What Is the Herfindahl-Hirschman Index (HHI)? Formula and Example

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The Herfindahl-Hirschman Index (HHI) is a measure of market concentration calculated by squaring the market share of every firm in a market and adding the results. With shares written as whole-number percentages, the HHI runs from close to zero in a market of many small competitors to 10,000 in a pure monopoly. The higher the number, the more the market’s output or sales sit with a few large firms. Antitrust agencies, most prominently the U.S. Department of Justice (DOJ) and the Federal Trade Commission (FTC), use it to screen mergers for competition concerns.

What the HHI Measures

The HHI describes the size of firms relative to the market they compete in. It condenses the whole distribution of market shares into one number that rises as the market moves toward monopoly and falls as sales spread across more, smaller competitors. It does not count firms or measure prices or profits directly.

The squaring step is what makes the HHI distinctive. A firm with 10% of a market contributes 100 points. A firm with 50% contributes 2,500 points, twenty-five times as much, even though its share is only five times larger. This reflects the idea that a large firm’s ability to influence prices grows faster than its share.

HHI Formula

The HHI equation is:

HHI = s₁² + s₂² + s₃² + … + sₙ²

where sₙ is the market share of firm n, expressed as a whole-number percentage (40 for 40%, not 0.40), and n is the number of firms in the market.

Scale and range

• Maximum: one firm with 100% share gives 100² = 10,000.
• Equal-sized firms: with n firms of equal share, each has 100/n percent, and the HHI equals 10,000 ÷ n. Ten equal firms produce 1,000; a hundred equal firms produce 100.
• Minimum: the index approaches zero as the number of firms grows very large and each share shrinks toward zero. It never reaches exactly zero in a market with at least one seller.

For any given number of firms, the HHI is lowest when shares are equal. Any inequality among the same firms raises it.

Whole numbers vs. decimals

Some textbooks and academic papers compute the index with shares as decimals (0.40 instead of 40). That version runs from near 0 to 1 and is sometimes called the normalized or decimal Herfindahl index. The two are the same measure on different scales: multiply the decimal result by 10,000 to get the conventional figure. Mixing scales is a common error. An HHI of “0.29” and one of “2,950” can describe very similar markets.

Example of the HHI

Take a hypothetical industry with four firms:

1. Firm A: 40% market share
2. Firm B: 30% market share
3. Firm C: 15% market share
4. Firm D: 15% market share

HHI = 40² + 30² + 15² + 15² = 1,600 + 900 + 225 + 225 = 2,950

Firms A and B together hold 70% of the market but contribute 2,500 of the 2,950 points, about 85% of the index. Under the 2010 U.S. thresholds described below, 2,950 places this market in the highly concentrated range.

Measuring a merger

Now suppose, hypothetically, Firms C and D merge into one firm with 30% of the market:

HHI = 40² + 30² + 30² = 1,600 + 900 + 900 = 3,400

The index rises by 450 points. There is a shortcut for this: when two firms with shares a and b combine and nothing else changes, the HHI increases by 2 × a × b. Here, 2 × 15 × 15 = 450. This change, often written ΔHHI, is the figure regulators look at alongside the post-merger level. The shortcut assumes the merged firm keeps the combined share of both parties, which is the standard screening assumption rather than a forecast of what customers will actually do.

Same number of firms, very different HHI

The count of firms tells you little on its own. Consider a hypothetical market of 20 firms:

• If one firm holds about 48.59% and each of the other 19 holds about 2.71%, the HHI is roughly 2,500.
• If the leader holds about 35.82% and the other 19 hold about 3.38% each, the HHI is roughly 1,500.
• If all 20 firms hold 5% each, the HHI is 500.

Twenty firms appear in every case, yet the index ranges from a competitive reading to the edge of high concentration. The size of the largest firm drives the result.

How to Interpret HHI Values

The thresholds most often cited come from the 2010 Horizontal Merger Guidelines issued jointly by the DOJ and FTC (Section 5.3):

• Below 1,500: unconcentrated
• 1,500 to 2,500: moderately concentrated
• Above 2,500: highly concentrated

Under those guidelines, a merger producing a highly concentrated market with an HHI increase of more than 200 points was presumed likely to enhance market power. Smaller increases, or increases in moderately concentrated markets, could still prompt closer review.

