How the Gini coefficient works
Line a group up from poorest to richest and ask, at every point along the line, what share of total income the people so far have received. Plotting that answer gives the Lorenz curve, proposed by Max O. Lorenz in 1905. Under perfect equality the curve is the straight 45° diagonal — the bottom 30% of people hold 30% of the income, and so on. Real distributions sag below it. Corrado Gini's 1912 insight was to turn that sag into a single ratio: call the area between the diagonal and the curve A, and the rest of the triangle under the diagonal B, and the Gini coefficient isG = A ÷ (A + B). No sag means G = 0; the deepest possible sag — one person with everything — pushes G toward 1. Because it is a pure ratio, doubling every income leaves it unchanged, which is what lets one scale compare a ten-person team with a whole country.
The Gini formula
G = 2 Σᵢ i·x₍ᵢ₎ ÷ (n Σ x₍ᵢ₎) − (n + 1) ÷ n
G = Σᵢ Σⱼ |xᵢ − xⱼ| ÷ (2 n² μ)
where x₍ᵢ₎ is the i-th smallest income (i = 1…n) and μ is the mean. The two forms give exactly the same number. The first — thesorted closed form — is what this calculator computes. The second says the same thing in plain terms: the Gini is the average absolute gap between every pair of incomes, expressed as a fraction of twice the mean.
Worked example
Take the calculator's default group: ten people earning between $12,000 and $250,000 a year. Here is how the single Gini figure is built up:
| Step | Amount |
|---|---|
| The groupten incomes from $12,000 to $250,000, entered in any order — the engine sorts them poorest-first | 10 incomes |
| Mean incometotal income ÷ number of people | $71,600 |
| Median incomethe middle earner — well below the mean because the top incomes stretch the tail | $46,000 |
| Bottom 50% sharecumulative income share of the poorest five, read off the Lorenz curve — it would be 50% under perfect equality | 17.6% |
| Top 10% sharehere the single highest earner — it would be 10% under perfect equality | 34.92% |
| = Gini coefficient of 0.4712sorted closed form: G = 2 Σ i·x₍ᵢ₎ ÷ (n Σ x) − (n + 1) ÷ n — equivalently 47.12 on the 0–100 scale | 0.4712 |
Computed with this calculator's default incomes — open the tool above and you'll see the same numbers, then paste in your own list.
Reading a Gini figure — bands, not verdicts
For national income Ginis measured after taxes and transfers, a useful rule of thumb is: below roughly 0.30 is relatively equal, 0.30–0.40 is moderate, and above 0.40 is high by developed-country standards. We deliberately don't print country rankings here — the figures move with each survey year and depend heavily on definitions — so for current, comparable values consult theOECD income inequality indicator. Before comparing any two Ginis, check three things. First, income or wealth: wealth Ginis run far higher because many people own little or nothing while still earning. Second, market or disposable income: redistribution through taxes and transfers typically lowers a country's Gini by a wide margin, so pre-tax and post-transfer figures are not comparable. Third, remember the number is a summary, not a fingerprint — two quite different distributions can share the same Gini, which is exactly why this calculator also shows the Lorenz curve and the top-10% and bottom-50% shares.
Inequality math is share-of-total math: work the percentages by hand with ourpercentage calculator, turn an hourly wage into the annual figure you'd paste into the list above with thesalary calculator, or compare what the same income actually buys in two cities with thecost of living calculator.
Frequently asked questions
What is the Gini coefficient?
The Gini coefficient is the most widely used single-number summary of inequality. It runs from 0, where every person has exactly the same income, to 1, where one person has everything and everyone else has nothing. Corrado Gini proposed it in 1912. Formally it equals half the average absolute difference between every pair of incomes, divided by the mean income — so a Gini of 0.40 says that two people picked at random differ, on average, by 80% of the mean income. Statistical agencies often report the same figure multiplied by 100, so 0.40 and 40 describe the same distribution.
What is a Lorenz curve?
A Lorenz curve, introduced by Max O. Lorenz in 1905, plots the cumulative share of income against the cumulative share of the population, ordered from poorest to richest. Under perfect equality the curve is the 45-degree diagonal: the bottom 20% of people earn 20% of the income, and so on. Any real distribution bows below that line. The Gini coefficient is pure geometry on this picture — the area between the diagonal and the curve (A) divided by the entire triangle under the diagonal (A + B). A deeper bow means a larger area A and a higher Gini.
What counts as a 'good' Gini coefficient?
There is no official threshold, but as rough bands for national income Ginis measured after taxes and transfers: below about 0.30 reads as relatively equal, 0.30 to 0.40 as moderate, and above 0.40 as high by developed-country standards. Whether any figure is "good" depends on what a society is willing to trade for it, and country numbers shift year to year with the economy and the survey design. Rather than memorizing league tables, check the OECD income inequality indicator linked under Sources for current, methodologically comparable values across countries.
What is the difference between an income Gini and a wealth Gini?
Same formula, very different data. An income Gini measures a flow — what people earn over a year — while a wealth Gini measures a stock — what they own at a point in time. Wealth Ginis are almost always far higher, because many people hold zero or negative net wealth while still earning an income: a country can post a wealth Gini above 0.80 alongside an income Gini near 0.30. When you see a Gini quoted, also check whether income is measured before taxes ("market" income) or after taxes and transfers ("disposable" income); redistribution typically lowers the figure substantially.
What are the limitations of the Gini coefficient?
It compresses an entire distribution into one number, so two very different distributions can share the same Gini — one driven by a wide gap at the top, another by deprivation at the bottom. It says nothing about absolute living standards: a poor country and a rich one can post identical Ginis. And it is only as good as the data underneath, which is why household-versus-individual units, pre-tax versus post-transfer income, and underreported top incomes all move the figure. Read it as a summary alongside the Lorenz curve and share statistics like the top 10% and bottom 50%, not as a verdict.
Sources
The official figures this page quotes are drawn from the primary sources above — check them (or a qualified professional) before relying on a result.
Disclaimer: This calculator is foreducation and illustration only. A Gini computed from a short list is a property of that list, not a national statistic — official figures come from large household surveys with equivalized incomes and careful treatment of taxes, transfers, and top incomes. Results here are a textbook calculation, and nothing on this page is financial, tax, or policy advice.