HHI calculator: Herfindahl-Hirschman Index and merger test

How it works

The Herfindahl-Hirschman Index (HHI) takes each firm's market share in percent, squares it, and adds up the squares.

HHI = s1² + s2² + s3² + ... + sn²

A monopoly scores 100² = 10,000. A market of many tiny firms scores close to zero. Squaring is the point: big shares count for far more than small ones, so one giant moves the index more than several mid-sized rivals with the same combined share.

If you have sales, revenue or capacity figures instead of shares, switch the input to sales. The tool divides each firm's figure by the total and multiplies by 100, so the shares add up to 100. Entries of zero or less are dropped. If you type shares that do not reach 100, because of rounding or an "others" slice you left out, the tool shows the gap and computes the index from the shares you entered.

Next to the HHI you get:

• CR4, the combined share of the four largest firms. It says nothing about how that share is split among them.
• Equivalent number of firms, 10,000 divided by the HHI. This is how many equal-sized firms would produce the same index.
• A concentration band under the 2023 Merger Guidelines of the US Department of Justice and Federal Trade Commission. Above 1,800 is highly concentrated, 1,000 to 1,800 moderately concentrated, below 1,000 unconcentrated. For contrast, the tool also shows the bands of the 2010 Horizontal Merger Guidelines, which put the lines at 2,500 and 1,500.
• A merger check. Pick two firms and the tool assumes their shares simply add together. The HHI then rises by exactly 2 × s1 × s2. Under the 2023 guidelines, a merger is presumed to harm competition when it raises the HHI by more than 100 points and either leaves the market above 1,800 or creates a firm with more than 30% of it.

Worked example

The tool opens with five firms holding 30%, 25%, 20%, 15% and 10%.

The squares are 900 + 625 + 400 + 225 + 100, so the HHI is 2,250. That is above the 1,800 line, and the 2023 guidelines would call the market highly concentrated. The 2010 guidelines would have called the same market moderately concentrated, since 2,250 sits between 1,500 and 2,500.

CR4 is 30 + 25 + 20 + 15 = 90%. The equivalent number of firms is 10,000 / 2,250, about 4.4. In concentration terms, the market behaves like four or five equal rivals rather than five uneven ones.

Now merge the 15% and 10% firms. The new firm holds 25%, and the HHI rises by 2 × 15 × 10 = 300 points, to 2,550. An increase of more than 100 in a market above 1,800 meets the 2023 test, so the deal is presumed harmful. The 30% share route does not apply here, since the merged firm has 25%, but one route is enough.

The older rules would also have objected. The merged market lands just over 2,500, and the 2010 guidelines presumed harm from increases of more than 200 points in highly concentrated markets.

Our explainer on concentration ratios in agribusiness runs several made-up markets through CR4 and the HHI side by side, including this kind of merger.

What it can't tell you

The index is only as good as the market definition behind it. Draw the market narrowly, say one crop's seed in one region, and shares rise. Draw it broadly and they fall. Agencies and merging firms spend much of a case arguing over this step, and no calculator can do it for you.

The merger arithmetic assumes the combined firm keeps both old shares. In real markets some customers leave, rivals expand, and prices may change. The guidelines treat the HHI test as a starting presumption that the parties can try to rebut, and courts make the final call. Guidelines are not statute.

High concentration does not prove that a firm abuses its position, and low concentration does not prove that a market works. Buyer power, barriers to entry, vertical integration and links between supposed rivals, such as shared shareholders, joint ventures or licensing deals, all sit outside a list of shares. The story of the top ten seed companies shows how much control can run through trait licenses rather than sales.

Small firms barely move the HHI, because their squares are tiny. Leaving out a long tail of them changes little. Lumping them into a single "others" entry does the opposite and overstates the index, so enter small firms one by one or leave them out and accept the gap.

Sources

• US Department of Justice and Federal Trade Commission, Merger Guidelines (December 2023), Guideline 1 and its concentration thresholds.
• US Department of Justice and Federal Trade Commission, Horizontal Merger Guidelines (2010), section 5.3 on market concentration.
• Albert O. Hirschman (1945) and Orris C. Herfindahl (1950), who devised versions of the index independently.

Questions

How do you calculate the HHI?

Square each firm's market share in percent and add the results. Shares of 50, 30 and 20 give 2,500 + 900 + 400 = 3,800.

What does an HHI of 2,500 mean?

It is the score of four equal firms with 25% each. Under the 2023 US guidelines it counts as highly concentrated, being above 1,800. Under the 2010 guidelines it sat at the top of the moderately concentrated band, because only scores above 2,500 counted as highly concentrated.

What HHI is considered highly concentrated?

Above 1,800 under the 2023 US Merger Guidelines, and above 2,500 under the 2010 guidelines they replaced. Competition authorities in other countries set their own thresholds.

Why is the HHI sometimes between 0 and 1?

Some sources write shares as decimals, 0.30 instead of 30. The index then runs from 0 to 1. Multiply it by 10,000 to compare it with the US thresholds.

What is the difference between the HHI and CR4?

CR4 adds up the shares of the four largest firms and ignores everyone else. The HHI uses every firm and weights the large ones more heavily, so two markets with the same CR4 can have very different HHIs if one of them has a single dominant firm.