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

Frequently Asked Questions

What HHI level triggers antitrust review?

The US DOJ considers markets with HHI above 2,500 as highly concentrated. Mergers that increase HHI by more than 200 points in concentrated markets are presumed to enhance market power and face scrutiny.

What are equivalent firms?

The reciprocal of the normalized HHI (or 10000/HHI) gives the number of equal-size firms that would produce the same HHI. An HHI of 3000 is equivalent to about 3.3 equal-size firms.

Can HHI be used outside antitrust?

Yes. HHI measures concentration in any context: portfolio diversification (concentration across assets), ecological diversity (species abundance), market research (brand concentration), and voting power analysis.

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