Theil Index Calculator
The Theil Index Calculator is a sophisticated, accurate online tool designed for economists, researchers, policymakers, and students to measure income or resource inequality using the Theil index—a powerful entropy-based metric developed by econometrician Henri Theil in 1967. Unlike the Gini coefficient, the Theil index is fully decomposable, allowing analysis of inequality within and between subgroups (e.g., regions, sectors, or demographic groups). This calculator implements the standard Theil T index with high precision using peer-reviewed formulas.
Calculate Theil Index (Theil T)
Enter individual or household values (e.g., incomes, wealth, land holdings) separated by commas, spaces, or one per line. Values must be positive numbers.
About the Theil Index Calculator
This Theil Index Calculator uses the general entropy formula for Theil's T index: T = (1/n) Σ [(y_i / μ) × ln(y_i / μ)], where y_i is each individual's value, μ is the population mean, and n is the number of observations. This measure belongs to the generalized entropy class (α=1) and satisfies key axioms including decomposability, making it ideal for multilevel inequality analysis.
The index ranges from 0 (perfect equality) to ln(n) (maximum inequality—one unit holds everything). It is particularly valued for its additive decomposability property.
Importance of the Theil Index
The Theil index is one of the most advanced and theoretically sound measures of inequality in economics and social sciences. Its key advantage is perfect decomposability: total inequality can be expressed as the sum of within-group and between-group components. This enables researchers to quantify how much inequality arises from differences between regions, industries, or ethnic groups versus within them.
International organizations (UNDP, World Bank) and academic studies frequently use the Theil index for regional inequality analysis, globalization impact assessment, and policy evaluation. It is more sensitive to changes at the top of the distribution than some other measures.
When and Why You Should Use This Tool
Use the Theil Index Calculator when you need to:
- Measure overall inequality in income, wealth, or resource distribution
- Decompose inequality sources (requires grouped data in future extensions)
- Compare inequality across countries, regions, or time periods
- Analyze agricultural income disparities among farmers
- Study sectoral or regional contributions to national inequality
- Conduct rigorous academic or policy research requiring decomposable metrics
Choose Theil over Gini when decomposability or entropy interpretation is important.
User Guidelines and How to Use the Calculator
- Enter positive numerical values representing individual units (e.g., household incomes in currency units).
- Values can be separated by commas, spaces, or line breaks.
- Click "Calculate Theil Index".
- View the Theil T value, mean, and interpretation.
- Lower values indicate greater equality; higher values indicate greater inequality.
This version computes the overall Theil T index. Future grouped input can enable full decomposition.
Example Calculation
Data: 10,000 | 20,000 | 30,000 | 50,000 | 80,000
Mean μ = 38,000
Theil T = (1/5) Σ [(y_i/μ) ln(y_i/μ)] ≈ 0.132
Interpretation: Moderate level of inequality
Purpose of the Theil Index Calculator
This free, scientifically accurate tool democratizes access to advanced inequality measurement, supporting evidence-based policy in development economics, regional planning, and agricultural economics. Understanding the sources of inequality is crucial for designing targeted interventions, such as progressive taxation, regional development programs, or land redistribution.
In agriculture, high Theil indices may reveal disparities between smallholder and commercial farmers or between regions with different agro-ecological conditions.
Learn more on Wikipedia's Theil index page.
Advantages over Gini: Full decomposability, clear information-theoretic meaning (redundancy in income message), and sensitivity to transfers at different distribution levels via generalized forms.
Limitations: Requires positive values (zero income causes issues); less intuitive than Gini for general audiences.
The Theil index complements other measures, providing deeper insights into inequality structure and dynamics.
For agriculture and development resources, visit Agri Care Hub.
Its mathematical foundation in information theory ensures rigorous, comparable results across contexts and scales.
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