How this instrument works
The Graham number is Benjamin Graham's arithmetic test for how much a defensive investor should be willing to pay for a share of common stock, built from two figures already on the income statement and balance sheet: trailing earnings per share and book value per share. Graham set two ceilings separately in Security Analysis — no more than 15 times earnings, and no more than 1.5 times book value — then folded both into one number instead of applying them as separate filters.
The formula multiplies 22.5 (which is 15 times 1.5) by EPS and by book value, then takes the square root — a geometric mean rather than a simple average, so the result sits closer to whichever input is smaller. A share priced at or below the Graham number satisfies both of Graham's separate multiples at once; one strong figure cannot mask a weak one, which is the entire point of pairing an earnings measure with an asset measure.
The number breaks down where the inputs do: negative earnings or negative book value make the product under the square root negative, so the calculation has no usable answer and only works for companies with a record of profit and positive equity. It also says nothing about debt loads, growth prospects, or asset quality — a capital-intensive utility and an asset-light software firm can carry the same book value per share for very different reasons, and the formula treats them identically.
- Enter Earnings per share, $ — use trailing twelve-month EPS from the latest income statement, not a forward estimate.
- Enter Book value per share, $ — shareholder equity divided by shares outstanding, taken straight from the balance sheet.
- Read the Graham number — Graham's ceiling for what a defensive buyer should pay, combining both multiples into one figure.
- Compare the Graham number to the stock's current price: a price at or below it clears both the earnings and book-value tests at once.
Worked example — $3 EPS and $25 book value
Take a company reporting $3.00 in trailing earnings per share and $25.00 in book value per share on its balance sheet. Multiply 22.5 by 3 by 25 to get 1,687.5, then take the square root: the Graham number comes out to $41.08 a share.
That $41.08 is not a prediction of where the stock will trade — it is the ceiling Graham set for a defensive buyer. If the market price sits at or below $41.08, the stock clears both of his separate tests (15 times the $3.00 EPS is $45.00, and 1.5 times the $25.00 book value is $37.50) taken together as a geometric mean rather than either alone.
Questions
What does the 22.5 in the Graham number formula represent?
It is Graham's two ceilings multiplied together: no more than 15 times earnings per share, and no more than 1.5 times book value per share, combined as 15 × 1.5 = 22.5. Taking the square root of that product turns two separate limits into one number instead of requiring an investor to check both ratios by hand.
Why does the Graham number use a square root instead of an average?
A square root of a product is a geometric mean, and a geometric mean leans toward the smaller of the two inputs, unlike a simple average. That matters here because Graham wanted one weak figure — thin earnings or a thin asset base — to pull the ceiling down, not get smoothed over by a strong figure on the other side.
Can the Graham number handle a company with negative earnings?
No. Negative EPS or negative book value makes the product under the square root negative, and the formula has no real answer, so this sheet will not return a usable figure for a loss-making company or one with negative shareholder equity. Graham designed the test for established, profitable companies, not turnarounds or early-stage names.
How is the Graham number different from just looking at the P/E ratio?
The P/E ratio checks earnings alone; the Graham number checks earnings and book value together, so a stock cannot pass on a cheap-looking P/E if its balance sheet is thin, or vice versa. A retailer with a low P/E but heavy debt and little tangible equity can still fail the combined test even though the P/E alone looks attractive.
Does a stock price below the Graham number mean it is a buy?
No — it means the stock clears Graham's arithmetic ceiling for a defensive, conservatively financed buyer, nothing more. The formula ignores debt, growth rate, competitive position, and why the market is pricing the shares where it is; a price below the Graham number is a starting filter for further reading, not a verdict on the company.
Why do asset-light companies almost always fail the Graham number test?
Software, services, and other asset-light businesses often carry little shareholder equity relative to their earnings power, because their value sits in intangibles like code, brand, or customer relationships that accounting book value does not capture. A thin book value per share drags the Graham number down regardless of how strong the earnings are, so the test systematically understates value for this kind of company.
References
- Columbia Business School — Heilbrunn Center for Graham & Dodd Investing
- SEC Investor.gov — investing basics glossary
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.