How this instrument works
The Gini coefficient compresses an entire income distribution into one number between 0 and 1. Plot cumulative share of population against cumulative share of income and you get the Lorenz curve; if income were split perfectly evenly, that curve would sit exactly on the diagonal. The Gini coefficient is twice the area trapped between the actual Lorenz curve and that diagonal — so a population where the curve barely bows away from equal sharing scores near 0, and one where it sags toward the bottom-right corner scores toward 1.
National statistical offices rarely publish every household's income; they publish grouped shares, most often by quintile — five bands of 20% of the population each, with each band's share of total income. This instrument reconstructs the Lorenz curve from exactly those five numbers and applies the trapezoidal rule, connecting straight lines between the four intermediate points plus the fixed corners (0,0) and (1,1), then computing the area beneath. It is the same shortcut national statistical agencies, the World Bank, and the OECD lean on whenever individual-level microdata is not the input available.
Because it draws straight lines between only five points, the trapezoidal method always understates the inequality a full individual-level calculation would show — it cannot see the spread of incomes hiding inside a single quintile. The gap is small for realistic distributions but grows as the underlying distribution gets more extreme, which is why even a quintile split with one group holding everything and the rest holding nothing tops out at 0.8 here rather than the theoretical maximum of 1.0.
- Enter Income share, bottom 20% — the percentage of total income held by the poorest fifth of the population.
- Fill in Income share, 2nd 20%, Income share, middle 20%, and Income share, 4th 20% with each band's percentage of total income.
- Enter Income share, top 20% last, and confirm the five fields sum to 100 — they describe one whole population.
- Read the four cumulative income share figures; they are the Lorenz-curve points the calculation walks between.
- Check the Gini coefficient reading at the bottom: nearer 0 means income is spread evenly, nearer 1 means it concentrates at the top.
Worked example — a 5/10/15/22/48 income split
Suppose the bottom fifth of a population holds 5% of total income, the second fifth 10%, the middle fifth 15%, the fourth fifth 22%, and the top fifth 48%. Cumulating those in order gives Y1 = 0.05, Y2 = 0.15, Y3 = 0.30, and Y4 = 0.52 — four interior points that, together with the fixed corners at (0,0) and (1,1), trace this population's Lorenz curve.
Summing 0.2 times each adjacent pair of those cumulative shares and subtracting the total from 1 returns a Gini coefficient of 0.392. That sits in the range economics texts describe as moderate inequality — well above the high-0.2s typically reported for the most equal Nordic economies, and well below the 0.6-plus reported for the world's most unequal ones.
Questions
What does a Gini coefficient of 0.392 actually mean?
It means the area trapped between the Lorenz curve and the line of perfect equality is 19.6% of the triangle beneath that line, doubled by the formula so the coefficient always lands between 0 and 1. A reading near 0.39 falls in the range economics texts label moderate inequality — uneven, but far short of extreme concentration. The number is only meaningful compared against another period or country computed the same way.
Why can this calculator never return a Gini of exactly 1.0?
Because it works from five grouped quintile shares rather than every individual income, the trapezoidal method tops out at 0.8 even in the most extreme case it can represent — one quintile holding all the income, the other four holding none. A full calculation from individual records on that same extreme population would read higher, approaching the theoretical maximum of 1.0. Grouped-data approximations understate inequality; using more groups narrows the gap.
Do the five income share fields need to add up to 100?
Yes. Each field is one quintile's percentage of the population's total income, and since the five quintiles together account for everyone, the shares must sum to 100. If your source figures total something else, the cumulative shares and the resulting Gini coefficient will not describe a coherent population — check the underlying data before trusting the output.
How does this differ from a poverty rate or median income figure?
A poverty rate counts people below one fixed income line, and median income names a single midpoint; neither describes the spread above or below it. The Gini coefficient instead summarizes how evenly income is spread across the whole population in one number. A country's poverty rate can fall while its Gini coefficient rises, if income growth concentrates further toward the top.
Where do real quintile income shares come from?
National statistical agencies and bodies such as the World Bank and OECD publish quintile or decile income-share tables built from household surveys and tax records, usually inside their inequality or poverty reports. Enter those published shares directly to reproduce a reported Gini coefficient, or adjust one share to see how a shift in distribution would move the result.
Can this formula measure wealth or consumption instead of income?
Yes. The trapezoidal Lorenz-curve method works on any quantity split into ordered population shares — wealth, consumption, or land holdings included. Enter each quintile's share of that quantity in place of income; the arithmetic and the 0-to-1 reading stay identical, though wealth Gini coefficients typically run well above income Gini coefficients, since wealth concentrates more heavily than income does in most countries.
References
- U.S. Census Bureau — Income inequality and the Gini index
- World Bank — Gini index (World Bank estimate), indicator metadata
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.