TL;DR: The Graham Number is the square root of 22.5 multiplied by earnings per share multiplied by book value per share. For a company with earnings per share of $3.00 and book value per share of $20.00, the calculation is the square root of 1,350, which is about $36.74. That figure is a ceiling reference from Benjamin Graham's framework, not a target price, and it only works when both inputs are positive.
Key Takeaways
- The formula is Graham Number equals the square root of 22.5 times EPS times book value per share.
- Both earnings per share and book value per share must be positive, or the formula produces no usable result.
- The 22.5 factor comes from Graham's limits of a price to earnings ratio of 15 and a price to book ratio of 1.5, multiplied together.
- A result above the current price does not by itself mean a stock is cheap, and a result below the price does not by itself mean it is expensive.
- State the earnings basis you use: Graham's defensive criterion used average earnings over the preceding three years, while an alternative implementation uses trailing twelve-month diluted EPS. Compare the method with the background in our guide to what the Graham Number is.
What are the four steps to calculate the Graham Number?
Step one is to find earnings per share. Graham's defensive criterion used average earnings over the preceding three years; an alternative implementation uses trailing twelve-month diluted EPS, and whichever basis is used should be stated. Step two is to find book value per share: equity attributable to common shareholders, excluding preferred equity, divided by common shares outstanding at the period end, as reported on the balance sheet. Step three is to multiply 22.5 by both figures. Step four is to take the square root of that product. The result is expressed in the same currency per share as the inputs.
Consistency matters more than speed here. State the earnings period and the balance-sheet date separately. Graham's defensive criterion used three-year average earnings. An alternative calculation can use trailing twelve-month diluted EPS. Use the reported EPS denominator and period-end common shares for book value per share; do not force those share counts to match. Keep currencies and stock-split adjustments consistent, and explain material changes between reporting dates. Write each input down with its source and date before you calculate, so you can repeat the calculation later and get the same answer.
What does a worked example look like, checked step by step?
Take a hypothetical company with earnings per share of $3.00 and book value per share of $20.00. First multiply the two inputs: $3.00 times $20.00 equals $60.00. Next multiply by 22.5: $60.00 times 22.5 equals 1,350. Finally take the square root of 1,350. Since 36 squared is 1,296 and 37 squared is 1,369, the answer sits between 36 and 37, at about $36.74. That is the Graham Number for these inputs.
Now place it in context without turning it into a call. If the shares traded at an illustrative $30.00, the price would sit below the $36.74 reference. If they traded at $45.00, the price would sit above it. In Graham's framework the number was a maximum price a defensive investor would pay for a stock meeting his other criteria, not a prediction of where the price will go. The calculation tells you where a ceiling sits under one strict set of assumptions. It does not grade the business, its debt, or its future earnings.
Where do EPS and book value per share come from?
Earnings per share comes from the income statement: use the diluted figure reported in the filing, whose numerator and denominator already carry the applicable dilution adjustments. Book value per share comes from the balance sheet: equity attributable to common shareholders, excluding preferred equity and noncontrolling interests, divided by common shares outstanding at the period end. Both appear in quarterly and annual filings, and many data providers display them directly, though displayed figures should be checked against the filing when the result will inform a decision.
Two traps recur. First, book value reflects accounting values, not market values, so a company whose main assets are brands, software, or other intangibles may report a book value far below the economic value of those assets. Second, share buybacks reduce equity and can shrink book value per share even in a healthy, profitable company. Neither trap makes the formula broken. Both mean the output needs interpretation, which is why Graham paired the number with qualitative requirements about earnings stability, dividend record, and moderate debt.
When can the Graham Number not be calculated?
The screen yields a meaningful reference only when both inputs are positive. One negative input produces a negative product under the root, which has no real square root. A zero input produces a result of zero, and two negative inputs produce a real number, but neither case is a usable valuation reference. A company with negative equity, which can happen after large buybacks or accumulated losses, sits outside the screen the same way. In those cases the honest answer is that this tool does not apply, rather than forcing a number by using absolute values or substituting a different earnings figure without saying so.
The formula also fits some industries poorly. Banks and insurers carry balance sheets structured very differently from industrial companies, and an asset light growth company can trade far above any Graham Number for years, because the market is pricing future earnings the formula deliberately ignores. Knowing when a method is silent is part of using it well. For a broader valuation approach that starts from cash flow instead, see our explainer on reverse DCF.
FAQ
What is 22.5 in the Graham Number formula? It is the product of Graham's two ceiling ratios: a price to earnings ratio of 15 times a price to book ratio of 1.5 equals 22.5. Graham allowed a trade-off between the two: one ratio could run higher if the other ran lower, provided their product did not exceed 22.5. That product is the single factor used in the square root.
Should I use trailing or forward EPS? Graham's method was built on reported figures, not forecasts, and his defensive earnings criterion used average earnings over the preceding three years rather than a single trailing year. Using forward estimates changes the character of the tool from a check based on recorded results to a check based on predictions. If you test both, label them separately and do not average them.
What if a company pays no dividend? The formula itself does not require a dividend, since it uses only earnings and book value. Graham's wider defensive criteria did look for a dividend record, but that is a separate screen from the calculation.
Is the Graham Number the same as intrinsic value? No. It is one conservative reference figure derived from two accounting inputs. Intrinsic value estimates, such as a discounted cash flow, build in future cash flows and a discount rate. The two approaches can give very different answers for the same company.
Sources
- U.S. Securities and Exchange Commission, Beginners' Guide to Financial Statements (https://www.sec.gov/about/reports-publications/beginners-guide-financial-statements).
- Benjamin Graham, The Intelligent Investor, chapter 14 for the defensive investor's price criteria and the 22.5 product, and chapter 20 for the margin of safety concept.
Educational content, not financial advice. Any worked example uses hypothetical, illustrative figures chosen for round numbers. It is not a projection of any security's returns and not a recommendation to buy or sell any security.
