Human Development Index (HDI): Formula & Rankings

In 30 seconds

The Human Development Index (HDI) is the United Nations Development Programme’s (UNDP) summary measure of a country’s achievements in health, education and living standards. It runs from 0 to 1.
It uses four indicators: life expectancy at birth, expected years of schooling, mean years of schooling and GNI per capita (PPP $).
Each indicator becomes an index: $ (\text{actual} – \text{min}) / (\text{max} – \text{min}) $. Income is logged first. The HDI is the geometric mean of the three dimension indices.
In the latest report (HDR 2025, data for 2023), Iceland ranks first at 0.972 and South Sudan last at 0.388. Pakistan scores 0.544 and ranks 168th of 193.
Exam point: the HDI is broader than GDP per capita, but it ignores inequality, the environment and the quality of education. Use the IHDI and PHDI to evaluate it.

What is the Human Development Index?

For decades, a country’s progress was judged mainly by its income per person. The HDI asks a wider question: are people living longer, learning more and earning enough to live decently?

Key termHuman Development Index (HDI): a summary measure of average achievement in three key dimensions of human development: a long and healthy life, access to knowledge and a decent standard of living. It is the geometric mean of normalised indices for each dimension^[2].

The idea came out of the human development approach, developed by the economist Mahbub ul Haq and anchored in Amartya Sen’s work on human capabilities^[5]. A capability is what a person is actually able to do or be, such as reading, staying healthy or taking part in community life. The first Human Development Report, published by UNDP in 1990, introduced the approach^[5]^[6].

UNDP says the HDI was created to emphasise that people and their capabilities, not economic growth alone, should be the ultimate criteria for assessing a country’s development^[4].

The index is produced each year by UNDP’s Human Development Report Office (HDRO). The most recent edition is the Human Development Report 2025: A matter of choice: People and possibilities in the age of AI, released on 6 May 2025^[1]. Its HDI values refer to the year 2023. As of mid-2026, UNDP described the 2026 report as still in development^[9], so the 2025 report holds the latest official rankings.

Common mistakeStudents often write “HDI 2025 shows Pakistan’s 2025 score”. It does not. The report is published in 2025, but the data refer to 2023. Always state the data year.

The three dimensions and four indicators

The HDI combines three dimensions. Each one is measured by one or two indicators^[2].

Dimension	Indicator	What it captures
Long and healthy life	Life expectancy at birth (years)	How long a newborn could expect to live if current death rates stayed the same
Knowledge	Expected years of schooling	Years of schooling a child entering school now can expect to receive
Knowledge	Mean years of schooling	Average years of schooling completed by adults aged 25 and older
Decent standard of living	Gross national income (GNI) per capita, 2021 PPP $	Average income per person, adjusted for differences in prices between countries

Key termPurchasing power parity (PPP): a conversion rate that adjusts incomes for differences in the cost of living, so that one PPP dollar buys roughly the same basket of goods in every country. The HDI uses GNI per capita in constant 2021 PPP dollars^[2].

Notice the two education indicators look in different directions. Expected years of schooling looks forward: it tells you about today’s children. Mean years of schooling looks back: it tells you about today’s adults. A country that has recently expanded schooling scores higher on the first than the second.

The current set of indicators dates from the 2010 Human Development Report, which also switched from an arithmetic mean to a geometric mean^[7]. Older textbooks that mention adult literacy and GDP per capita describe the pre-2010 method.

The HDI formula: goalposts, dimension indices and the geometric mean

The four indicators use different units: years, and dollars. You cannot add years to dollars. So the first job is to convert each indicator into a number between 0 and 1. UNDP does this with fixed minimum and maximum values called goalposts.

Step 1: the goalposts

The goalposts act as “natural zeros” and “aspirational targets”^[2]. The HDR 2025 technical notes set them as follows^[2].

