Herfindahl Index Calculator Formula

Understand the math behind the herfindahl index calculator. Each variable explained with a worked example.

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Formulas Used

HHI

hhi = pow(s1, 2) + pow(s2, 2) + pow(s3, 2) + pow(s4, 2)

Normalized HHI (0-1)

normalized_hhi = (pow(s1, 2) + pow(s2, 2) + pow(s3, 2) + pow(s4, 2)) / 10000

Equivalent Firms

equivalent_firms = 10000 / (pow(s1, 2) + pow(s2, 2) + pow(s3, 2) + pow(s4, 2))

Total Market Share (%)

total_share = s1 + s2 + s3 + s4

Variables

VariableDescriptionDefault
s1Firm 1 Market Share (%)40
s2Firm 2 Market Share (%)30
s3Firm 3 Market Share (%)20
s4Firm 4 Market Share (%)10

How It Works

How to Calculate the Herfindahl-Hirschman Index

Formula

HHI = Sum of (si)^2

where si is each firm's market share as a percentage. HHI ranges from near 0 (highly competitive) to 10,000 (monopoly with 100% share). US DOJ guidelines: HHI < 1,500 = unconcentrated, 1,500-2,500 = moderately concentrated, > 2,500 = highly concentrated.

Worked Example

Four firms with market shares: 40%, 30%, 20%, 10%.

s1 = 40s2 = 30s3 = 20s4 = 10
  1. 01HHI = 40^2 + 30^2 + 20^2 + 10^2
  2. 02= 1600 + 900 + 400 + 100 = 3000
  3. 03HHI = 3000 (highly concentrated)
  4. 04Normalized = 3000 / 10000 = 0.30
  5. 05Equivalent equal-size firms = 10000/3000 ≈ 3.33

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