid balance. Drop the call into an ETL step that standardizes rotor inertia columns, a CAD plugin that stores SI while displaying the unit a local engineer expects, or a control-design pipeline that keeps every plant model in kilogram square metres.
Technical questions
Which mass moment of inertia units can I convert?
kg_m2 (kg·m²), g_cm2 (g·cm²), and lb_ft2 (lb·ft²). Common aliases such as kgm2, gcm2, and lbft2 are accepted. Unknown names return an invalid_input error.
How much does the API cost?
$0.002 per successful request. The browser tool is free. Invalid input is not charged.