TL;DR: A Graham number calculator computes the square root of 22.5 times earnings per share times book value per share. For a company with earnings per share of $3.20 and book value per share of $18.50, the product inside the root is 22.5 times $3.20 times $18.50, which equals 1,332, and the square root of 1,332 is about $36.50. That figure is the highest price Benjamin Graham's defensive rules implied for the stock. It is a ceiling built from two reported numbers, not a valuation of the business and not a recommendation.
Key Takeaways
- The formula is Graham number equals the square root of (22.5 x EPS x book value per share). The 22.5 is Graham's combined cap: a P/E of 15 times a price to book of 1.5.
- Both inputs come from reported financials. Use trailing earnings per share and the most recent book value per share, and write down which periods you used.
- The calculation breaks when either input is negative. A loss making company or one with negative equity has no meaningful Graham number.
- Compare the result with the price as a discipline check, the way what is the Graham number explains, and run the manual steps in how to calculate the Graham number once before trusting any calculator output.
- A calculator removes arithmetic errors. It does not remove input errors, which are the ones that matter.
What does a Graham number calculator actually do?
It does one multiplication chain and one square root. That is the whole machine. The reason a dedicated calculator exists is that the two inputs live in different places: earnings per share comes from the income statement, book value per share comes from the balance sheet divided by the share count, and investors routinely pair mismatched periods, a trailing EPS with a stale book value, or a diluted share count with a basic one. A calculator that forces you to enter both figures with their dates removes the most common silent error, which is not the square root.
The 22.5 factor is not magic. Graham's defensive investor rules capped the price at 15 times earnings and at 1.5 times book value. Multiplying the two caps gives 22.5, and the square root converts the product back into a per share price. When you use a calculator, you are accepting those two caps as your discipline. An investor who thinks a P/E of 15 is the wrong cap for a given business should change the factor deliberately, and should say so in their notes, rather than quietly accepting the default.
A worked example, with every step shown
Take a hypothetical company with trailing earnings per share of $3.20 and book value per share of $18.50. Multiply the two inputs: $3.20 times $18.50 equals $59.20. Multiply by the factor: $59.20 times 22.5 equals 1,332. Take the square root: the square root of 1,332 is about 36.50, so the Graham number is $36.50 per share.
Read the checks the number contains. At $36.50, the implied P/E is $36.50 divided by $3.20, about 11.4, and the implied price to book is $36.50 divided by $18.50, about 1.97. Notice the second figure exceeds Graham's 1.5 cap. That is how the combined formula behaves when earnings are strong relative to book value: it trades the two caps against each other rather than enforcing each one separately. An investor who wants both caps enforced individually should compute 15 times EPS ($48.00) and 1.5 times book value ($27.75) and take the lower figure. The single formula and the two cap method answer slightly different questions, and confusing them is a common calculator mistake.
When does the calculator refuse to answer?
When exactly one of earnings per share and book value per share is negative, the product inside the root is negative and no real square root exists. When both are negative, which happens after heavy buybacks or accumulated losses, the product is positive and a root exists on paper, but the figure is meaningless for a screen built for profitable companies. Calculators variously display zero, an error, or a meaningless positive figure built from absolute values. All three responses hide the real information, which is that the company sits outside the population Graham's rules were built for: profitable, asset backed businesses. The correct response to a broken Graham number is not a workaround. It is a different tool, such as a DCF calculator built on cash flow, or the admission that this valuation shortcut does not apply.
How should you use the output in a research process?
As a first screen and a discipline anchor, in that order. As a screen, a price far above the Graham number tells you the market is paying for growth, intangibles, or quality that the formula deliberately ignores, which is useful information about expectations. As an anchor, the number gives a defensive investor a pre-committed ceiling, decided before emotion and narrative attach to a stock. What it should never become is a target price. Graham presented the figure as a limit for a specific defensive style, inside a full checklist of financial strength tests, most of which a calculator does not run. Pair it with the stock research checklist so the formula stays one input among several.
FAQ
Is the Graham number the same as the Benjamin Graham formula? No. The Graham number uses earnings and book value. The Benjamin Graham formula estimates intrinsic value from earnings, a growth rate, and a bond yield adjustment. They share an author and a conservative spirit, and nothing else.
Which EPS should I enter, basic or diluted? Diluted, because it counts the shares that options and convertibles can create. Pair it with book value per share computed on the same diluted count so the two inputs describe the same company.
What if the stock trades below its Graham number? It passes one arithmetic screen. It may still be cheap for a reason: declining earnings, weak finances, or an industry in retreat. Graham required several other tests, including financial strength and earnings stability, before the price test meant anything.
Can I use the Graham number for growth companies? You can compute it, but it will almost always sit far below the price, because the formula gives no credit for future growth. That gap measures how much of the price is growth expectation. It does not prove the stock is overvalued.
Sources
- Benjamin Graham, The Intelligent Investor, chapter on defensive investor stock selection, for the 15 times earnings and 1.5 times book value caps and the combined formula.
- Investor.gov (U.S. Securities and Exchange Commission), investor education material on financial statements, accessed October 2026.
- Every worked example in this post was computed directly from the stated inputs shown in the text.
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.
