Herfindahl-Hirschman Index Calculator

The Herfindahl-Hirschman Index calculator measures market concentration from the market shares of all firms in a defined market. Enter shares as percentages such as 40, 30, 20, and 10, or switch to decimal mode and enter 0.40, 0.30, 0.20, and 0.10. The calculator converts decimals to percentages, checks the data, normalizes an incomplete total to 100%, and adds the squared shares. The resulting HHI is reported on the conventional 0-to-10,000 scale.

HHI is widely used in competition economics because it captures both the number of firms and the distribution of their shares. A market containing many similarly sized suppliers produces a lower index than a market dominated by one or two suppliers. Unlike a simple four-firm concentration ratio, HHI includes every entered firm and gives greater weight to large shares through squaring.

The result is useful for analysts, students, journalists, procurement teams, and businesses conducting an initial concentration screen. It is not a verdict on whether conduct or a merger is lawful. Competition agencies begin with market definition and concentration evidence, then assess competitive effects, entry, repositioning, buyer power, efficiencies, and the facts of the industry.

How to Use the HHI Calculator

1. Choose Percentages (0 to 100) if your data are written as 35%, 25%, and so on. Choose Decimals (0 to 1) if the same shares are written as 0.35 and 0.25.
2. Enter one share per line or separate shares with commas, spaces, or semicolons.
3. Include all identified competitors in the relevant market, not only the largest four.
4. Select Calculate HHI. The calculator displays the normalized HHI, the raw HHI, the entered share total, and the equivalent number of equal-sized firms.
5. If the entered total is not 100%, review why. Rounding may explain a total such as 99.9%. A much lower total may mean that firms are missing or that an "other" category should be included.

The explicit input-format switch prevents a common 10,000-fold scaling error. Squaring percentage shares gives the standard agency scale: 50² + 50² = 5,000. Squaring decimal shares without conversion gives 0.50, which is mathematically equivalent only on the 0-to-1 scale. This calculator converts decimal shares to percentage points before presenting the result.

The HHI Formula

For firms numbered 1 through n, with percentage market shares s:

HHI = s₁² + s₂² + … + sₙ²

A monopoly has one 100% share, so its HHI is 100² = 10,000. A market with four equal firms has an HHI of 4 × 25² = 2,500. If 100 equal firms each hold 1%, the HHI is 100 × 1² = 100. In general, n equal firms produce an HHI of 10,000 ÷ n.

When inputs are decimal fractions, the equivalent formula is the sum of squared fractions multiplied by 10,000:

HHI = 10,000 × (p₁² + p₂² + … + pₙ²)

Here p is a share between 0 and 1. Thus four shares of 0.25 yield 10,000 × (4 × 0.25²) = 2,500. Decimal and percentage methods produce exactly the same standard-scale answer when applied consistently.

Percentage and Decimal Normalization

Market-share datasets often fail to total exactly 100. Published values may be rounded, small suppliers may be grouped, or the observations may cover only a sample. This calculator uses proportional normalization for its headline HHI:

Normalized share = entered share ÷ entered total × 100

Suppose entered shares are 40, 30, and 20, totaling 90. Their normalized shares are 44.444%, 33.333%, and 22.222%. The normalized HHI is approximately 3,580.25. The raw sum of squares is only 2,900 because ten percentage points are absent. Both values are displayed so the adjustment is transparent.

Normalization is mathematically useful but cannot repair the wrong market definition or missing competitive data. If the omitted 10% belongs to one firm, adding a 10% competitor would give an HHI of 3,000. If it belongs to ten firms with 1% each, the HHI would be 2,910. Normalizing the known firms assumes they represent the market in their observed proportions, which is a substantive assumption. For formal analysis, investigate missing shares instead of treating normalization as a substitute for evidence.

A total slightly above or below 100 because of independent rounding usually needs no special concern. For example, 33.3 + 33.3 + 33.3 totals 99.9, and proportional normalization restores three equal shares. A total of 75 should prompt a data check.

Worked Examples

Example 1, four equal firms. Shares are 25%, 25%, 25%, and 25%:

HHI = 25² + 25² + 25² + 25² = 2,500.

The same calculation in decimal mode uses 0.25 four times and also returns 2,500.

Example 2, a dominant supplier. Shares are 60%, 25%, 10%, and 5%:

HHI = 60² + 25² + 10² + 5² = 3,600 + 625 + 100 + 25 = 4,350.

The 60% firm contributes 3,600 points by itself. This illustrates why HHI is especially sensitive to large firms.

