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HHI Calculator (Herfindahl-Hirschman Index)

Calculate the Herfindahl-Hirschman Index (HHI) from firm market shares, from an equal number of firms, or the HHI change from a merger. See the market concentration level instantly.

Author: Naeem Ullah
•Last Updated: July 7, 2026•
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Active Calculation FormulaHHI = Σ (Market Share_i)²

Adjust Variables

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share1
Min: 0 %Max: 100 %
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share2
Min: 0 %Max: 100 %
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share3
Min: 0 %Max: 100 %
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share4
Min: 0 %Max: 100 %
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share5
Min: 0 %Max: 100 %
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Real-Time Results
HHI0
Market Concentration—
Equivalent Number of Firms0
All calculations are compiled with double-precision floating math directly in this browser frame. Perfect precision guaranteed.

Interactive Step-by-Step Calculation Proofs

View how variables resolve algebraically down to peer-reviewed standard outputs.

Why Use This Calculator

The Herfindahl-Hirschman Index (HHI) is the standard measure economists and antitrust regulators use to gauge how concentrated a market is among its competing firms. It's calculated by squaring the market share of every firm in the market (expressed as a percentage from 0–100) and summing the results: HHI = Σ (Market Share)². Because shares are squared, HHI weights larger firms disproportionately — a market with one dominant firm produces a much higher HHI than a market with the same number of firms sharing business more evenly. The U.S. Department of Justice and FTC classify markets using HHI thresholds: below 1,500 is unconcentrated, 1,500–2,500 is moderately concentrated, and above 2,500 is highly concentrated. HHI is central to merger review — regulators also examine ΔHHI (the increase in HHI caused by a proposed merger), since a merger that pushes ΔHHI above 100 in a moderately concentrated market, or above 200 in a highly concentrated one, is presumed to raise antitrust concerns. This calculator supports all three common HHI questions: computing HHI directly from a list of market shares, estimating HHI for a hypothetical market of N equally sized firms, and calculating the ΔHHI impact of a two-firm merger.

Mathematical Formula Explanation

Calculated standard benchmarks are based on direct functional dependencies. The primary calculation logic follows this formula:

HHI = Σ (Market Share_i)²

From Market Shares sums the square of each firm's share directly. From Equal-Sized Firms is a simplified special case of that same formula — when every firm holds an identical share (100 ÷ N), the sum of squares reduces algebraically to 10,000 ÷ N, so this mode skips entering each share individually. Merger Impact (ΔHHI) is a different calculation entirely: rather than computing a market's total HHI, it isolates just the increase two merging firms' combined share would add, using the identity that the cross-term between two shares (2 × Share A × Share B) is exactly the amount their combination adds to the sum-of-squares total.

Worked Examples (Step-by-Step)

These examples show HHI computed from five actual firm shares, from a hypothetical market of equally sized competitors, and the ΔHHI impact of a proposed two-firm merger.

Case Scenario 1

Example 1: HHI From Five Firms' Market Shares

“A market has five firms with shares of 30%, 25%, 20%, 15%, and 10%. What is the HHI, and how concentrated is the market?”

Given Inputs
  • SHARE1: 30
  • SHARE2: 25
  • SHARE3: 20
  • SHARE4: 15
  • SHARE5: 10
Computed Outputs
  • HHISHARES: 2,250
  • CONCENTRATIONSHARES: 2
  • EQUIVFIRMSSHARES: 4.44
Case Scenario 2

Example 2: HHI for a Market of 3 Equal Firms

“A hypothetical market has exactly 3 firms, each with an equal market share. What is the HHI?”

Given Inputs
  • NUMFIRMS: 3
Computed Outputs
  • SHAREPERFIRM: 33.33
  • HHIEQUAL: 3,333.33
  • CONCENTRATIONEQUAL: 3
Case Scenario 3

Example 3: HHI Change From a Proposed Merger

“A moderately concentrated market has a pre-merger HHI of 1,800. Two firms holding 15% and 10% market share propose to merge. What is the ΔHHI, and is the market still moderately concentrated afterward?”

Given Inputs
  • PREMERGERHHI: 1,800
  • SHAREA: 15
  • SHAREB: 10
Computed Outputs
  • DELTAHHI: 300
  • POSTMERGERHHI: 2,100
  • CONCENTRATIONPOST: 2

Frequently Asked Questions (FAQ)

The Herfindahl-Hirschman Index (HHI) is a measure of market concentration calculated by squaring the market share of each firm competing in a market and summing the results. It ranges from close to 0 (many firms, each with a tiny share) to 10,000 (a single firm with 100% of the market, i.e., a monopoly). Economists and antitrust regulators use it to assess how competitive or concentrated an industry is.

The formula is: HHI = Σ (Market Share_i)², where market shares are expressed as percentages from 0 to 100. For example, four firms with 40%, 30%, 20%, and 10% shares produce an HHI of 40² + 30² + 20² + 10² = 1,600 + 900 + 400 + 100 = 3,000.

Step 1: Express every firm's market share as a percentage (0–100). Step 2: Square each share. Step 3: Sum all the squared values. A market of two firms with 60% and 40% shares gives HHI = 60² + 40² = 3,600 + 1,600 = 5,200 — a highly concentrated market, since one firm holds a majority share.

Under the U.S. Department of Justice and Federal Trade Commission's Horizontal Merger Guidelines, markets are classified as: Unconcentrated (HHI below 1,500), Moderately Concentrated (HHI between 1,500 and 2,500), and Highly Concentrated (HHI above 2,500). Higher HHI values indicate less competition and greater potential for firms to exercise market power over pricing.

Regulators evaluate both the resulting market's HHI level and the change in HHI (ΔHHI) caused by a proposed merger, calculated as ΔHHI = 2 × Firm A's Share × Firm B's Share. Under DOJ/FTC guidelines, mergers producing a ΔHHI above 100 in an already moderately concentrated market, or above 200 in an already highly concentrated market, are presumed likely to enhance market power and typically draw closer antitrust scrutiny.

The maximum HHI is 10,000, which occurs only in a pure monopoly where a single firm holds 100% of the market (100² = 10,000). The minimum HHI approaches 0 as the number of equally sized competing firms grows very large, since each firm's share — and its square — becomes vanishingly small.

Either convention works as long as you interpret the result on the matching scale. Using percentages (0–100) — the DOJ/FTC convention and what this calculator uses — produces HHI values from 0 to 10,000. Using decimal fractions (0–1) instead produces HHI values from 0 to 1; multiplying that decimal-based HHI by 10,000 converts it to the standard percentage-based scale.

The concentration ratio (CR4) simply sums the market shares of the top 4 firms, ignoring everyone else and treating all top firms equally regardless of their relative size. HHI uses every firm in the market (not just the top few) and squares each share, which gives more weight to dominant firms and better captures how lopsided a market really is. Two markets can have identical CR4 values but very different HHI values if their internal share distribution differs.

Sources & Methodology

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