HHI Calculator

Understanding the Herfindahl-Hirschman Index (HHI)

The Herfindahl-Hirschman Index (HHI) is the premier economic and legal metric used to measure market concentration, evaluate industry competitiveness, and screen proposed mergers and acquisitions. Adopted by the United States Department of Justice (DOJ), the Federal Trade Commission (FTC), the European Commission, and competition regulators worldwide, the index quantifies how market power is distributed across participating firms.

Unlike simple concentration ratios such as the four-firm concentration ratio (CR4), which only sum the market shares of top competitors, HHI squares every market participant's percentage share. By squaring the percentages, the index places disproportionately greater weight on dominant market leaders. A market where one company holds 60% of the market and four hold 10% each faces far more severe competitive risks than an industry with ten equal-sized competitors, even though both have the same total share. When assessing consumer harm and market power, analysts frequently evaluate HHI alongside the deadweight loss calculator to estimate monopoly deadweight loss, the cross-price elasticity calculator to properly delineate relevant antitrust markets, and the Lerner Index calculator to quantify direct firm markup power above marginal cost.

The Mathematical Formula for HHI

The standard formulation of the Herfindahl-Hirschman Index calculates the sum of the squares of each firm's market share expressed as a whole percentage (from 0 to 100):

In this equation, $s_i$ represents the percentage market share of firm $i$, and $N$ is the total number of firms in the relevant market. The resulting index score ranges between near zero and 10,000:

• Near 0 (Perfect Competition): An infinitely fragmented market with thousands of microscopic competitors, each holding a fraction of one percent.
• 10,000 (Pure Monopoly): A single firm controlling 100% of the market, yielding $100^2 = 10{,}000$.

Equivalent Number of Equal-Sized Competitors (Numbers-Equivalent)

A highly intuitive way to interpret an HHI score is calculating its numbers-equivalent ($N_{eq}$). This metric determines the exact number of identically sized firms that would yield the exact same HHI score:

For example, an HHI of 2,500 is structurally equivalent in concentration to a market with exactly four equal-sized firms ($10{,}000 / 2{,}500 = 4.0$). If an HHI reaches 5,000, market concentration is equivalent to a pure duopoly of two equal firms. For evaluating broader structural inequality across firms or wealth distributions, analysts also utilize the Gini coefficient calculator.

Antitrust Regulatory Thresholds: 2023 vs 2010 Merger Guidelines

Antitrust agencies rely on specific HHI thresholds to categorize markets and determine whether a proposed horizontal merger violates Section 7 of the Clayton Act. In December 2023, the DOJ and FTC officially issued updated Merger Guidelines that lowered the bar for highly concentrated markets back to historic benchmarks, superseding the 2010 standards.

Evaluating M&A Mergers and Calculating Delta HHI

When two companies in the same market merge, the market concentration index increases. Remarkably, you do not need to recalculate every rival firm's square to determine the exact change in concentration ($\Delta\mathrm{HHI}$). Because the merged firm's new share is $s_1 + s_2$, the change in HHI is mathematically equal to twice the product of the merging firms' market shares:

For example, suppose Firm A controls 20% of a market and Firm B controls 15%. If Firm A acquires Firm B, the market concentration index jumps by:

Under Guideline 1 of the 2023 DOJ/FTC Merger Guidelines, if the post-merger HHI exceeds 1,800 and the transaction produces a $\Delta\mathrm{HHI}$ greater than 100 points, the government presumes the merger is likely to substantially lessen competition. When companies expand their market control, examining the resulting profitability with the economic profit calculator helps evaluate whether sustained supernormal returns stem from superior efficiency or market power.

Comprehensive Worked Example

Consider a regional broadband internet market with five commercial providers:

• Provider 1: 35% market share
• Provider 2: 25% market share
• Provider 3: 20% market share
• Provider 4: 10% market share
• Provider 5: 10% market share

Step 1: Calculate Pre-Merger HHI

The pre-merger HHI is 2,450. Under the current 2023 guidelines, this market is already highly concentrated (above 1,800). Under the older 2010 guidelines, it would have been classified as moderately concentrated (below 2,500). The effective number of competitors is $10{,}000 / 2{,}450 = 4.08$ equal firms.

Step 2: Propose Merger Between Provider 2 and Provider 4

Provider 2 (25%) proposes acquiring Provider 4 (10%). The combined entity would command a 35% market share, tying Provider 1 as the market leader.

Antitrust Finding: The post-merger market reaches an HHI of 2,950, and the delta is +500 points. Because post-merger HHI exceeds 1,800 and $\Delta\mathrm{HHI} > 100$, regulators would attach a strong legal presumption that the transaction produces anticompetitive harm, requiring the merging parties to provide compelling evidence of efficiencies or structural remedies.

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