Workforce Diversity Index (Blau, Shannon & Simpson

People Analytics & DEI: Mathematical Diversity Indices

To move beyond simplistic percentage quotas, organizational psychologists and DEI researchers use established mathematical diversity indices:

• Blau's Index of Diversity (Peter Blau, 1977): The standard categorical metric measuring heterogeneity). It represents the probability that two randomly selected employees will belong to different demographic cohorts.

• The Maximum Diversity Limit ((k-1) / (k)): For 2 groups (e.g. binary gender), maximum Blau is 0.50; for 5 groups, maximum Blau is 0.

• Normalizing by D_ allows fair comparisons across teams with different category counts.

• Shannon-Wiener Entropy (H') & Pielou's Evenness (J): Originating in information theory and ecology, Shannon entropy measures both the richness (number of distinct groups) and equitability (evenness of distribution between groups).

How to Use This Calculator

Enter your Demographic / Department Group A Headcount (e.g. 45), Demographic / Department Group B Headcount (e.g. 30), Demographic / Department Group C Headcount (e.g. 15), Demographic / Department Group D Headcount (e.g. 8), and Demographic / Department Group E Headcount (e.g. 2). Verify your units match the formula standard (SI vs imperial) before entering values.

The Formula

Workforce Demographic \& Diversity Analytics (Peter Blau, 1977) equations:

Group Proportions: p_i = (n_i) / (N) (N = Σ n_i)

Blau's Index of Diversity: D_Blau = 1 - Σ_i=1^k p_i^2

Maximum Possible Blau for k Categories: D_ = (k - 1) / (k)

Normalized Diversity Score (\%) = (D_BlauD_) × 100\% = ((k) / (k - 1) D_Blau) × 100\%

Shannon-Wiener Entropy Index: H' = -Σ_i=1^k p_i (p_i)

Pielou's Evenness Equitability: J = (H') / ((k))

Worked Example

For example, assessing a company of 100 employees across 5 demographic cohorts with headcounts of 45, 30, 15, 8, and 2: Proportions are . Sum of squared proportions is . The Blau Index is \ (84.8\% of theoretical max 0.800 for 5 groups). The Shannon Entropy is \ with a Pielou Evenness index \ = 0.790.

Understanding Your Result

Force in Newtons (N): 1 N = 1 kg·m/s². Reference values: 1 kg object at Earth's surface weighs 9.81 N, atmospheric pressure 101,325 Pa (N/m²). Pressure benchmarks: car tire 30–35 psi (207–241 kPa), blood pressure systolic 120 mmHg (16 kPa), deep sea at 3,000m depth ~300 atm (30 MPa). Torque = Force × moment arm length — doubling the wrench length doubles the torque for the same applied force. Always verify whether gauge or absolute pressure is required for the application.