A Graham number calculator applies one of the most quoted formulas in value investing: the square root of 22.5 multiplied by earnings per share and book value per share. Benjamin Graham set it out as a rough upper bound on what a defensive investor might pay for a company's shares, and it survives in screens seventy years later mostly because it is memorable and needs only two inputs. Both of those virtues are also its limitations, and this page treats them as the substance rather than a footnote.
Arb Digital publishes it in the free tools library beside the intrinsic value calculator, which discounts a stream of future earnings rather than screening on two balance-sheet-derived ratios, and the DCF calculator, which models cash flows explicitly. The Graham number is a screen. Those are models. Confusing the two is the single most common error made with this formula, because a screen is designed to shorten a list and a model is designed to produce an estimate, and the Graham number is very bad at the second job.
What This Graham Number Calculator Does
It takes earnings per share, book value per share and a screen constant, and returns the square root of their product. It then decomposes that result into the two ratio limits the constant encodes, so you can see which of the two a given company passes or fails. It also reports the price you entered as a percentage of the number, and the gap between them.
The decomposition matters more than the headline. Graham's 22.5 is not an empirical constant discovered in data. It is 15 multiplied by 1.5 — a price-to-earnings ceiling of fifteen times and a price-to-book ceiling of one and a half times, multiplied together so the two constraints can be tested with one square root instead of two comparisons. Any company whose P/E times P/B comes in under 22.5 is trading below its Graham number, and any company above it is not. The grid on this page shows both ratios and their product so that identity is visible rather than hidden inside a square root.
The page reports no verdict. It does not describe a share as cheap, undervalued, a bargain or a buy, and there is no threshold at which it changes colour or tone. It computes a published formula on figures you supplied and stops there.
How to Use It
- Use an averaged EPS, not the latest year. Graham's own writing asks for several years of earnings precisely because a single year swings on disposals, impairments and tax settlements. Enter the average and record how many years it covers in the years field so you do not later forget the basis.
- Take book value per share from ordinary equity only. Strip out preference capital and minority interests. Mixing a group equity figure with an ordinary share count inflates book value per share and inflates the result.
- Enter today's price yourself. Nothing on this page fetches a quote, because a hardcoded price would be wrong within minutes. The P/E ratio calculator and the EPS calculator are useful alongside if you are building either input from raw statements.
- Read the two component ratios before the headline. A company can sit below its Graham number on a very low price-to-book with an unremarkable P/E, or the reverse. Those are entirely different situations and the single number hides which one you are looking at.
- Change the constant only deliberately. Raising it to 30 is equivalent to allowing a 20× P/E against a 1.5× P/B, or a 15× P/E against a 2× P/B. It is a policy choice about your own limits, not a refinement of Graham's.
The Formula and How It Is Calculated
The formula is:
Graham number = √(22.5 × EPS × BVPS)
and the identity that produces it is that a price P satisfies both P ÷ EPS ≤ 15 and P ÷ BVPS ≤ 1.5 at their joint limit when P² = 15 × 1.5 × EPS × BVPS. Taking the square root of both sides gives the number. This is why the product of the two ratios, rather than either ratio alone, is the quantity being tested.
Worked example, matching the values the page loads with. Earnings per share of $4.50 and book value per share of $32.00 give 22.5 × 4.50 × 32.00 = 3,240. The square root of 3,240 is $56.9210, which is the Graham number. Against an entered price of $48.00, the price-to-earnings ratio is 48.00 ÷ 4.50 = 10.667 and the price-to-book ratio is 48.00 ÷ 32.00 = 1.500. Their product is 10.667 × 1.500 = 16.00, which is below the 22.5 constant, confirming the same conclusion the square root reached. The price is 48.00 ÷ 56.9210 = 84.33% of the number, a gap of $8.92 per share or 15.67% of the number.
Note what happens if either EPS or book value per share is negative or zero. The product inside the square root turns negative or collapses to zero, and the formula returns nothing usable. This page reports that explicitly rather than printing a zero or a NaN, because a loss-making company and a company with negative equity are not companies with a Graham number of zero — they are companies the formula cannot describe at all.
The Assumptions Built Into the Constant
Every number this page returns rests on four assumptions that Graham stated openly and that later readers routinely drop.
That fifteen times earnings is a reasonable ceiling. This reflects the interest rate environment and equity risk premiums of the mid twentieth century. In a period of very low long-term rates the same investor logic supports a higher multiple, and in a high-rate period a lower one. The constant is not indexed to anything, so it silently becomes stricter or looser as rates move.
That book value approximates what the assets are worth. This holds tolerably for a company whose value sits in factories, inventory and receivables. It fails for a company whose value sits in brands, software, research or customer relationships, because most internally generated intangibles never appear on a balance sheet at all. A business with genuinely valuable intangibles and a thin book value is excluded by the formula regardless of its economics.
That earnings are a stable, repeatable quantity. Cyclical companies pass the screen at the top of their cycle, when earnings are peaking and book value has been built up by retained profit, and fail it at the bottom. That is precisely backwards from how a value screen is meant to behave, and it is why an averaged EPS is not optional.
That the two limits should be multiplied. The product form allows a very low price-to-book to compensate for a high P/E and vice versa. Graham's defensive criteria as written applied both caps separately as well. Using only the product admits companies that fail one of the two original tests outright.
Sector context is the practical answer to most of this. NYU Stern's price and value to book ratio by sector data set shows how far apart typical price-to-book ratios sit between, say, regional banks and semiconductor designers. Comparing a company against its own sector's distribution tells you something; comparing it against a fixed 1.5 tells you mostly which industry it is in.
