How the HHI works
Counting firms tells you little about competition — a market with ten firms where one holds 91% behaves nothing like ten equal rivals. The HHI fixes that by squaring each share before summing, so dominance registers loudly: a 50% firm contributes 2,500 points on its own, while fifty 1% firms together add just 50. The index was proposed independently by Albert O. Hirschman in 1945 and Orris C. Herfindahl in 1950, and it carries a wonderfully intuitive inverse: divide 10,000 by the HHI and you get the "numbers equivalent" — the number of equal-sized firms that would produce the same score. An HHI of 2,500 means the market is as concentrated as four equal firms, whatever the actual firm count.
The formula
HHI = Σ sᵢ² = s₁² + s₂² + … + sₙ²
ΔHHI (merger of A and B) = 2 · sA · sB
where each sᵢ is a firm's market share inpercentage points (a 30% share enters as 30), so the index runs from near 0 to 10,000 for a monopoly. Under the 2023 Merger Guidelines: HHI < 1,000 unconcentrated, 1,000–1,800 moderately concentrated, > 1,800 highly concentrated.
Worked example
Take a market of 5 firms holding 30%, 25%, 20%, 15%, 10% — the calculator's default scenario, including a proposed merger of the two smallest firms:
| Step | Amount |
|---|---|
| Market shares5 firms summing to 100% of the market | 30% + 25% + 20% + 15% + 10% |
| Square each share and add: Σ sᵢ²30² + 25² + 20² + 15² + 10² = 900 + 625 + 400 + 225 + 100 | 2,250 |
| Numbers equivalent: 10,000 ÷ HHIthe market is exactly as concentrated as 4.44 equal-sized firms | 4.44 firms |
| Merger check: the 15% and 10% firms combineΔHHI = 2 × 15 × 10 = 300 → post-merger HHI 2,550; a change above 100 in a market above 1,800 triggers the 2023 presumption | 2,250 → 2,550 |
| = HHI of 2,250 — the market is highly concentratedabove the 1,800 line of the 2023 Merger Guidelines (the 2010 guidelines drew it at 2,500) | 2,250 |
Computed with this calculator's default settings — open the tool above and you'll see the same numbers, then paste in your own market shares.
Merger review: the thresholds journalists quote
The HHI's day job is antitrust. The DOJ and FTC's 2023 Merger Guidelines presume a merger may substantially lessen competition when it leaves the post-merger HHI above 1,800 and raises the index by more than 100 points (the guidelines also flag deals that give the merged firm more than a 30% share with a ΔHHI over 100). Mind the vintage when reading coverage: the 2023 guidelines returned to the 1,000/1,800 bands used from 1982 to 2010, while the 2010 Horizontal Merger Guidelines had drawn the lines at 1,500 and 2,500 with a presumption at 2,500 — so the same deal can sound alarming under one set of numbers and routine under the other. The delta has a clean closed form — merging firms A and B adds exactly 2·sA·sBpoints — which is why two mid-sized firms merging can move the index more than a giant absorbing a minnow.
Concentration math pairs naturally with other market measures: size up the merging companies themselves with ourmarket cap calculator, see how pricing power shows up in unit economics with themargin calculator, or measure what competition is worth to buyers and sellers with theconsumer & producer surplus calculator.
Frequently asked questions
What is the Herfindahl–Hirschman Index?
The HHI is the standard measure of market concentration: square every firm’s market share (in percentage points) and add the squares. A pure monopoly scores 100² = 10,000; a market split among thousands of tiny firms scores near zero. Because the shares are squared, the index is driven by the biggest players — one 50% firm contributes 2,500 points while fifty 1% firms together contribute only 50. It is named for the economists Orris Herfindahl and Albert Hirschman, who proposed it independently, and it is the concentration screen U.S. antitrust agencies use in merger review.
What HHI counts as a concentrated market?
Under the DOJ/FTC 2023 Merger Guidelines, a market below 1,000 is unconcentrated, 1,000–1,800 is moderately concentrated, and above 1,800 is highly concentrated. Those bands restore the cutoffs used from 1982 to 2010. The 2010 Horizontal Merger Guidelines had drawn the lines higher — 1,500 and 2,500 — so news coverage and older textbooks often quote those instead. When you read that a merger pushes a market past a threshold, check which vintage of guidelines the writer is using; this calculator classifies on the 2023 bands and notes the difference.
Why square the market shares?
Squaring makes the index weight big firms far more than small ones, which matches the economics: pricing power comes from dominant positions, not from a fringe of small competitors. Two markets can have identical firm counts but very different competitive dynamics — ten equal 10% firms score 1,000, while one 91% giant plus nine 1% firms scores 8,290. A simple sum of shares would call both 100. Squaring also gives the index its elegant “numbers equivalent” property: 10,000 divided by the HHI tells you how many equal-sized firms would produce the same concentration.
What is ΔHHI in a merger?
When two firms with shares sA and sB merge, the combined firm’s squared share is (sA + sB)² = sA² + sB² + 2·sA·sB — so the index rises by exactly ΔHHI = 2·sA·sB. That delta is the agencies’ screen for how much a deal concentrates the market. Under the 2023 Merger Guidelines’ first guideline, a merger that leaves the post-merger HHI above 1,800 with a change above 100 points is presumed to substantially lessen competition — a structural presumption the merging parties must then rebut.
How does the HHI compare with the CR4 concentration ratio?
The four-firm concentration ratio (CR4) simply adds the market shares of the four largest firms. It is easy to compute but blind to structure within the top four: a market led by four 20% firms and one led by a 65% giant with three 5% followers both have a CR4 of 80, yet the second is far more concentrated. The HHI distinguishes them — 1,600-plus versus roughly 4,300 — because squaring registers dominance. That is why the agencies moved from CR4 screens in early guidelines to the HHI, though CR4 still appears in Census industry data and textbooks.
Sources
- U.S. Department of Justice & Federal Trade Commission — 2023 Merger Guidelines (DOJ Antitrust Division)
- OpenStax, Principles of Economics 3e — Corporate Mergers (concentration ratios and the HHI)
The official figures this page quotes are drawn from the primary sources above — check them (or a qualified professional) before relying on a result.
Disclaimer: This calculator is foreducation and illustration only. Real merger review turns on how the relevant market is defined — product and geography — and agencies weigh entry, efficiencies, and other evidence beyond the HHI screen. A threshold crossed here is a textbook presumption, not a legal conclusion, and nothing on this page is legal, financial, or investment advice.