Dimension	Indicator	Minimum	Maximum
Health	Life expectancy at birth (years)	20	85
Education	Expected years of schooling (years)	0	18
Education	Mean years of schooling (years)	0	15
Standard of living	GNI per capita (2021 PPP $)	100	75,000

UNDP justifies each choice^[2]. No country in the 20th century had life expectancy below 20 years, while 85 is a realistic aspirational target. Eighteen years of expected schooling is roughly a master’s degree. The $100 income floor allows for unmeasured subsistence production. Income above $75,000 does not raise the HDI at all; nine countries, including Norway, Qatar and Switzerland, exceeded this ceiling in 2023.

Step 2: the dimension index

Each indicator is converted using the same formula^[2]:

\[ \text{Dimension index} = \frac{\text{actual value} – \text{minimum value}}{\text{maximum value} – \text{minimum value}} \]

This tells you how far a country has travelled from the minimum towards the maximum. An index of 0.6 means it has covered 60% of the distance.

For education, you apply the formula to each of the two indicators and then take their simple (arithmetic) average:

\[ I_{\text{Education}} = \frac{1}{2}\left(\frac{\text{EYS}}{18} + \frac{\text{MYS}}{15}\right) \]

Step 3: the income log transformation

Income is treated differently. UNDP argues that the link between income and capabilities is likely to be concave: each extra dollar adds less to what people can do than the dollar before. (the technical notes cite Anand and Sen 2000)^[2]. So the income index uses natural logarithms (ln) of the actual, minimum and maximum values:

\[ I_{\text{Income}} = \frac{\ln(\text{GNI pc}) – \ln(100)}{\ln(75{,}000) – \ln(100)} \]

The log has a neat property. Every doubling of income adds the same amount to the index, about $ \ln 2 / 6.620 \approx 0.105 $. Going from $5,000 to $10,000 adds 0.105. Going from $25,000 to $50,000 also adds 0.105, even though the second rise is five times larger in dollars. This is diminishing marginal returns to income, built straight into the formula.

Exam tipIf asked “why does the HDI use the log of income?”, give two points: (1) diminishing returns, because an extra $1,000 matters far more to a poor household than a rich one; (2) it stops very rich countries winning on income alone. Then mention the $75,000 cap, which does the same job at the top.

Step 4: the geometric mean

Finally, the three dimension indices are combined with a geometric mean^[2]:

\[ \text{HDI} = \left( I_{\text{Health}} \times I_{\text{Education}} \times I_{\text{Income}} \right)^{1/3} \]

Key termGeometric mean: for three numbers, multiply them together and take the cube root. It is never above the arithmetic mean, and the gap grows as the numbers become more unequal.

Why not just add and divide by three? Because an arithmetic mean allows perfect substitution. The geometric mean punishes uneven development. Suppose two countries both average 0.7. Country A scores 0.7 on everything. Country B scores 0.9, 0.9 and 0.3. The arithmetic mean gives both 0.700. The geometric mean gives A 0.700 but B only 0.624. Balanced progress is rewarded.

Common mistakeDo not take the geometric mean of all four indicators. Education’s two sub-indices are averaged arithmetically first. The geometric mean is applied only to the three dimension indices.

Worked example: calculating Pakistan’s HDI from official data

Now rebuild a real HDI. UNDP’s technical notes use Benin^[2]; here we use Pakistan, with its 2023 values from the HDR 2025 data tables^[3].

Worked example

Pakistan’s 2023 indicators (rounded) are: life expectancy at birth 67.6 years; expected years of schooling 7.9; mean years of schooling 4.3; GNI per capita $5,501 (2021 PPP). Calculate Pakistan’s HDI.

