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HDI is the geometric mean of three normalised indices: life expectancy scaled between 20 and 85 years, education from expected and mean years of schooling, and log GNI per capita scaled between 100 and 75,000 PPP dollars. The geometric mean means poor performance on any one dimension cannot be offset by the others.
Health index
Health = (Life expectancy - 20) / (85 - 20)
Education index
Education = [min(EYS/18, 1) + min(MYS/15, 1)] / 2
Income index
Income = (ln GNI - ln 100) / (ln 75,000 - ln 100)
HDI
HDI = cube root of (Health x Education x Income)
Indicative estimate only. Fees, entitlements, limits and formulas vary by jurisdiction, statute, policy wording and the facts of the case. This is not legal, tax, insurance or financial advice — confirm with a qualified professional or the relevant authority.
Because it makes the dimensions imperfectly substitutable. A country cannot compensate for very low life expectancy simply by having high income.
Because the contribution of income to human development diminishes as income rises — the difference between 1,000 and 2,000 dollars matters far more than between 40,000 and 41,000.