Gini Coefficient Calculator
From individual incomes, compute the Gini coefficient — a 0-to-1 measure of income inequality; 0 is perfect equality, 1 is full concentration.
Input Data
Results
At a glance:The Gini coefficient measures income/wealth inequality in [0,1]. 0 = perfect equality (everyone earns the same); 1 = one person holds all. Method: rank from poorest to richest, draw the cumulative Lorenz curve; Gini = (area between the equality diagonal and the Lorenz curve) ÷ (area under the diagonal). The farther the Lorenz curve bows from the diagonal, the more unequal. It is the most-used inequality gauge. Limits: it only sees the spread, not who is rich/poor, and is insensitive to the middle — pair with the top-share and median income.
Formula
Gini = (area between equality line and Lorenz curve) ÷ (area under equality line).
Sorted incomes: Gini via covariance-like formula: (2 × Σ i·y_i) ÷ (n × Σ y_i) − (n + 1) ÷ n.
$$\text{Gini} = 1 - 2B$$$$B = \tfrac{1}{2}x_1 y_1 + \tfrac{1}{2}(1 - x_1)(y_1 + 1)$$How to Use
- Enter comma-separated individual incomes (e.g. 10,20,30,40).
- View the Gini coefficient and Lorenz points.
Gini for sample income distributions
| Incomes | Gini | Reading |
|---|---|---|
| 10, 20, 30, 40 | 0.25 | Fairly equal |
| 5, 5, 5, 85 | 0.60 | Very unequal |
| 20, 20, 20, 20 | 0.00 | Perfect equality |
| 2, 2, 2, 94 | 0.69 | Extreme concentration |
Higher Gini = more unequal. The same count of people but different spread yields very different Gini (e.g. 0.25 vs 0.60).
Case Studies
Case 1: A fairly equal distribution
Four incomes sorted: 10, 20, 30, 40. Using the formula: Σ y = 100, Σ(i·y) = 1×10+2×20+3×30+4×40 = 300; Gini = (2×300)/(4×100) − (4+1)/4 = 600/400 − 1.25 = 1.5 − 1.25 = 0.25.
A Gini of 0.25 means fairly equal — the Lorenz curve is close to the diagonal. This is near the Nordic level of equality.
Case 2: A highly concentrated distribution
Four incomes: 5, 5, 5, 85 (one holds most). Σ y = 100, Σ(i·y) = 1×5+2×5+3×5+4×85 = 365; Gini = (2×365)/(4×100) − 1.25 = 730/400 − 1.25 = 1.825 − 1.25 = 0.575.
A Gini near 0.6 means high concentration — the bottom three share only 15%. Real Latin American/emerging markets often reach this. The Gini ignores who is rich/poor; pair with top-share and median income for the full picture.
FAQ
How do we read the Gini; what is the Lorenz curve?
The Gini is the area-ratio method. The Lorenz curve plots, after sorting from poorest to richest: x = cumulative population %, y = cumulative income %. If equal, 20% of people hold 20% of income, 40% hold 40% — a straight 45° diagonal (equality line). If unequal, the bottom 20% hold less than 20%, the curve bows down and away from the diagonal; the farther the bow, the more unequal. The Gini = (area between the diagonal and the Lorenz curve) ÷ (area under the diagonal), a 0–1 ratio. The formula with sorted y_i: Gini = [2 × Σ(i·y_i)] ÷ (n × Σy_i) − (n+1)/n, from the same area idea. So the Gini is a compact 'how far from the diagonal' number.
What is a 'high' Gini?
0 = perfect equality; 1 = one person holds all. Real-world: >0.4 is often 'relatively high inequality', >0.5 'high', <0.3 'relatively equal'. Examples: the Nordics ~0.25–0.30 (equal); the US ~0.40; some Latin American/emerging markets ~0.50+ (high). But thresholds are reference only; read with history, regions and other metrics — a single number cannot fully judge fairness.
Limits of the Gini?
Several. (1) It only sees the spread, ignores who is rich/poor — two groups with opposite extremes can share a Gini. (2) Insensitive to the middle — a change in the middle class barely moves it, but the poor/rich ends matter more. (3) Blind to absolute level — a poor and a rich country with the same spread have the same Gini, yet living standards differ. (4) Sensitive to grouping and top-data quality — hidden top wealth distorts it. So pair it with the top 10%/1% share, median vs mean income, and poverty rates for a true picture of fairness.
Why pair with the top 10% share and median income?
Because the Gini alone can mislead; these two fill its gaps. Top 10% (or 1%) income share directly shows 'how concentrated the top is' — the Gini cannot. A Gini of 0.45 may mean the top 10% take 35% (very concentrated) or 28% (moderate); the share tells which. Median income (the typical person's) vs mean shows the average pulled up by the rich — mean much above median signals the rich skew the average, hurting most. So: Gini = overall spread; top-share = elite concentration; median vs mean = typical-person reality. Together judge fairness more fully — why analysts rarely use the Gini alone.
What affects the Gini (education, tax, tech)?
Many structural factors move it. (1) Education/skill gaps — a skill-biased economy (tech, finance) widens high-skill premiums, raising it. (2) Tax/transfer — progressive tax + benefits redistribute, lowering it measurably (European welfare states lower than others partly via transfers). (3) Technology — capital-return concentration and platform scale raise top shares, pushing it up. (4) Globalisation/industrial shift — manufacturing jobs hollowing hurts mid incomes, widening gaps. (5) Inheritance/wealth — wealth gaps persist more than income (wealth Gini usually higher), passed across generations, entrenching inequality. So the Gini is not just a number but a mirror of education, tax, tech and institutional choices — and a key input to policy debate.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.