Step 1Health index: $ I_H = \dfrac{67.6 – 20}{85 – 20} = \dfrac{47.6}{65} = 0.732 $

Step 2Expected schooling index: $ \dfrac{7.9 – 0}{18 – 0} = 0.439 $. Mean schooling index: $ \dfrac{4.3 – 0}{15 – 0} = 0.287 $

Step 3Education index: $ I_E = \dfrac{0.439 + 0.287}{2} = 0.363 $

Step 4Income index: $ I_I = \dfrac{\ln(5{,}501) – \ln(100)}{\ln(75{,}000) – \ln(100)} = \dfrac{8.613 – 4.605}{11.225 – 4.605} = \dfrac{4.008}{6.620} = 0.605 $

Step 5Multiply: $ 0.732 \times 0.363 \times 0.605 = 0.161 $

Step 6Cube root: $ \text{HDI} = (0.161)^{1/3} = 0.544 $

Pakistan’s HDI is 0.544, exactly the official figure in HDR 2025^[3]. That is just below the 0.550 cut-off, so Pakistan falls in the “low human development” group. The breakdown shows why: health (0.732) and income (0.605) are moderate, but education (0.363) is very weak. Adults average only 4.3 years of school. If you had used an arithmetic mean instead, you would get 0.567 and Pakistan would wrongly appear in the “medium” group. The geometric mean pulls the score down because one dimension lags far behind.

Try the same steps for Saudi Arabia (life expectancy 78.7, expected schooling 16.9, mean schooling 11.6, GNI per capita $50,299)^[3]. You should get a health index of about 0.904, education 0.858, income 0.940 and an HDI of 0.900, matching the official value.

Exam tipKeep three decimal places at each step and say which goalposts you used. Examiners award method marks even if a rounding slip changes the last digit.

HDI categories and how to read the diagram

Since the 2014 report, UNDP has grouped countries using fixed cut-off points^[2]:

Category	HDI value	Group average, 2023
Very high human development	0.800 and above	0.914
High human development	0.700 to 0.799	0.777
Medium human development	0.550 to 0.699	0.656
Low human development	Below 0.550	0.515

Sources: cut-offs from the technical notes^[2]; group averages from the HDR 2025 data^[3].

Diagram Put GNI per capita (PPP $, from $100 to $75,000) on the horizontal axis and the income index (0 to 1) on the vertical axis. The curve starts at 0 at $100, rises steeply and then flattens: a concave curve. Mark two points to show diminishing returns: moving from $1,000 to $2,000 raises the index from 0.348 to 0.453; moving from $40,000 to $75,000 (nearly double) raises it from 0.905 to 1.000. At $75,000 the curve hits 1 and becomes a flat horizontal line, labelled “cap”: extra income adds nothing. A second, straight line from (20 years, 0) to (85 years, 1) on a life expectancy axis shows that the health index, by contrast, is linear: every extra year adds the same 0.015.

Latest HDI rankings (HDR 2025)

The HDR 2025 ranks 193 countries. The world HDI was 0.756 in 2023, up from 0.608 in 1990^[3].

Top and bottom countries

Rank	Country	HDI 2023	Life expectancy	Mean years of schooling	GNI per capita (2021 PPP $)
1	Iceland	0.972	82.7	13.9	69,117
2	Norway	0.970	83.3	13.1	112,710
2	Switzerland	0.970	84.0	13.9	81,949
4	Denmark	0.962	81.9	13.0	76,008
5	Germany	0.959	81.4	14.3	64,053
5	Sweden	0.959	83.3	12.7	66,102
190	Chad	0.416	55.1	2.3	1,748
191	Central African Republic	0.414	57.4	4.0	1,100
192	Somalia	0.404	58.8	1.9	1,475
193	South Sudan	0.388	57.6	5.7	688

Source: UNDP HDR 2025 data tables^[3]. Countries with equal values share a rank.

Look at Norway. Its income is far above $75,000, but the cap means the extra income earns it nothing. Iceland, with much lower income, edges ahead thanks to higher mean years of schooling (13.9 against 13.1).

Selected countries

Country	HDI rank	HDI 2023	Category	Life expectancy	Expected schooling	Mean schooling	GNI per capita (2021 PPP $)
United Kingdom	13	0.946	Very high	81.3	17.8	13.5	54,372
United Arab Emirates	15	0.940	Very high	82.9	15.6	13.0	71,142
United States	17	0.938	Very high	79.3	15.9	13.9	73,650
Saudi Arabia	37	0.900	Very high	78.7	16.9	11.6	50,299
India	130	0.685	Medium	72.0	13.0	6.9	9,047
Pakistan	168	0.544	Low	67.6	7.9	4.3	5,501
World	–	0.756	–	73.4	13.0	8.8	20,327

Source: UNDP HDR 2025 data tables^[3].

