Income CV calculator
Five incomes averaging 44,000 with a standard deviation of 20,591.260282 have a coefficient of variation of 0.467983, or 46.798319%. Enter a list of incomes to get a measure of inequality that does not depend on the currency, with the mean and spread alongside. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Incomes
- 20,000, 30,000, 40,000, 50,000, 80,000
- N
- 5
- Mean income
- 44,000
- Std income
- 20,591.260282
- Sum squared deviations
- 2,120,000,000
A society where incomes average twenty thousand with a standard deviation of eight thousand has the same CV as one where incomes average forty thousand with a standard deviation of sixteen thousand, even though absolute spreads double. This income coefficient of variation calculator accepts a list of non-negative incomes, returns mean income, population and sample standard deviations, the CV as a ratio and as a percent, and a coarse inequality band for classroom and report use.
What the income coefficient of variation measures and when to use it
Absolute income spreads are hard to compare when averages differ. A region with mean income ten thousand and standard deviation two thousand is not twice as unequal as a poorer region with mean five thousand and standard deviation one thousand; both share the same relative dispersion. The coefficient of variation answers that comparison by dividing the standard deviation of incomes by mean income, yielding a dimensionless ratio that can also be multiplied by one hundred and reported as a percentage.
Population CV uses the population standard deviation—square root of the average squared deviation from the mean—over the arithmetic mean of the same list. Sample CV uses the sample standard deviation with Bessel’s correction (divide by n minus one) when you treat the list as a survey sample rather than a complete census.
Development economists, labor analysts, and public-finance instructors use income CV alongside the Gini coefficient, the Palma ratio, and percentile ratios: CV is sensitive to the whole distribution, is simple to teach after mean and variance, and is scale-free so a change of currency or a proportional raise does not invent fake inequality. Negative incomes are outside the classical non-negative income distribution assumed here and are rejected. A single observation cannot measure dispersion across people, so the list must contain at least two finite non-negative values.
Because every step is a finite sum of products of known numbers followed by a square root and a division, the procedure is classical and fully deterministic: the same income list always yields the same mean, the same standard deviations, and the same CV ratio and percentage.
How this calculator validates incomes and computes CV
Optionally send decimals as an integer from zero through twelve (default six) to control half-up rounding on every reported numeric field. After validation the core walks the list once to accumulate the sum and form mean income, rejects a non-positive mean, then walks again to accumulate the sum of squared deviations from that mean. Population standard deviation is the square root of that sum divided by n; sample standard deviation is the square root of the same sum divided by n minus one.
Population CV is population standard deviation divided by mean income; the percentage form multiplies that ratio by one hundred. Sample CV and its percentage follow the same pattern. A microscopic clamp prevents floating round-off on a zero-spread list from inventing a negative sum of squares.
What you can do with it
Development and labor-economics homework
Students enter a list of wages or household incomes and verify mean, standard deviation, and income CV as ratio and percent against textbook worked examples.
LMS and exam auto-grading
Mark income-inequality items with a deterministic oracle that rejects negative incomes, single observations, and zero mean instead of inventing infinity.
Policy notebooks and survey extracts
Batch-compute scale-free income CV for multiple regions or years without spreadsheet formula drift on the std-over-mean step.
FAQ
What is the income coefficient of variation formula?
CV = σ / μ, where μ is mean income and σ is the population standard deviation of the same list. Sample CV uses the sample standard deviation (divide by n − 1). Both are also returned as percentages (ratio times 100).
How is this different from a generic coefficient of variation calculator?
Generic CV tools accept any signed numbers without an inequality interpretation.
What happens if mean income is zero or an income is negative?
CV is undefined when the mean is zero, and this calculator rejects negative incomes as outside a classical non-negative income distribution. Validation failures are not charged.
Is the income coefficient of variation calculator free?
The browser tool runs free on your device.
How is the CV worked out for five incomes averaging 44,000?
Divide the standard deviation by the mean. With a population standard deviation of 20,591.260282, the CV is 0.467983, or 46.798319%. Treated as a survey sample, it rises to 52.322111%, labelled moderate inequality.
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/econ/coefficient-of-variation-income \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"incomes":[20000,30000,40000,50000,80000]}'const res = await fetch("https://api.kit.forhosting.com/econ/coefficient-of-variation-income", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"incomes": [
20000,
30000,
40000,
50000,
80000
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/econ/coefficient-of-variation-income",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"incomes": [
20000,
30000,
40000,
50000,
80000
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/econ/coefficient-of-variation-income", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"incomes":[20000,30000,40000,50000,80000]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"incomes":[20000,30000,40000,50000,80000]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/econ/coefficient-of-variation-income", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"incomes": [
20000,
30000,
40000,
50000,
80000
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "econ.coefficient_of_variation_income",
"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
The coefficient of variation of an income distribution is the standard deviation of incomes divided by mean income: a unitless, scale-free inequality measure that lets you compare relative dispersion across countries, years, or samples with different currency units and average living standards. Empty lists, single observations, negative values, and a zero mean fail with invalid_input so pipelines never invent infinity. The arithmetic is fully deterministic, runs free in your browser, and is available over the API at $0.002 per successful request with no language model and no external statistics service on the hot path.
What the income coefficient of variation measures and when to use it
One hard rule is universal: when mean income is zero, division is undefined, so this capability fails with invalid_input rather than inventing infinity or NaN.
How this calculator validates incomes and computes CV
Call the capability with a required array field named incomes: at least two non-negative finite numbers whose mean is strictly positive. The engine also accepts the aliases income, values, distribution, wages, and earnings, so scripts that already speak in those terms do not need a rename step. Validation rejects a missing field, a non-array, a list shorter than two, lists longer than the published maximum, any entry that is not a finite number, any negative entry, and a list whose mean is exactly zero, all with invalid_input and without charging balance. A coarse inequality_band label maps the population CV into classroom ranges such as low, moderate, high, or very high inequality for slides; it is not a legal or regulatory standard.
Practical use, limits, pricing, and delivery
Use the browser tool when you want an immediate income coefficient of variation while checking a development-economics homework answer, comparing relative wage dispersion across two plants, or explaining why zero mean income cannot define CV without installing a statistics package. There is no language model, no external statistics service, and no randomness, so the capability 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. Accepted lists stay bounded for Worker isolates: up to one hundred thousand incomes cover classroom tables, survey extracts, and typical microsimulation excerpts while still finishing quickly. Results are fully deterministic: the same incomes always yield the same mean_income, std_income, coefficient_of_variation, cv_percent, sample fields, sum_squared_deviations, and inequality_band. Wire the endpoint into inequality tutorials, spreadsheet-migration tests, coding-interview sandboxes for economists, or preprocessing steps where you already prefer closed-form two-pass CV over approximate streaming sketches or opaque black-box calculators that hide whether they divide by n or by n minus one when they print a single coefficient of variation field. Pair the CV with your own Gini or top-share calculations when you need a full inequality dashboard; this endpoint certifies only the scale-free std-over-mean form for a non-negative income list.
Technical questions
How do I compute the coefficient of variation of an income distribution?
Send JSON with incomes (an array of at least two non-negative numbers with positive mean) to econ.coefficient_of_variation_income. The response returns mean_income, std_income, coefficient_of_variation, cv_percent, sample forms, inequality_band, and formula.