The DOJ and FTC replaced the 2010 document with new Merger Guidelines in December 2023. Those guidelines treat a market with an HHI above 1,800 as highly concentrated and presume that a merger raising the HHI by more than 100 points in such a market substantially lessens competition. Many textbooks and older explanations still teach the 1,500 and 2,500 cutoffs, so the year of the guidelines matters when you read a cited threshold.

Under either set of numbers, these levels are screening presumptions. The parties to a merger can rebut them with evidence about how the market actually works, and agencies can challenge deals that fall below them.

As a reading aid, the effective number of firms is 10,000 ÷ HHI. It tells you how many equal-sized firms would produce the same index. A market with an HHI of 1,400 behaves, by this measure, like a market of about seven equal competitors, even if it contains dozens of firms of uneven size. In the four-firm example above, 2,950 corresponds to about 3.4 equal firms, and after the merger, 3,400 corresponds to about 2.9.

Why the HHI Is Used

The HHI’s main advantage is that it is simple to compute and needs only market share data. Because it weights firms by size, it captures inequality among the leaders, which simpler measures miss. Very small firms add almost nothing to the total (a 1% firm adds 1 point), so an HHI computed from the largest firms plus an estimate for the rest is usually close to the full figure. The error grows when many mid-sized firms are left out.

Merger review is its best-known application. Agencies define a relevant market, estimate pre-merger shares, then compute the post-merger HHI and the change. The calculation helps decide which deals get a closer look.

The same arithmetic works for any set of shares that add up to a whole, so analysts apply it outside antitrust as well, for example to measure how concentrated a portfolio is across holdings, how dependent a company is on a few customers, or how evenly a country’s exports or imports spread across trading partners.

HHI vs. the Concentration Ratio

The measure most often confused with the HHI is the concentration ratio, usually written CR4 (or CRn). It adds the market shares of the four (or n) largest firms. In the four-firm example, CR4 is 100%.

The two differ in what they capture:

• Concentration ratio: adds raw shares of the top few firms and ignores every other firm. A market with four firms at 25% each and a market with one firm at 97% and three at 1% both have a CR4 of 100%.
• HHI: uses every firm and squares each share. The first of those markets scores 2,500; the second scores about 9,412.

That sensitivity to the size gap among leaders is why the HHI largely replaced concentration ratios in U.S. merger analysis.

Limitations of the HHI

Market definition decides the answer. The index depends entirely on which products and which geography count as “the market.” Draw the market broadly and a dominant firm can look small. Suppose a hypothetical industry has ten firms with about 10% each: the HHI is about 1,000, which reads as competitive. If one of those firms makes 80% to 90% of the sales of a particular product line, it may hold near-monopoly power in that segment that the industry-wide figure hides.

Geography can mask local monopolies. Firms with similar national shares may each operate in separate regions. The national HHI looks low while each firm faces little or no competition where it actually sells.

The share measure matters. Shares can be computed from revenue, unit sales, capacity or deposits, and each can produce a different HHI for the same market.

It is a snapshot. The index reflects shares at one point in time. It says nothing about entry barriers, how quickly shares shift or whether new competitors could appear.

Structure is not behavior. A concentrated market can still be competitive, and a market with a moderate HHI can still see coordinated pricing. The HHI flags where to look; it does not settle the question.

For these reasons, regulators treat the HHI as one input alongside evidence about pricing, customer switching and entry.

History of the HHI

Albert O. Hirschman, a German-born economist, introduced the idea in his 1945 book National Power and the Structure of Foreign Trade to measure how concentrated a country’s imports and exports were across trading partners, giving greater weight to the largest shares. Orris C. Herfindahl, an American economist, developed the same index independently in his 1950 doctoral dissertation, Concentration in the U.S. Steel Industry, applying it to firms within an industry, and acknowledged Hirschman’s work in a footnote. The index is still often called simply the Herfindahl index, and U.S. antitrust agencies have used it as their standard concentration measure in merger guidelines.

FAQs

The Bottom Line

Anyone reading a merger review or an antitrust argument should check which guidelines a cited HHI threshold comes from, since the 2023 cutoffs are stricter than the 2010 ones. The number depends heavily on how the market, its geography and its share measure are defined. Regulators use the HHI to flag deals for closer study, then weigh it against evidence on pricing, customer switching and entry.