The UAE ranks above the United States despite slightly lower income, thanks to life expectancy about 3.6 years higher. India shares rank 130 with Bangladesh, both at 0.685^[3].

Human Development Index, 1990–2023: Saudi Arabia, India and Pakistan (HDI (0–1))

Saudi ArabiaIndiaPakistan

Source: UNDP Human Development Report 2025, composite indices time series [3] Consistent time series published with HDR 2025 (data year 2023). Category cut-offs: 0.550 medium, 0.700 high, 0.800 very high. Years are unevenly spaced after 2015.

The chart shows how the HDI has moved since 1990. Saudi Arabia crossed into “very high” (0.801) in 2010. India’s HDI rose by more than half, from 0.446 to 0.685. Pakistan’s progress was steady until about 2019 and then flattened: its HDI was 0.540 in 2019 and 0.544 in 2023^[3].

Common mistakeDo not compare a country’s rank in HDR 2023/24 with its rank in HDR 2025 to claim it “rose four places”. UNDP revises past data with each report, so ranks from different reports are not comparable. Use the consistent time series published with the latest report^[3].

HDI vs GDP per capita

GDP or GNI per capita measures one thing: average income. The HDI adds health and education. The interesting cases are where the two disagree. The table below ranks all 193 countries by GNI per capita, using the HDR 2025 data^[3], and compares that with their HDI rank:

Pair	GNI per capita (2021 PPP $)	HDI 2023	HDI rank	Main difference
Sri Lanka	12,616	0.776	89	Life expectancy 77.5 years
Equatorial Guinea	12,762	0.674	133	Life expectancy 63.7 years
Nigeria	5,569	0.560	164	Mean schooling 7.6 years
Pakistan	5,501	0.544	168	Mean schooling 4.3 years
Qatar	105,353	0.886	43	4th by income, 43rd by HDI
United Kingdom	54,372	0.946	13	26th by income, 13th by HDI

Sri Lanka and Equatorial Guinea have almost the same income per person, yet Sri Lanka is 44 places higher on the HDI. The gap comes mainly from health: Sri Lankans can expect to live almost 14 years longer. Similar income has not produced similar lives. Qatar is the fourth-richest country by GNI per capita but only 43rd by HDI. This is exactly the question UNDP designed the HDI to raise^[4].

Exam tipWhen a question asks you to compare GDP and HDI, use a pair of countries with similar income and different HDI. It proves in one sentence that income does not automatically become health and education. Then explain why: spending choices, public services or inequality.

Still, the two are closely linked. Income is one third of the HDI, rich countries can afford hospitals and schools, and healthy, educated workers are more productive.

The IHDI and other UNDP indices

UNDP itself admits that the HDI “does not reflect on inequalities, poverty, human security, empowerment”^[4]. It publishes companion indices to fill some of these gaps^[2].

Inequality-adjusted HDI (IHDI). Discounts each dimension by its level of inequality, using the Atkinson inequality measure. If everyone were equal, IHDI would equal HDI. The gap is the “loss” due to inequality^[2].
Gender Development Index (GDI) is female HDI divided by male HDI (1 = parity). The Gender Inequality Index (GII) measures gender gaps in reproductive health, empowerment and work.
Multidimensional Poverty Index (MPI). Counts household deprivations in health, education and living standards.
Planetary pressures–adjusted HDI (PHDI). Adjusts the HDI for carbon dioxide emissions and material footprint per person^[2].

Country	HDI	IHDI	Loss due to inequality (%)	PHDI	GDI
Norway	0.970	0.909	6.3	0.723	0.995
United Kingdom	0.946	0.869	8.1	0.827	0.979
United Arab Emirates	0.940	0.866	7.9	0.585	0.957
United States	0.938	0.832	11.3	0.686	1.009
India	0.685	0.475	30.7	0.656	0.874
Pakistan	0.544	0.364	33.1	0.529	0.838

Source: UNDP HDR 2025 data tables, 2023 values^[3]. Saudi Arabia has no published IHDI for 2023.

