Normalization
To make indicators comparable and to facilitate analysis, the data are normalized by assigning the value 0 to the least desirable indicator values and the value 1 to the most desirable indicator values or targets, which are determined by experts, standards, laws, etc.
For example, HIV/AIDS prevalence rate per cent of population had a maximum value of 23.4% over all countries in 2011 (most recent data). Given its significant potential for rapid spread, even a value of 2% for this indicator is considered to be very bad. The Joint United Nations Programme on HIV/AIDS provides an upper bound of 0.9% on the average HIV prevalence rate (UNAIDS 2007). The least desirable value is chosen as twice the upper bound. All HIV/AIDS prevalence rates greater than or equal to 1.8% are assigned the value 0. The rate 0%, which is the target for this indicator, corresponds to 1.
Let c be an indicator and z_{c} its value for the country whose sustainability we want to assess. The target of c can be a single value T_{c} or an interval on the real line of the form [τ_{c}, T_{c}] representing a range of equally desirable values for the indicator. Least desirable values can be sole points or sets of values below or above some critical threshold. Critical values are denoted υ_{c} and U_{c}, so that all values z_{c} ≤ υ_{c} or z_{c} ≥ U_{c} are assigned a normalized value 0.
In practice υ_{c} is the minimum value of z_{c} over all countries under examination and U_{c} its maximum. In some cases though we choose these numbers differently. For example, we have U_{AIDS} = 1.8% whereas the maximum HIV/AIDS prevalence rate worldwide is 23.4%. Thus, if an indicator must be at most equal to T_{c} to be sustainable, then we have the case of Fig. 2. Here we do not need υ_{c} and τ_{c}. An HIV/AIDS prevalence rate of 0.9% is assigned the normalized value 0.5 because it is halfway between the target 0% and the critical threshold 1.8% of least desirable values.
Similarly, if an indicator must be at least equal to τ_{c} to be sustainable, we have the case of Fig. 3 and we do not need T_{c} and U_{c}.
Finally, if an indicator must lie in [τ_{c}, T_{c}] to be sustainable, then we have the full diagram of Fig. 4.
A normalized value x_{c} for z_{c} is calculated as follows:
\[{x_c} = \left\{ {\begin{array}{*{20}{l}}0&{{z_c} \le {\upsilon _c}}\\{\frac{{{z_c}  {\upsilon _c}}}{{{\tau _c}  {\upsilon _c}}}}&{{\upsilon _c} < {z_c} < {\tau _c}}\\1&{{\tau _c} \le {z_c} \le {T_c}}\\{\frac{{{U_c}  {z_c}}}{{{U_c}  {T_c}}}}&{{T_c} < {z_c} < {U_c}}\\0&{{U_c} \le {z_c}}\end{array}} \right.\]The target and least desirable values for each indicator are given in the following table.
Component  Basic Indicator  Type^{a}  Thresholds^{b,c} 

^{a}SB = smaller is better; LB = larger is better; NB = nominal is best.  
^{b}υ, τ, T, and U are thresholds of target (sustainable) and unsustainable values. Values in the interval [τ, T] are assigned the sustainability index 1. Values ≤ υ or ≥ U indicate poor performance and are assigned the sustainability index 0. Values in (υ, τ) or (T, U) are scaled in (0, 1) by linear interpolation.  
