Atkinson Index Calculator

What Is the Atkinson Index Calculator?

The Atkinson Index Calculator measures income inequality using a welfare-based formula that lets you set how much weight to give to the poorest members of a distribution. Enter any list of income or wealth values, choose an inequality aversion parameter (epsilon), and the calculator returns the Atkinson index on a 0 to 1 scale, the Equally Distributed Equivalent (EDE) income, a welfare sacrifice figure, and a comparison against 19 countries. The index was formalised by British economist Anthony B. Atkinson in his 1970 paper in the Journal of Economic Theory and has since become one of the most widely used welfare-theoretic inequality measures in academic economics and government statistics. The UNDP Human Development Report publishes Atkinson(1) values for most countries as part of its standard inequality metrics alongside the Gini coefficient and income quintile ratios.

What sets the Atkinson index apart from the Gini coefficient is that it is derived from an explicit social welfare function. When you work out a Gini, you are measuring a purely statistical property of the distribution: the average absolute difference between all income pairs. When you work out an Atkinson index, you are simultaneously making a normative judgement about how much the welfare of low-income individuals matters relative to high-income individuals. Given that different analysts and policymakers hold different views on this, the epsilon parameter encodes that judgement directly into the measure rather than hiding it as an unstated assumption. This makes the Atkinson index especially useful in policy analysis where the redistributive value being evaluated is explicit, as in means-tested benefit design, progressive tax modelling, or university bursary allocation.

Choosing Epsilon: How Inequality Aversion Changes the Result

The inequality aversion parameter epsilon is the most important input in the Atkinson index, and it is also the one most commonly misunderstood. At epsilon = 0, the index has no aversion to inequality at all and equals zero for any distribution. As epsilon increases, the index gives increasingly more weight to transfers at the bottom of the income distribution. The US Census Bureau's description of the Atkinson index explains it this way: as epsilon approaches 1, the index becomes more sensitive to the lower end of the distribution; as epsilon falls toward 0, it becomes more sensitive to the upper end.

In practice, three epsilon settings dominate the academic and government literature:

That said, the difference between epsilon = 1 and epsilon = 2 can be dramatic. A country with moderate median inequality but a small group in extreme poverty (such as India at approximately A(1) = 0.46 and A(2) above 0.65) will show a larger jump from epsilon = 1 to epsilon = 2 than a country with diffuse, spread-out inequality. The multi-epsilon comparison panel in this calculator is designed specifically to surface that difference, which is not visible from a single Gini or single-epsilon Atkinson value.

Atkinson Index Values by Country: A Global Reference

Country-level Atkinson(1) values from the Luxembourg Income Study (LIS) and UNDP provide the most authoritative benchmarks for comparison. These values reflect household disposable income after taxes and transfers, making them comparable across countries with different tax systems. As a result, they consistently show Nordic countries achieving lower Atkinson values than their pre-tax distributions would suggest, because of the redistributive effect of progressive taxation and universal social insurance.

On top of that, the relationship between the Gini and Atkinson(1) is not fixed. India has a lower Gini than Brazil (approximately 36 vs 53) but a similar Atkinson(1) of around 0.46, because India's income distribution has a heavier concentration of very poor households at the extreme bottom, which the Atkinson index at epsilon = 1 picks up more strongly than the Gini does. The Luxembourg Income Study's Atkinson data files are the standard academic reference for these cross-national comparisons.

Accuracy and Limitations of the Atkinson Index

The Atkinson index formula is exact for the data you enter: there is no estimation error or rounding within the calculation itself. What introduces uncertainty is the quality of the input data and the choice of epsilon. For income data drawn from surveys, the American Community Survey or UK Family Resources Survey both carry sampling error that can shift A(1) by 1 to 3 percentage points for a single country-year observation. For very small datasets (under 30 values), the empirical distribution is a poor approximation of the underlying population distribution and the result should be treated as illustrative rather than authoritative.

The most structural limitation is that the Atkinson index requires all incomes to be strictly positive. A dataset with any zero or negative incomes will cause the formula to break down, particularly at epsilon values above 1, because raising a zero or negative value to a fractional power is undefined. In practice, researchers handle this by truncating incomes at a small positive floor (such as £1 or $1) or by using consumption expenditure instead of income when zero-income observations are common in low-income country surveys. The FAO technical note on welfare-based inequality measures covers this truncation problem in detail for agricultural household data where zero-income seasons are common. If you need to measure inequality across a distribution that includes both income and wealth (some of which may be negative), the Gini coefficient or our Gini Coefficient Calculator is more appropriate because it can handle negative values with a correction term.

The Most Common Atkinson Index Reporting Error

The mistake I see most often in policy reports is publishing a single Atkinson value without specifying the epsilon used. An Atkinson(0.5) of 0.22 and an Atkinson(2.0) of 0.22 are completely different statements about a distribution: at epsilon = 0.5, a score of 0.22 suggests moderate inequality by global standards; at epsilon = 2.0, the same score would indicate a remarkably equal distribution, comparable to the most equal Scandinavian countries. With that in mind, always pair every Atkinson figure with its epsilon in parentheses: A(0.5) = 0.22, not simply A = 0.22. This turns up most often in advocacy reports and journalism where the index is cited without the parameter, making cross-study comparison impossible for the reader. If you are comparing your dataset against published country benchmarks, make sure you are using the same epsilon. The multi-epsilon comparison table in this calculator is specifically designed to prevent this problem by showing four epsilon values simultaneously so you can see how much the choice of epsilon changes the verdict before reporting a single number. You can also cross-check your results against our Theil Index Calculator, which provides the complementary Theil T at epsilon = 1 via the relationship A(1) = 1 minus e to the power of negative T.