What Graham Himself Said Later
The formula is usually presented as Graham's settled view. It was not. In his later writing and interviews he moved away from detailed individual security analysis of exactly this kind, arguing that the sheer volume of research capacity in the market had eroded the advantage that painstaking single-company work once provided, and favouring simple, mechanical, diversified criteria applied across many holdings rather than a precise number for one.
That shift matters for how the output on this page should be read. The number was never intended as a valuation of a single company that you then act on. It was one filter in a defensive framework that also required adequate size, a strong financial condition, earnings stability over a decade, an uninterrupted dividend record and demonstrated earnings growth. Applying the square root and ignoring the other five conditions is using a fraction of the method and calling it the method.
It also excludes whole sectors by construction. Banks and insurers carry balance sheets where book value means something quite different from a manufacturer's. Asset-light service businesses often show book values close to zero. High-growth companies reinvesting everything rarely clear the P/E leg. A screen that structurally cannot see most of the modern index is not neutral, and the companies it does surface share characteristics that have nothing to do with being mispriced. FINRA's overview of value investing sets out the wider approach this formula came from, which is a more useful frame than the formula alone.
Reading the Gap Between Price and the Number
The percentage in the grid is the one figure people most often over-interpret. A price at 84% of the Graham number does not mean a 16% gain is available, is likely, or is owed. It means that, on the two inputs you typed, the market is quoting less than the formula's ceiling. Prices sit below simple screens for reasons the screen cannot see: a deteriorating end market, an accounting question, a pending regulatory decision, a controlling shareholder, or a currency the reported earnings are exposed to.
The reverse is equally true. A price well above the number is not evidence of overvaluation. It is evidence that the market is pricing something the formula does not measure, which for most profitable companies is future growth and returns on incremental capital — neither of which appears anywhere in a square root of current earnings and current book value.
If you want a number that at least attempts to price the future, the DCF calculator and the dividend discount model calculator do so explicitly, and both make their assumptions visible so you can argue with them. FINRA's guide to the financial performance metrics every investor should know covers where EPS, book value and the ratios derived from them actually come from in a filing.
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See Content Marketing Services Talk to Arb DigitalCommon Mistakes to Avoid
- Using a single year's EPS — one good year lifts the number by the square root of the earnings increase, so a 44% earnings spike raises the Graham number by 20% on its own. Average several years or the screen tracks the cycle instead of the business.
- Treating the output as a target price — it is a ceiling derived from two arbitrary ratio caps, not a forecast, an estimate of worth, or a level the price is expected to reach.
- Applying it to banks, insurers or asset-light businesses — book value carries a different meaning in financials and barely exists in services, so the price-to-book leg of the test is measuring something incomparable.
- Ignoring negative inputs — a loss or negative equity makes the formula undefined, not zero. Screens that coerce it to zero rank the worst companies as the cheapest.
- Using the formula alone — Graham's defensive criteria included size, financial strength, ten-year earnings stability, a dividend record and growth. The square root was the last step, not the whole test.
Related Free Tools From Arb Digital
Build the earnings input with the EPS calculator and check the multiple with the P/E ratio calculator. For approaches that model the future rather than screening on the present, use the intrinsic value calculator, the DCF calculator or the dividend discount model calculator. The return on equity calculator shows what the book value is actually earning, and the enterprise value calculator reframes the whole thing on a capital-structure-neutral basis. Everything else is in the free online tools hub.
Frequently Asked Questions
It is the square root of 22.5 multiplied by earnings per share and book value per share. Benjamin Graham used it as a rough upper limit on what a defensive investor might pay, and the constant 22.5 is simply his price-to-earnings cap of 15 multiplied by his price-to-book cap of 1.5. It is a screening filter rather than a valuation model.
From multiplying two of Graham's own ratio limits together. He suggested a defensive investor should not pay more than about fifteen times average earnings or more than about one and a half times book value. Multiplying those caps gives 22.5, which allows both constraints to be tested with a single square root instead of two separate comparisons.
No, and this page deliberately makes no such claim. It means the price is below the ceiling that two fixed ratio caps produce from the earnings and book value figures you entered. Prices sit below simple screens for many reasons the screen cannot see, including deteriorating markets, accounting questions and pending regulatory decisions.
The formula becomes undefined, because the product inside the square root turns negative. A loss-making company or one with negative shareholders' equity does not have a Graham number of zero, it has no Graham number at all. This page reports that instead of printing a misleading figure that would rank such companies as the cheapest in a screen.
Because book value understates businesses whose value sits in brands, software, research or customer relationships, since most internally generated intangibles never appear on a balance sheet. Banks and insurers carry balance sheets where book value means something different again. The screen therefore surfaces a narrow, structurally similar group of companies.
He moved away from it. In later years he argued that the amount of research capacity in the market had eroded the advantage of painstaking single-company analysis, and he favoured simple mechanical criteria applied across a diversified group of holdings. The formula was also only one of several defensive conditions he set, alongside size, financial strength and earnings stability.
Only if you have a specific reason and understand what you are changing. Raising it to 30 is equivalent to permitting a twenty times price-to-earnings ratio against the same one and a half times price-to-book, or fifteen times earnings against two times book. That is a decision about your own limits, not a technical improvement to the original.
The Graham number is a screen built from two current ratios and contains no view of the future at all. An intrinsic value estimate discounts projected future earnings or cash flows back to today, so it depends on growth and discount rate assumptions you have to defend. They answer different questions, and the screen is a poor substitute for the model.
This tool applies a published screening formula to figures you supply. It is not investment advice, not a valuation, and not a recommendation to buy, sell or hold any security. The output is a mathematical consequence of your inputs and the assumptions described above, several of which are widely disputed. Decisions about your money should involve a licensed financial adviser who is regulated to advise on them.