^{c}Sources of indicator data:


PR(LAND)  Municipal waste (kg per capita per year)  SB  T = 300.0, U = 817.5 
PR(LAND)  Nuclear waste (tons per capita per year)  SB  T = 0, U = 0.0593 
PR(LAND)  Hazardous waste (tons per capita per year)  SB  T = 0, U = 1.0881 
PR(LAND)  Population growth rate (percent)  SB  T = 0, U = 1.2 
PR(LAND)  Pesticide consumption (kg per hectare)  SB  T = 3.22, U = 8.00 
PR(LAND)  Fertilizer consumption (kg per hectare)  SB  T = 162.471, U = 477.333 
ST(LAND)  Desertification of land (percent of dryland area)  SB  T = 0, U = 100 
ST(LAND)  Forest area (percent of what existed in 2000)  LB  υ = 0, τ = 100 
RE(LAND)  Forest change (annual rate)  LB  υ = 0.0690, τ = 0.0257 
RE(LAND)  Protected area (percent of total land area)  LB  υ = 0.2592, τ = 53.7527 
RE(LAND)  Glass recycling (percent of apparent consumption)  LB  υ = 0, τ = 100 
RE(LAND)  Paper recycling  LB  υ = 0, τ = 100 
PR(WATER)  Pesticide consumption (kg per hectare)  SB  T = 3.22, U = 8.00 
PR(WATER)  Fertilizer consumption (kg per hectare)  SB  T = 162.471, U = 477.333 
PR(WATER)  Water withdrawals (percent of internal resources)  SB  T = 22.7287, U = 90.8123 
ST(WATER)  BOD emissions (kg per capita per day)d1  SB  T = 0.0090, U = 0.0146 
ST(WATER)  Phosphorous concentration (mg per liter of water)  SB  T = 0.1764, U = 0.6700 
ST(WATER)  Metals concentration (microSiemens per centimeter)  SB  T = 438.8, U = 2,247.4 
RE(WATER)  Public wastewater treatment plants (percent of population connected)  LB  υ = 0, τ = 86.64 
PR(BIOD)  Threatened mammals (percentage)  SB  T = 0, U = 35.46 
PR(BIOD)  Threatened birds (percentage)  SB  T = 0, U = 33.16 
PR(BIOD)  Threatened plants (percentage)  SB  T = 0, U = 8.45 
PR(BIOD)  Threatened fishes (percentage)  SB  T = 0, U = 55.10 
PR(BIOD)  Threatened amphibians (percentage)  SB  T = 0, U = 20.72 
PR(BIOD)  Threatened reptiles (percentage)  SB  T = 0, U = 20.75 
ST(BIOD)  Desertification of land (percent of dryland area)  SB  T = 0, U = 100 
ST(BIOD)  Forest area (percent of what existed in 2000)  LB  υ = 0, τ = 100 
RE(BIOD)  Forest change (annual rate)  LB  υ = 0.0690, τ = 0.0257 
RE(BIOD)  Protected area (percent of total land area)  LB  υ = 0.2592, τ = 53.7527 
PR(AIR)  Ozone depleting substances (metric tons per capita)  SB  T = 0, U = 0.1475 
PR(AIR)  Greenhouse gas emissions (tons of CO2 equivalent per capita)  SB  T = 0.0057, U = 0.0368 
ST(AIR)  Mortality from poor air quality (deaths per 100,000 population)  SB  T = 12.8, U = 1,805.2 
ST(AIR)  Urban NO2 concentration (mg/m3 of air)  SB  T = 18.20, U = 109.16 
ST(AIR)  Urban SO2 concentration (mg/m3 of air)  SB  T = 1.33, U = 97.07 
ST(AIR)  Urban TSP (total suspended particulates) concentration (mg/m3 of air)  SB  T = 18.92, U = 320.00 
RE(AIR)  Renewable energy production (percent of total primary energy supply)  LB  υ = 0, τ = 20 
PR(POLICY)  Military spending (percent of GDPd2)  SB  T = 1.5471, U = 8.4135 
PR(POLICY)  Refugees per capita (country of origin)  SB  T = 0.00025, U = 0.01000 
PR(POLICY)  Poverty (percent of population below national poverty line)  SB  T = 0, U = 29.6 
ST(POLICY)  Political rights (values in [1, 7])d3  SB  T = 1, U = 3 
ST(POLICY)  Civil liberties (values in [1, 7])d3  SB  T = 1, U = 3 
ST(POLICY)  Gini indexd4  SB  T = 25.79, U = 50.00 
ST(POLICY)  Corruption Perceptions Index (values in [0, 10])d5  LB  υ = 3, τ = 8 