Example 3, five uneven firms. Shares are 35%, 25%, 20%, 12%, and 8%:

HHI = 1,225 + 625 + 400 + 144 + 64 = 2,458.

Example 4, ten equal firms. Each holds 10%:

HHI = 10 × 10² = 1,000.

Example 5, decimal shares. Enter 0.40, 0.30, 0.20, and 0.10 in decimal mode:

HHI = 10,000 × (0.16 + 0.09 + 0.04 + 0.01) = 3,000.

Example 6, merger change. Before a merger, shares are 30%, 20%, 20%, 15%, 10%, and 5%. HHI is 900 + 400 + 400 + 225 + 100 + 25 = 2,050. If the 20% and 15% firms combine, post-merger shares are 35%, 30%, 20%, 10%, and 5%, producing 1,225 + 900 + 400 + 100 + 25 = 2,650. The change, or delta, is 600 points.

For two merging firms with shares a and b, the HHI increase is 2ab. That follows because (a + b)² − a² − b² = 2ab. In the example, 2 × 20 × 15 = 600.

Interpreting HHI in Competition Policy

The U.S. Department of Justice and Federal Trade Commission's 2023 Merger Guidelines, Guideline 1, describe markets with HHI below 1,000 as unconcentrated, HHI from 1,000 to 1,800 as moderately concentrated, and HHI above 1,800 as highly concentrated. The Guidelines state a structural presumption for a merger that significantly increases concentration and creates or further consolidates a highly concentrated market; they identify a post-merger HHI above 1,800 together with an increase above 100 points as one relevant threshold. They also discuss a separate presumption when the merged firm's share exceeds 30% and the HHI increase exceeds 100.

Those current U.S. bands differ from the thresholds in the agencies' 2010 Horizontal Merger Guidelines. Analysts should identify which policy document, jurisdiction, and date they are applying rather than carrying an old threshold table into a current assessment. The calculator labels concentration using the 2023 U.S. bands and clearly identifies that basis.

The European Commission's Guidelines on the assessment of horizontal mergers use HHI and the change in HHI as initial indicators, while emphasizing that these are not presumptions of either competitive harm or its absence. The Guidelines describe circumstances in which the Commission is unlikely to identify horizontal competition concerns, including post-merger HHI below 1,000, post-merger HHI from 1,000 to 2,000 with a delta below 250, or post-merger HHI above 2,000 with a delta below 150, subject to listed special circumstances. These screens are not interchangeable with the U.S. 2023 labels.

The UK Competition and Markets Authority's Merger Assessment Guidelines (CMA129) focus on whether a merger may result in a substantial lessening of competition. Concentration measures can inform that assessment, but the framework does not reduce the legal test to one universal HHI cutoff. Similar caution applies in other jurisdictions.

Market Definition Comes First

An HHI is only as meaningful as the relevant market used to calculate it. A competition market generally has a product dimension and a geographic dimension. Defining "all beverages worldwide" may yield a very different index from defining "carbonated soft drinks sold through supermarkets in one country." If customers view two products as close substitutes, excluding one may exaggerate concentration. If transport costs or regulation prevent distant suppliers from constraining local prices, a broad geographic market may understate it.

The shares also need a defensible denominator. Depending on the industry, agencies may examine revenue, unit sales, capacity, reserves, number of customers, or another measure that reflects competitive significance. Current sales can understate a firm with substantial available capacity; capacity can overstate a supplier unable to serve key customers. In bidding markets, win rates and participation patterns may matter alongside conventional shares.

Choose one period and one consistent source where possible. Avoid mixing one firm's worldwide revenue with competitors' domestic unit sales. Document estimates and the treatment of imports, captive production, vertically integrated supply, fringe firms, and an "other" category. Sensitivity testing across plausible market definitions is more informative than false precision in a single HHI.

What the Equivalent Number of Firms Means

The calculator reports 10,000 ÷ HHI, sometimes called the effective or numbers-equivalent count of equal-sized firms. An HHI of 2,500 corresponds to four equal firms; 2,000 corresponds to five. This does not claim that the market literally contains that many businesses. It translates an uneven distribution into the number of equal firms that would generate the same HHI.

For example, a market may contain ten firms but have an effective count of 3.2 because most share sits with three large suppliers. The measure is intuitive for comparison, but it does not reveal which firms are close competitors, whether products are differentiated, or whether customers can switch.

Limitations and Common Mistakes

Using only the largest firms. HHI is defined over all firms in the market. Omitting the competitive fringe generally changes both the total and the distribution.

