Hong Life CalculatorsUnderstanding the HHI calculator — concept and principle
This calculator computes the Herfindahl-Hirschman Index (HHI), the standard measure of market concentration, from the market shares of the firms in a market. It classifies the market under the 2023 US Merger Guidelines and, if you pick two merging firms, shows the change in HHI and whether the merger falls under the structural presumption. Competition lawyers, economists and students use it.
How it is calculated
- HHI = s1² + s2² + … + sn², with shares in percent
- Range: close to 0 for many tiny firms, up to 10,000 for a single firm
- Change from merging firms with shares a and b = (a + b)² − a² − b² = 2ab
- Equivalent number of equal-sized firms = 10,000 ÷ HHI
- 2023 Merger Guidelines: 1,000–1,800 moderately concentrated; above 1,800 highly concentrated; a merger that raises HHI by more than 100 in a highly concentrated market is presumed likely to enhance market power
The principle
Squaring the shares gives large firms much more weight than small ones, so the index reflects both the number of firms and how unequal they are. Ten firms with 10% each give an HHI of 1,000; one firm with 50% and five with 10% give 3,000. When two firms merge, only their combined share changes, which is why the increase is simply 2ab. Small firms add little to the index, so leaving out a few tiny ones understates the HHI only slightly.
Worked example
Defaults: shares 28, 22, 18, 12, 10, 6, 4; firms 4 and 5 merge.
- HHI = 784 + 484 + 324 + 144 + 100 + 36 + 16 = 1,888, which is above 1,800: Highly concentrated.
- Firms counted: 7; shares add up to 100%.
- Equivalent equal-sized firms = 10,000 ÷ 1,888 = 5.3.
- Change from merging 12% and 10% = 2 × 12 × 10 = 240; HHI after = 2,128.
- Change above 100 in a highly concentrated market: Presumed to raise market power.
How to read the result
The HHI is a screening tool. A merger flagged by the presumption is not automatically blocked; agencies then look at entry, competitive effects and efficiencies. The result depends heavily on how the market is defined: a narrower market gives higher shares and a higher HHI.
Common mistakes
- Entering shares as fractions (0.28) instead of percentages (28).
- Using shares from different market definitions.
- Applying older thresholds (1,500 and 2,500 from the 2010 Guidelines) to the 2023 framework, or the reverse.
- Treating a high HHI as proof of anticompetitive conduct.
Frequently asked questions
What HHI is considered highly concentrated?
Under the 2023 US Merger Guidelines, above 1,800.
Why is the merger change 2ab?
Before the merger the two firms add a² + b²; after, they add (a + b)². The difference is 2ab.
Do other countries use the same thresholds?
Not necessarily. Competition authorities set their own guidelines; check the rules where the deal is reviewed.
Sources: U.S. Department of Justice, Antitrust Division, "Herfindahl-Hirschman Index" (updated January 2024) · U.S. Department of Justice and Federal Trade Commission, Merger Guidelines (2023), section 2.1