RE(POLICY)  Environmental laws and enforcement (values in [0, 1])d6  LB  υ = 0.1774, τ = 0.5974 
RE(POLICY)  Tax revenue (percent of GDP)  LB  υ = 9.4523, τ = 21.3757 
PR(WEALTH)  GDP implicit deflator (annual percent growth rate)  SB  T = 1.3221, U = 3.0871 
PR(WEALTH)  Imports (percent of GDP)  SB  T = 47.9642, U = 84.2983 
PR(WEALTH)  Unemployment (percent of total labor force)  NB  υ = 0.7, τ = 4.0, T = 7.0, U = 12.0 
PR(WEALTH)  Unemployment gender gap (percent)  SB  T = 0, U = 6.5 
ST(WEALTH)  Poverty (percent of population below national poverty line)  SB  T = 0, U = 29.6 
ST(WEALTH)  Central government debt (percent of GDP)  SB  T = 77.9, U = 176.2 
ST(WEALTH)  GNI per capita PPPd7  LB  υ = 24,620, τ = 36,091 
RE(WEALTH)  Exports (percent of GDP)  LB  υ = 5.4856, τ = 50.3272 
RE(WEALTH)  Foreign direct investment (percent of GDP)  LB  υ = 2.8982, τ = 3.3123 
PR(HEALTH)  Mortality from poor air quality (deaths per 100,000 population)  SB  T = 12.8, U = 1,805.2 
PR(HEALTH)  Infant mortality rate (deaths per thousand)  SB  T = 2.63, U = 98.20 
PR(HEALTH)  Maternal mortality rate (deaths per 100,000 live births)  SB  T = 6.83, U = 690.00 
PR(HEALTH)  HIV/AIDS prevalence rate (percent of population aged 1549)  SB  T = 0, U = 1.8 
PR(HEALTH)  Tuberculosis prevalence rate (per 100,000 population)  SB  T = 0, U = 993 
PR(HEALTH)  Malaria cases (per thousand people)  SB  T = 0, U = 0.0012 
ST(HEALTH)  Life expectancy (years)  LB  υ = 47.7764, τ = 80.9659 
ST(HEALTH)  Immunization against measles (percent of population)  LB  υ = 76, τ = 100 
ST(HEALTH)  Immunization against DPT (percent of population)d8  LB  υ = 83, τ = 100 
ST(HEALTH)  Daily per capita calorie supply  LB  υ = 1,604, τ = 3,486 
RE(HEALTH)  Number of doctors (per thousand people)  LB  υ = 0.0080, τ = 3.7843 
RE(HEALTH)  Hospital beds (per thousand people)  LB  υ = 0.1000, τ = 3.1767 
RE(HEALTH)  Public health expenditure (percent of GDP)  LB  υ = 0.2589, τ = 8.2798 
RE(HEALTH)  Access to improved water sources (percent of population)  LB  υ = 40, τ = 100 
RE(HEALTH)  Access to improved sanitation (percent of population)  LB  υ = 9, τ = 100 
PR(KNOW)  Primary education ratio of students to teaching staff  SB  T = 12.8785, U = 76.0736 
PR(KNOW)  Secondary education ratio of students to teaching staff  SB  T = 10.9696, U = 66.8171 
PR(KNOW)  Tertiary education ratio of students to teaching staff  SB  T = 14.88, U = 45.50 
ST(KNOW)  Male expected years of schooling  LB  υ = 5.8829, τ = 12.0000 
ST(KNOW)  Female expected years of schooling  LB  υ = 4.0826, τ = 12.0000 
ST(KNOW)  Primary net school enrollment (percent of children)  LB  υ = 33.0700, τ = 98.2542 
ST(KNOW)  Secondary net school enrollment (percent of children)  LB  υ = 8.70, τ = 93.16 
ST(KNOW)  Literacy rate (percent of population)  LB  υ = 28.6724, τ = 100 
ST(KNOW)  Knowledge Economy Index (KEI; values in [0, 10])d9  LB  υ = 4.07, τ = 8.61 
RE(KNOW)  Public expenditure on research and development (percent of GDP)  LB  υ = 0, τ = 2.2627 
RE(KNOW)  Public expenditure on education (percent of GDP)  LB  υ = 1.2291, τ = 5.8321 
RE(KNOW)  Personal computers (per thousand people)  LB  υ = 0, τ = 406 
RE(KNOW)  Internet users (per hundred people)  LB  υ = 0.26, τ = 78.11 
RE(KNOW)  Expenditure on information and communication (percent of GDP)  LB  υ = 0, τ = 5.6465 