Poverty Gap Index Calculator

What Is the Poverty Gap Index Calculator?

The Poverty Gap Index Calculator works out all three Foster-Greer-Thorbecke (FGT) poverty measures, P0, P1, and P2, from a poverty line and a list of individual incomes or grouped income brackets. Economists, NGOs, and government planners use the poverty gap index specifically because the more commonly cited poverty headcount ratio only counts how many people are poor and says nothing about how poor they are. Most online poverty gap tools ask you to type in an already-aggregated total gap figure and return a single average; this calculator instead takes raw income data directly and returns the full FGT family, headcount, depth, and severity, together in one pass.

Given that poverty reduction programs are usually judged on headcount movement alone, a government or NGO can look successful on paper while leaving its poorest households almost untouched. Working out P1 and P2 alongside P0 makes that gap visible, and is exactly the combination the World Bank's own poverty methodology recommends reporting together rather than in isolation.

How the FGT Measures Are Calculated

For every person whose income falls below the poverty line z, the calculator works out their individual gap ratio, (z minus their income) divided by z. People at or above the line contribute zero. P0, the headcount ratio, is simply the proportion of the total population below the line. P1, the poverty gap index, averages every individual's gap ratio across the entire population, not just the poor, which is why P1 is always smaller than or equal to P0. P2, the poverty severity index, squares each gap ratio before averaging, so a household far below the line contributes disproportionately more to P2 than to P1, in line with the original 1984 framework set out by Foster, Greer, and Thorbecke.

The calculator also reports the income gap ratio, P1 divided by P0, which isolates the average shortfall among only the people who are poor, and the total poverty gap in your currency unit, which is the amount of income transfer theoretically required to lift every poor person exactly up to the poverty line.

P0 vs P1 vs P2: Why Showing All Three Matters

A region can cut its headcount ratio quickly by raising incomes for households that were only marginally below the poverty line, since that requires the smallest transfer per person. That same strategy can leave P1 and especially P2 almost unchanged if the households furthest below the line receive no extra support, a pattern Brookings Institution's review of World Bank poverty measurement flags as a reason to never judge a program on the headcount ratio alone.

Depth Tiers and Real-World Benchmarks

World Bank Poverty and Inequality Platform data, measured against the international poverty line, shows poverty gap index values below 2 percent in countries such as China and Indonesia, where extreme poverty has been largely eliminated, climbing to 1 to 4 percent in middle-income economies such as Brazil, Mexico, and Bangladesh, and exceeding 20 percent in fragile, low-income states such as Madagascar, Chad, and the Democratic Republic of Congo. Comparing your own computed P1 against these benchmarks only makes sense if you use the same poverty line and survey methodology, since a poverty gap index calculated against a national poverty line is not directly comparable to one calculated against the international $2.15-a-day line. If you also want to measure income inequality directly within your dataset alongside its poverty depth, our Gini Coefficient Calculator computes that companion statistic from the same kind of income data.

Accuracy and Limitations

The FGT calculations here are exact for the income data and poverty line you enter, but the poverty gap index has a well-documented structural limitation: it does not capture inequality among the poor themselves. Economist Amartya Sen pointed out that transferring income from a slightly poor household to a much poorer one, while keeping the total gap unchanged, leaves P1 completely unaffected even though the distribution among the poor has become more unequal. This is exactly why P2 is reported alongside P1 rather than treated as redundant, since P2 does respond to that kind of transfer through its squared term.

The calculator also depends on accurate income reporting. Self-reported income surveys, the basis for most real-world World Bank poverty estimates, are known to understate income at the very top and bottom of a distribution, so treat results from small or self-reported samples as directional rather than exact.

The Most Common Poverty Gap Reporting Mistake

The mistake I see most often is a program reporting a falling headcount ratio as proof that poverty depth is also improving, without checking P1 or P2 at all. A falling P0 with a flat or rising P1 is a specific, recognisable pattern: it means resources reached people closest to the poverty line first, while the deepest poverty went largely unaddressed. Before crediting a program with reducing poverty broadly, I check whether the income gap ratio, P1 divided by P0, has also fallen. If P0 drops but the income gap ratio stays flat or rises, the people still classified as poor are, on average, just as poor as before, even though fewer of them remain above the line on paper.