The Herfindahl index calculator above squares every firm's market share, adds the squares, and reports the result on both scales in which the Herfindahl-Hirschman Index is published. It also gives the effective number of firms, the four-firm and eight-firm concentration ratios, and a normalised version that adjusts for how many firms are in the market at all.
Arb Digital treats the index as a definition rather than a verdict. The arithmetic is fixed and uncontroversial; what any given value implies about competition is a matter for the guidelines in force in a particular jurisdiction at a particular time, and those get revised. The two threshold fields are therefore inputs, and you should set them from the current guidelines you are working under rather than trusting a number embedded in a web page. Where the question is about how unequally a total is spread rather than how concentrated a market is, our Gini coefficient calculator is the right measure instead.
What This Herfindahl Index Calculator Does
It accepts either percentage shares or raw revenues. In revenue mode it divides each firm by the total to get shares first, which removes the most common source of error — shares that were rounded to whole numbers and no longer sum to one hundred. In percentage mode it checks the sum and tells you if it is off, because an incomplete list of firms understates the index.
The output is given on the fractional zero-to-one scale, where shares are expressed as decimals, and on the zero-to-ten-thousand scale, where they are expressed as whole percentages. The two are the same number scaled by ten thousand, and confusing them is the single most frequent mistake with this index. A value of 0.25 and a value of 2,500 are the same market.
Alongside the index the tool computes the effective number of firms, which is one divided by the fractional index, and the concentration ratios CR4 and CR8, which are simply the combined shares of the largest four and eight firms. Those two families answer different questions and are worth reading together, because a market can have a modest HHI and a very high CR4 if the top firms are similar in size to each other but far larger than the rest.
How to Use It
- List every firm in the market, one per line. Omitting the small ones raises the index, because their squared shares are missing from the sum.
- Choose revenue mode if you have raw figures. It avoids the rounding problem entirely and is the safer route.
- Set the two thresholds from the guidelines that actually apply to your analysis, and record which edition you used in the source field.
- Read the effective number of firms as a sanity check. If it says four and you listed twenty, most of those twenty are very small.
- Compare CR4 with the index. Where they disagree, the shape of the distribution below the top firms is doing the work.
The Formula and How It Is Calculated
The index is HHI = ∑ si², the sum of the squared market shares of every firm in the market. If shares are decimals the result runs from zero to one; if they are whole percentages it runs from zero to ten thousand. A pure monopoly gives 1 or 10,000. N equal firms give 1/N or 10,000/N.
Work the default through by hand. The shares are 35, 25, 20, 12 and 8 percent, which sum to 100. Squaring each gives 1,225, 625, 400, 144 and 64. Adding those gives an HHI of 2,458 on the ten-thousand scale, or 0.2458 as a fraction. The effective number of firms is 1 ÷ 0.2458 = 4.07, so this market behaves roughly as if it had four equal competitors rather than the five it actually has. CR4 is 35 + 25 + 20 + 12 = 92 percent.
The normalised index adjusts for firm count. It is (H − 1/N) ÷ (1 − 1/N) on the fractional scale, which rescales so that N equal firms score zero rather than 1/N. Here that is (0.2458 − 0.2) ÷ 0.8 = 0.0573, a small figure because the five firms are not wildly unequal in size. Note how differently the two measures behave: the raw index says this market is fairly concentrated, and the normalised index says the shares within it are fairly even. Both are true and they are answering different questions.
The Two Scales, and Who Uses Which
The scale confusion is worth spelling out because it produces order-of-magnitude errors in otherwise careful analysis. Squaring decimal shares gives a number between zero and one; squaring percentage shares gives a number between zero and ten thousand. Both are called the HHI.
The United States antitrust agencies work on the zero-to-ten-thousand scale, and their published Department of Justice page on the Herfindahl-Hirschman Index sets out how the index is computed and how it is used in merger review, alongside the thresholds in the Merger Guidelines current at the time of reading. The European Commission also uses the ten-thousand scale in merger control; the Commission's merger legislation pages collect the notices and guidelines that set out its approach. Academic industrial organisation literature more often uses the fractional scale, because it makes the reciprocal relationship with the effective number of firms immediate.
Thresholds change. Agencies have revised the boundaries between unconcentrated, moderately concentrated and highly concentrated markets more than once, and the change in concentration caused by a merger — the delta — carries at least as much weight in review as the level. That is why this page asks you to supply the thresholds rather than printing figures that may already be out of date, and why it labels the classification with whatever source you name.