Two lessons stand out. First, inequality cuts Pakistan’s score by a third, to 0.364. Second, the PHDI changes the rich-country picture. The UAE falls from 0.940 to 0.585 once its high emissions and resource use are counted, while the UK falls much less, to 0.827^[3].

Criticisms and evaluation of the HDI

It ignores distribution. The HDI uses national averages. A rich minority can lift the average while many people are left behind. The IHDI was built to answer this^[2]^[4].
Goalposts and weights are judgement calls. Why 85 years and not 90? Why $75,000? Why equal weight on each dimension? Different choices would change some rankings.
Hidden trade-offs. Martin Ravallion showed that the HDI’s formula implies a monetary value for an extra year of life, and that this implied value is far lower in poor countries than in rich ones^[8].
Quantity, not quality. Years of schooling say nothing about what children learn.
Narrow scope. The HDI leaves out political freedom, security, unpaid work and the environment. The PHDI addresses only the last of these.
Data quality and lags. Some figures are modelled estimates, especially for fragile states. The latest rankings describe 2023, not today.

On the other side of the scale, the HDI has real strengths. It is easy to calculate and explain. The geometric mean rewards balanced development. And it has changed the conversation: governments now report on health and education outcomes, not just growth rates. UNDP also supports national reports, such as Pakistan’s National Human Development Report^[10], which apply the same tools inside a single country.

Exam tipA strong evaluation does not just list criticisms. It weighs them. For example: ignoring inequality matters greatly for Pakistan, where the IHDI is a third below the HDI, but much less for Norway, where the loss is 6%.

Practice questions

EasyQ1. A country has life expectancy at birth of 74 years. Calculate its health index. Show worked answer

$ I_H = \dfrac{74 – 20}{85 – 20} = \dfrac{54}{65} = 0.831 $. The country has covered 83.1% of the distance between the minimum (20) and maximum (85) goalposts.

EasyQ2. Country X has an HDI of 0.712 and Country Y an HDI of 0.548. Which human development category is each in? Show worked answer

Country X: 0.712 lies between 0.700 and 0.799, so it is high human development. Country Y: 0.548 is below 0.550, so it is low human development, just short of the medium threshold.

MediumQ3. Calculate the income index for GNI per capita of $20,000 (2021 PPP). Then explain why doubling income to $40,000 raises the index by the same amount as doubling from $5,000 to $10,000. Show worked answer

$ I_I = \dfrac{\ln(20{,}000) – \ln(100)}{\ln(75{,}000) – \ln(100)} = \dfrac{9.903 – 4.605}{11.225 – 4.605} = \dfrac{5.298}{6.620} = 0.800 $. Because $ \ln(2x) – \ln(x) = \ln 2 $, any doubling of income adds $ \ln 2 / 6.620 = 0.105 $ to the index, whatever the starting level. This builds diminishing returns into the HDI: an extra $20,000 earns the same 0.105 as an extra $5,000 at a lower level.

MediumQ4. Suppose a country has dimension indices of health 0.8, education 0.6 and income 0.7. Calculate its HDI, and explain why it is lower than the simple average of the three indices. Show worked answer

Product: $ 0.8 \times 0.6 \times 0.7 = 0.336 $. HDI $ = (0.336)^{1/3} = 0.695 $. The arithmetic mean is $ (0.8 + 0.6 + 0.7)/3 = 0.700 $. The geometric mean falls further below the arithmetic mean the more unequal the indices are, so the weak education score pulls the HDI down. Unbalanced development is penalised.

ExamQ5. Evaluate the view that the Human Development Index is a better measure of economic development than GDP per capita. [15 marks] Show worked answer

Knowledge and understanding (up to 4 marks): define HDI as the geometric mean of health, education and income indices, using life expectancy, expected and mean years of schooling and GNI per capita (PPP). Define GDP per capita as total output divided by population.

