Number density converter
Move a particle count per volume between textbook, lab and datasheet units: 1000000 per cubic meter is exactly 1 per cubic centimeter, and all nine units pass through per cubic meter, so conversions stay consistent both ways. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Value
- 1,000,000
- From
- m-3
- To
- cm-3
- Result
- 1
- From label
- per cubic metre
- To label
- per cubic centimetre
- Per m3
- 1,000,000
Number density counts how many particles, atoms, molecules, or other discrete entities occupy a unit volume of space, gas, plasma, solid, or fluid. Physicists, chemists, materials scientists, and engineers often receive values in per cubic metre from SI textbooks, per cubic centimetre from solid-state and semiconductor literature, or per litre from chemistry and process notes—and need a trustworthy conversion without rebuilding inverse-volume factors by hand.
Supported units and exact conversion factors
The converter accepts nine number density families under stable canonical codes: m-3 for entities per cubic metre (SI), cm-3 and mm-3 for per cubic centimetre and millimetre, um-3 for per cubic micrometre, L-1 and mL-1 for per litre and per millilitre, km-3 for per cubic kilometre, and in-3 plus ft-3 for per cubic inch and foot.
Volume factors follow SI definitions: one cubic centimetre is exactly ten to the minus six cubic metres so one per cubic centimetre equals one million per cubic metre; one cubic millimetre is ten to the minus nine; one cubic micrometre is ten to the minus eighteen; one litre is exactly one thousandth of a cubic metre so one per litre equals one thousand per cubic metre; one millilitre matches one cubic centimetre; one cubic kilometre is one billion cubic metres; one cubic inch is exactly zero point zero two five four metres cubed; and one cubic foot is zero point three zero four eight metres cubed.
Because the intermediate is always m⁻³, converting A to B and B to A is consistent up to the published twelve-decimal rounding, and there is no pairwise matrix that can drift out of sync. Mass density, volume charge density, and particle fluence (per area) are intentionally out of scope so number-density users get predictable n-only results under one clear convention.
Everyday uses in labs and datasheets
Use the free in-browser number density converter when you need a quick m⁻³ to cm⁻³, L⁻¹ to m⁻³, or cm⁻³ to mL⁻¹ check while reading a solid-state physics paper, plasma diagnostics note, chemistry lab procedure, atmospheric science report, or materials datasheet. Open the page, enter the number and units, and copy the result without installing a spreadsheet, a unit library, or a desktop calculator pack. Source inputs follow the same retention rules as other KIT parse items, and results are safe to cache because the algorithm is fully deterministic.
Authors shipping mobile apps or chatbots can map the result and formula fields directly into cards that show both the number and the conversion path students, process engineers, and lab technicians expect on paper.
What you can do with it
Semiconductor and solid-state labs
Convert carrier and defect densities between m⁻³ SI reports and the cm⁻³ units common in device literature so doping and trap counts stay comparable across tools.
Chemistry and process notes
Students and process engineers convert per-litre particle counts into SI per-cubic-metre values with exact litre factors and clear errors on typos.
FAQ
How is per litre related to per cubic metre?
One litre is exactly 0.001 m³. The converter multiplies by 1000 so 1 L-1 equals exactly 1000 m-3 with stable twelve-decimal rounding.
What if I send an unknown unit?
The message names the bad field and lists supported units; validation failures are not charged.
Is the number density converter free?
The browser tool runs free on your device.
Does it convert mass density or fluence?
No. This capability only converts number density n (count per volume). Mass density (kg/m³) and particle fluence (per area) are out of scope.
How do I convert per cubic meter to per cubic centimeter?
Divide by one million, because a cubic centimeter is a millionth of a cubic meter. For example, 1000000 particles per cubic meter are exactly 1 particle per cubic centimeter.
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/number-density \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"value":1e+25,"from":"m-3","to":"cm-3"}'const res = await fetch("https://api.kit.forhosting.com/conv/number-density", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"value": 1e+25,
"from": "m-3",
"to": "cm-3"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/conv/number-density",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"value": 1e+25,
"from": "m-3",
"to": "cm-3"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/conv/number-density", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"value":1e+25,"from":"m-3","to":"cm-3"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"value":1e+25,"from":"m-3","to":"cm-3"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/conv/number-density", 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": 1e+25,
"from": "m-3",
"to": "cm-3"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "conv.number_density",
"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 converts a numeric number density from one supported unit to another with fixed SI volume definitions (inch exactly 0.0254 m, litre exactly 0.001 m³), routes every pair through m⁻³ as the intermediate base, and returns deterministic JSON for APIs, SDKs, and free browser use. Unknown unit names fail with a clear invalid_input error so forms and pipelines never silently invent a factor.
Supported units and exact conversion factors
Friendly aliases such as 1/m3, m⁻³, per cubic meter, /cm3, particles/cm3, 1/L, per litre, /in3, and µm-3 are normalized so forms can pass short codes or spelled names. Every request multiplies the input value by the exact per-cubic-metre factor for the source unit, then divides by the factor for the target.
Request shape, response fields, and unknown-unit errors
The error message names the bad field and lists the supported set so clients can correct forms without guessing. Negative values are allowed when you need signed residual or difference workflows; zero converts cleanly to zero in every target unit. Send a JSON body with three required fields: value as a finite number, from as the source unit string, and to as the target unit string. Aliases amount, quantity, n, and density are accepted for value; unit_from and source for from; unit_to and target for to. On success the response echoes the canonical from and to codes, human-readable from_label and to_label strings, the converted result, the intermediate per_m3 quantity in entities per cubic metre, the dimensionless factor from source to target, a short formula line suitable for UI display, the method tag number_density_si, and the fixed list of units_supported. Missing value, non-finite numbers such as NaN or Infinity, missing unit fields, and any token that does not map to a supported unit fail with invalid_input and are not charged after the engine rejects the request. Identical inputs always yield identical JSON because the path is pure arithmetic with no randomness, no remote lookup, and no dependence on the wall clock, which makes the endpoint safe to pin in continuous-integration goldens and SDK contract tests. Semiconductor carrier densities near ten to the twenty-two per cubic centimetre and dilute gas concentrations per litre share the same code path, so extreme magnitude pairs remain well-defined as long as IEEE double precision can represent the intermediate product.
Browser use, API pricing, and everyday workflows
Switch to the prepaid API when a materials LIMS, semiconductor process controller, atmospheric chemistry model, physics homework checker, or simulation plugin must convert number density at scale under a stable KIT contract at $0.002 per successful item; validation failures that raise invalid_input do not consume balance after rejection. Pair this endpoint with mass density or fluence tools when a product pipeline needs several measure families, or call it alone when search traffic is specifically for number density conversion—particles per cubic metre, centimetre, millimetre, micrometre, litre, millilitre, kilometre, inch, and foot—rather than a general unit switchboard.
Integration use cases
Simulation and LIMS pipelines
Automate number density unit normalization in atmospheric, plasma, and materials pipelines via a prepaid, deterministic API instead of ad-hoc spreadsheet factors.
Technical questions
Which number density units are supported?
m-3, cm-3, mm-3, um-3 (µm-3), L-1, mL-1, km-3, in-3, and ft-3, plus common spelled aliases such as 1/m3, per cubic centimetre, and per litre. Unknown names return invalid_input.