Mixing 0 to 1 and 0 to 100 scales. Entering 0.4 in percentage mode means 0.4%, not 40%. Select decimal mode for fractions.

Treating normalization as recovered information. Rescaling known shares does not tell you how missing share is distributed. Preserve the raw result and investigate the gap.

Equating concentration with market power. A high HHI can flag a market for closer analysis, but shares may not capture rapid entry, disruptive innovation, regulation, differentiated competition, or buyer responses. Conversely, a lower HHI does not guarantee effective competition if firms coordinate or customers face narrow alternatives.

Calling an HHI a legal decision. Enforcement policy and case law vary by jurisdiction and evolve. A screen should be read with the applicable official guidance and, for consequential matters, specialist economic and legal advice.

Ignoring measurement uncertainty. A reported HHI of 1,799 is not fundamentally different from 1,801 when shares are estimated. Calculate alternative plausible cases and explain assumptions.

Authoritative References

• U.S. Department of Justice and Federal Trade Commission, Merger Guidelines (2023), especially Guideline 1 and its concentration discussion: justice.gov/atr/2023-merger-guidelines.
• U.S. Department of Justice, Herfindahl-Hirschman Index explainer: justice.gov/atr/herfindahl-hirschman-index.
• European Commission, Guidelines on the assessment of horizontal mergers under the Council Regulation on the control of concentrations between undertakings, Official Journal C 31, 5 February 2004: EUR-Lex 52004XC0205(02).
• UK Competition and Markets Authority, Merger Assessment Guidelines (CMA129), current guidance page and 2021 printable guidelines: gov.uk/cma129.

Frequently Asked Questions

What is a good HHI? There is no universally "good" HHI. Under the 2023 U.S. Merger Guidelines, below 1,000 is labeled unconcentrated, 1,000 to 1,800 moderately concentrated, and above 1,800 highly concentrated. Those are screening categories, not performance grades or automatic legal outcomes. The appropriate interpretation depends on the jurisdiction, market definition, evidence, and question being studied.

Should I enter market shares as percentages or decimals? Either works if you select the matching mode. Percentage mode expects 40 for 40%; decimal mode expects 0.40. The calculator converts decimal fractions to percentage points before squaring, so 40, 30, 20, 10 and 0.40, 0.30, 0.20, 0.10 both produce an HHI of 3,000. Never combine the two formats in one list.

What if my market shares do not add to 100%? The headline HHI proportionally normalizes the entered shares to 100%, while also showing their raw total and raw HHI. A small discrepancy may be rounding. A large gap can indicate omitted firms, inconsistent data, or an undefined "other" category. For serious analysis, determine who owns the missing share and recalculate; different distributions of the missing share can materially change HHI.

How do I calculate the change in HHI after a merger? Calculate HHI using pre-merger shares, combine the merging firms' shares, and calculate it again. Subtract the pre-merger HHI from the post-merger HHI. If only firms with shares a and b merge and all else stays constant, the delta equals 2ab when shares are percentage points. Firms with 20% and 15% therefore create a 600-point increase.

Why does HHI square each firm's share? Squaring makes larger shares contribute disproportionately. A 40% firm contributes 1,600 points, while four separate 10% firms collectively contribute only 400. This property allows HHI to reflect both how many firms compete and how unevenly the market is divided, rather than treating a dominant firm like several small firms with the same combined share.

What is the maximum and minimum HHI? On the standard percentage scale, the maximum is 10,000 for a monopoly. The theoretical minimum approaches zero as the number of equal, tiny firms grows without bound. For a fixed number n of firms whose shares total 100%, the minimum occurs when all are equal and equals 10,000 divided by n. Four equal firms therefore have a minimum of 2,500 for any four-firm distribution.

Does a highly concentrated HHI prove that a merger is illegal? No. HHI is a structural screen. Agencies and courts consider market definition, the size and significance of the increase, head-to-head competition, entry, expansion, coordination, efficiencies, and other evidence under the governing law. A high index may support closer scrutiny or a presumption under a particular framework, but this calculator cannot produce a legal conclusion.

Can I use HHI for industries outside merger analysis? Yes. Researchers use the same sum-of-squared-shares concept to describe supplier concentration, customer concentration, portfolio allocation, biodiversity, and other distributions. Interpretation must fit the application. A procurement team measuring dependence on vendors, for example, should not automatically apply U.S. merger thresholds; those thresholds were designed for competition-policy screening.

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