Herfindahl–Hirschman Index Calculator
List the firms in a market with their market shares, or with their sales, and the calculator returns the Herfindahl–Hirschman Index, the four-firm concentration ratio and the equivalent number of equal-sized firms. Then pick two firms to merge and see the change in the index against the 2023 US Merger Guidelines. Free, no sign-up, and nothing leaves your browser.
Separate the name from the number with a comma, tab or semicolon (use semicolons if your numbers have decimal commas). A line with only a number is a firm with that number. A first line without numbers is read as a header.
Results
2,150
Herfindahl–Hirschman Index
Highly concentrated
Concentration (2023 Merger Guidelines)
4.65
Same as this many equal-sized firms
30%
Largest firm (CR1)
85%
Four largest firms (CR4)
6
Firms counted
The 2023 DOJ and FTC Merger Guidelines call a market highly concentrated when its HHI is above 1,800. The 2010 Horizontal Merger Guidelines used 1,500 and 2,500 as their bands.
Where the index comes from
| Firm | Share (%) | Share squared | Part of the HHI |
|---|---|---|---|
| Firm A | 30 | 900 | 41.9% |
| Firm B | 25 | 625 | 29.1% |
| Firm C | 20 | 400 | 18.6% |
| Firm D | 10 | 100 | 4.7% |
| Firm E | 10 | 100 | 4.7% |
| Firm F | 5 | 25 | 1.2% |
HHI = the sum of the squared shares = 2,150
Test a merger
Choose two firms to combine. The change in the index is 2 × the product of their shares.
Merger result
- Change in HHI = 2 × 10 × 10 = 200
- HHI after the merger = 2,150 + 200 = 2,350
- Merged firm’s share = 10 + 10 = 20%
Under Guideline 1 of the 2023 Merger Guidelines, this merger is presumed to substantially lessen competition.
The market would be highly concentrated (HHI of 2,350, above 1,800) and the HHI would rise by 200, more than 100.
A presumption is where the agencies start, not a finding. It can be rebutted, and a merger below these thresholds can still be challenged. This is an educational screen, not legal advice.
How to Use the HHI Calculator
- 1. List the firms. One per line, as a name and a number, such as Firm A, 30. A line with only a number counts as a firm too. Add up to as many firms as the market has.
- 2. Say what the numbers are. Choose market shares in percent, or sales or revenue, which the calculator converts to shares. If your shares do not add up to 100, you are told, and you can scale them.
- 3. Read the index. The HHI, the concentration verdict, CR1 and CR4, and the table of squared shares appear together, so you can see which firms drive the index.
- 4. Test a merger. Choose two firms. The calculator shows the change in the HHI, the index afterwards, the merged share, and whether the 2023 Guidelines' structural presumption applies.
How the Index Is Calculated
Herfindahl–Hirschman Index
HHI = s₁² + s₂² + … + sₙ², with each share s in percentage points
Concentration ratio
CR4 = the combined share of the four largest firms
Effect of a merger
ΔHHI = 2 × s₁ × s₂ for the two merging firms
Squaring gives large firms far more weight than small ones, which is the point: a market is more concentrated when a few big firms dominate it. The index runs from close to 0 for a market of many tiny firms to 10,000 for a monopoly, and a market of n equal-sized firms has an HHI of 10,000 ÷ n. Some economists write shares as fractions, so that the index runs from 0 to 1; the antitrust agencies use the 0 to 10,000 scale, and so does this calculator. A merger moves the index by twice the product of the two shares, because (a + b)² − a² − b² = 2ab.
Worked Example: Six Firms
| Firm | Share | Share squared |
|---|---|---|
| Firm A | 30 | 900 |
| Firm B | 25 | 625 |
| Firm C | 20 | 400 |
| Firm D | 10 | 100 |
| Firm E | 10 | 100 |
| Firm F | 5 | 25 |
The squares add up to an HHI of 2,150, and CR4 is 30 + 25 + 20 + 10 = 85%. The market behaves like 10,000 ÷ 2,150 ≈ 4.65 equal-sized firms, though it has six. Because 2,150 is above 1,800, the market is highly concentrated under the 2023 Guidelines. If Firm D and Firm E merge, the index rises by 2 × 10 × 10 = 200, to 2,350, and the merged firm holds 20%. A rise of more than 100 into a highly concentrated market triggers the presumption. If Firm E and Firm F merge instead, the rise is 2 × 10 × 5 = 100 exactly, which is not more than 100, so the presumption is not triggered.
The 2023 Merger Guidelines Thresholds
Guideline 1 of the 2023 Merger Guidelines, issued jointly by the Department of Justice and the Federal Trade Commission, says that markets with an HHI greater than 1,800 are highly concentrated, and that a change of more than 100 points is a significant increase. A merger is presumed to substantially lessen competition, or tend to create a monopoly, in two cases:
- the market is highly concentrated after the merger (HHI above 1,800) and the merger raises the HHI by more than 100 points; or
- the merged firm would hold a share of more than 30% and the merger raises the HHI by more than 100 points.
These restore the pre-2010 level. The 2010 Horizontal Merger Guidelines had used 1,500 and 2,500 as the bands, with a presumption at an increase above 200 in a highly concentrated market. The presumption is where the agencies start: the merging firms can rebut it, and a merger below the thresholds can still be challenged. Read the primary text in Guideline 1 on justice.gov.
Frequently Asked Questions
- What is a good or bad HHI?
- There is no good or bad value in itself, only how concentrated the market is. Under the 2023 Merger Guidelines, an HHI above 1,800 is highly concentrated. The lowest possible HHI for n firms is 10,000 ÷ n, when they are all the same size, so even a market of ten equal firms scores 1,000.
- How do you calculate the HHI?
- Write each firm's market share as a percentage, square each one, and add the squares. Shares of 50, 30 and 20 give 2,500 + 900 + 400 = 3,800. If you only have sales figures, divide each firm's sales by the market total first.
- How do you calculate the change in HHI from a merger?
- Multiply the two merging firms' shares together and double the result. Firms with 20% and 5% raise the HHI by 2 × 20 × 5 = 200. You do not need the other firms, since their squared shares do not change.
- What is the difference between HHI and CR4?
- CR4 adds up the shares of the four largest firms and ignores how they split it. The HHI uses every firm and weights large ones more. Two markets can share a CR4 of 80% and have very different HHIs, depending on whether one firm holds 70% of it or four firms hold 20% each.
- Why did the thresholds change in 2023?
- The 2023 Guidelines went back to 1,800 for a highly concentrated market and 100 for a significant increase. Those thresholds date from the 1982 guidelines, and the agencies raised them in 2010. The agencies now say the original thresholds better reflect both the law and the risks of competitive harm.
- Does the market definition matter?
- Greatly. The index is only as meaningful as the market it describes. Defining the market narrowly, say by product and region, raises the shares and the index, while a broad definition spreads them out. Merger reviews spend much of their effort on this question.
- What if my shares do not add up to 100?
- If you list only some firms, the index counts only those and is a lower bound; the missing firms would add more. If your numbers should add up to 100 and do not, tick the box to scale them proportionally. With sales or revenue, the calculator always divides by the total.