Analysis (up to 5 marks): HDI captures outcomes that matter for welfare beyond income. Logging income reflects diminishing marginal utility. The geometric mean rewards balanced development. Evidence: Sri Lanka and Equatorial Guinea have near-identical GNI per capita but HDIs of 0.776 and 0.674 (HDR 2025).

Evaluation (up to 6 marks): HDI still uses averages and ignores inequality: Pakistan’s IHDI (0.364) is a third below its HDI (0.544). Goalposts and weights are arbitrary (Ravallion 2012). Years of schooling ignore quality. HDI ignores environmental damage: the UAE’s PHDI is 0.585 against an HDI of 0.940. GDP is more timely and better for short-run analysis. Reach a judgement: HDI is a better measure of development because development is multidimensional, but it is best used alongside GDP, the IHDI and the PHDI rather than on its own.

Frequently asked questions

How is HDI calculated?

Turn each indicator into a 0–1 index using $ (\text{actual} – \text{min}) / (\text{max} – \text{min}) $, with income in natural logs. Average the two education indices. Then take the cube root of the product of the three dimension indices.

Which country has the highest HDI?

In the Human Development Report 2025, with data for 2023, Iceland ranks first with an HDI of 0.972, followed by Norway and Switzerland, both at 0.970.

What is Pakistan’s HDI rank?

168th of 193 in HDR 2025, with an HDI of 0.544: low human development, just below the 0.550 threshold.

Why does the HDI use a geometric mean?

It stops a high score in one dimension from fully compensating for a low score in another, so balanced progress is rewarded. UNDP adopted it in 2010.

References

UNDP Human Development Report Office (2025). “Human Development Report 2025: A matter of choice: People and possibilities in the age of AI”. United Nations Development Programme. https://hdr.undp.org/content/human-development-report-2025
UNDP Human Development Report Office (2025). “Human Development Report 2025 Technical Notes”. United Nations Development Programme. https://hdr.undp.org/sites/default/files/2025_HDR/hdr2025_technical_notes.pdf
UNDP Human Development Report Office (2025). “HDR 2025 Composite Indices Complete Time Series, 1990–2023” (data file). United Nations Development Programme. https://hdr.undp.org/sites/default/files/2025_HDR/HDR25_Composite_indices_complete_time_series.csv
UNDP Human Development Report Office (n.d.). “Human Development Index (HDI)”. Data Center, United Nations Development Programme. https://hdr.undp.org/data-center/human-development-index
UNDP Human Development Report Office (n.d.). “Human development”. United Nations Development Programme. https://hdr.undp.org/about/human-development
UNDP (1990). “Human Development Report 1990: Concept and Measurement of Human Development”. Oxford University Press for UNDP. https://hdr.undp.org/content/human-development-report-1990
UNDP (2010). “Human Development Report 2010 (20th Anniversary Edition): The Real Wealth of Nations: Pathways to Human Development”. Palgrave Macmillan for UNDP. https://hdr.undp.org/system/files/documents/human-development-report-2010-complete-english.human-development-report-2010-complete-english
Ravallion, M. (2012). “Troubling tradeoffs in the Human Development Index”. Journal of Development Economics, 99(2), 201–209. https://ideas.repec.org/a/eee/deveco/v99y2012i2p201-209.html
UNDP Jamaica (2026). “Global Human Development Report (HDR) team looks to Jamaica for climate crisis insights following hurricane Melissa” (press release, 16 June 2026). United Nations Development Programme. https://www.undp.org/jamaica/press-releases/global-human-development-report-hdr-team-looks-jamaica-climate-crisis-insights-following-hurricane-melissa
UNDP Pakistan (2018). “Pakistan National Human Development Report: Unleashing the Potential of a Young Pakistan”. United Nations Development Programme. https://files.acquia.undp.org/public/migration/pk/PK-NHDR.pdf

Human Development Index (HDI): Formula, Worked Calculation and Latest Rankings