Why Squaring Is the Whole Point
An obvious alternative would be to add up shares without squaring, but that always gives one hundred percent and tells you nothing. Squaring is what makes the index respond to inequality of size, and it does so in a specific way that is worth understanding rather than accepting.
Squaring gives disproportionate weight to large firms. A firm with a fifty percent share contributes 2,500 to the index; twenty-five firms with two percent each contribute 100 in total between them. That is deliberate. Competition concerns come from large firms, and a measure that treated a fifty percent firm as merely twenty-five times more significant than a two percent one would miss the point.
The practical consequence is that the tail barely matters. Adding a hundred tiny firms to a market dominated by three large ones moves the index very little, which means an incomplete list of small competitors is a much less serious error than a missing large one. It also means the index and a simple firm count can point in opposite directions, and the index is usually the more informative of the two.
Market Definition Determines the Answer
The most consequential input to this calculation is not a number you type. It is the boundary you drew around the market before you started counting, and it is where nearly all real disagreement about concentration lives.
Two boundaries matter. The product boundary: are two goods in the same market? If consumers switch readily between them when relative prices move, they probably are, and treating them separately inflates the measured concentration in both. The geographic boundary: a firm with ninety percent of one city and nothing elsewhere is a monopolist locally and a rounding error nationally, and both statements are correct at their own level.
Competition authorities have formal tests for this, generally variants of asking whether a hypothetical monopolist over the candidate market could profitably raise prices by a small amount. The relevant point for anyone using this calculator is simpler: an HHI quoted without the market definition that produced it is not a finding, and two analysts with different definitions will get different indices from the same underlying data without either making an arithmetic error. If you are measuring one brand's position rather than whole-market structure, our brand search share calculator does that specific job, and the market cap calculator handles company valuation rather than market share.
Arb Digital builds free tools that let you supply the thresholds instead of hard-coding someone else's.
Browse All Free Tools Talk To Our TeamCommon Mistakes to Avoid
- Mixing the two scales — 0.25 and 2,500 describe the same market, and comparing one against a threshold meant for the other is out by a factor of ten thousand.
- Omitting firms — an incomplete list raises the index, though the effect of missing small firms is much smaller than the effect of missing a large one.
- Quoting an index without its market definition — the boundary drawn around the market determines the answer more than any single share does.
- Using stale thresholds — agencies revise the concentration boundaries, and the change caused by a merger often matters as much as the resulting level.
- Treating a number as a conclusion — the index summarises structure, not conduct, and says nothing about entry barriers, buyer power or how firms actually behave.
Related Free Tools From Arb Digital
Measure how unequally a total is distributed with the Gini coefficient calculator, compute national output with the GDP calculator, track one brand's position with the brand search share calculator, value a company with the market cap calculator, or convert shares and changes with the percentage calculator. The full free online tools hub lists every economics tool we publish.
Frequently Asked Questions
It is the sum of the squared market shares of every firm in a market. Squaring makes it respond to how unequally shares are distributed as well as to how many firms there are.
Squaring decimal shares gives a figure between zero and one; squaring whole percentages gives a figure between zero and ten thousand. Both are called the HHI, and the tool reports both so a value can be matched to whichever convention a source uses.
The United States agencies and the European Commission both work on the zero-to-ten-thousand scale in merger control. Academic industrial organisation work more often uses the fractional scale.
Because agencies revise them, and different jurisdictions use different figures. Supplying them as inputs means the classification reflects the guidelines actually in force rather than a number frozen into a web page.
It is one divided by the fractional index, and it tells you how many equally sized firms would produce the same concentration. It is often more intuitive than the raw index.
A concentration ratio adds the shares of the largest few firms and ignores everything below the cut-off. The index uses every firm and weights each by the square of its share, so it distinguishes markets that share the same CR4.
Much less than leaving out a large one, because squaring makes small shares contribute very little. It still biases the index upward, so include everything you can.
Only if the question is about inequality of size rather than concentration. The Gini scores two equal firms and two hundred equal firms identically at zero, which is exactly the distinction competition analysis needs to make.
This page explains a defined statistic for educational purposes and offers no legal, regulatory or competition advice. Thresholds and their interpretation are set by the competition authority with jurisdiction; consult the current guidelines and a qualified adviser for any real matter.
