The Graham Number, Explained: The Maximum Price Benjamin Graham Would Pay for a Stock

The stock looks cheap. Its price-to-earnings ratio sits at 11 while the broader market trades near 25, and every screener you run flags it as a value. Then you glance at the price-to-book ratio: 2.6. The company sells for more than two and a half times its net assets, and your gut says that is no bargain at all. One ratio says buy, the other says walk away, and you are the one who has to decide which voice to trust.

Benjamin Graham, the father of value investing, had an answer for exactly this standoff: trust neither ratio alone. Combine them into a single ceiling price, and refuse to pay a dollar above it. That ceiling is the Graham Number — one formula, two inputs, and a hard line between a stock that deserves your research and one that does not.

What the Graham Number Is​

The Graham Number estimates the maximum price a defensive investor should pay for a stock. It comes from Graham's stock-selection rules in Chapter 14 of The Intelligent Investor, and it needs only two data points you can find on any quote page:

• EPS: earnings per share over the trailing twelve months (Graham himself preferred an average of recent years, more on that below)
• BVPS: book value per share from the latest reported balance sheet

The formula:

Graham Number = square root of (22.5 × EPS × BVPS)

The interpretation is deliberately blunt. If the market price sits below the Graham Number, the stock may be undervalued and is worth investigating further. If the price sits above it, the stock fails Graham's ceiling — a defensive investor passes, no matter how good the story sounds. The gap between the number and the price is your margin of safety, the central idea in Graham's philosophy: the distance between what something is worth and what you pay for it.

Note what the formula does not claim. It is not a price target, not a prediction of where the shares will trade next year, and not a buy signal on its own. It is a screen — a fast first gate that tells you whether deeper research is even warranted.

Where 22.5 Comes From​

The constant 22.5 looks arbitrary until you see the two rules hiding inside it. Graham insisted on two separate valuation ceilings for a defensive stock:

1. The price should be no more than 15 times average earnings — a P/E ratio of 15 or below.
2. The price should be no more than 1.5 times book value — a P/B ratio of 1.5 or below.

Multiply the two limits and you get 15 × 1.5 = 22.5. The algebra that turns those two rules into one number is short:

(P ÷ EPS) × (P ÷ BVPS) = 22.5

P² ÷ (EPS × BVPS) = 22.5

P² = 22.5 × EPS × BVPS

P = square root of (22.5 × EPS × BVPS)

So the Graham Number enforces both ceilings at once. A stock priced at or below its Graham Number satisfies the combined product of Graham's two limits; a stock above it breaks at least one of them badly enough that the product fails. That is why the formula resolves your opening dilemma: it refuses to let a low P/E excuse an absurd P/B, or a low P/B excuse an absurd P/E.

A Worked Example​

Take a fictional manufacturer, Acme Widgets. Its trailing-twelve-month earnings per share are $4.20, and its latest balance sheet shows book value per share of $38.00. The calculation runs:

1. Multiply the inputs by the constant: 22.5 × 4.20 × 38.00 = 3,591
2. Take the square root: the square root of 3,591 is approximately $59.93

Acme's Graham Number is about $59.93 per share. Now compare:

• At a market price of $42, Acme trades roughly 30 percent below its ceiling. It passes Graham's screen — a candidate worth researching, not an automatic buy.
• At a market price of $65, Acme trades above its ceiling. A defensive investor walks away regardless of the growth story the earnings call told.

The whole exercise takes sixty seconds with a quote page and a calculator, which is precisely the point. Graham designed his tests for investors who would rather spend their time on a short list of genuine candidates than on justifying stocks they already wanted to own.

How to Use It Without Fooling Yourself​

A screen is only as honest as the inputs you feed it. Four habits keep the Graham Number useful instead of decorative.

Average the earnings. Graham's original P/E test used average earnings over prior years rather than a single twelve-month figure, and that choice matters more than it looks. A cyclical manufacturer at peak earnings will print a Graham Number far above any sensible ceiling; the same company in a trough year will print one far below it. Averaging three to five years of EPS smooths both distortions. Whenever a single year looks unusually good or bad, reach for the average.

Use diluted EPS. Basic EPS divides earnings by shares currently outstanding; diluted EPS also counts options, convertible bonds, and other claims that could become shares. The diluted figure is the conservative one, and a defensive screen should always take the conservative input.

Apply it to one candidate set at a time. The number is most useful as a ranking tool across similar companies — five regional banks, four industrial distributors — computed with identical definitions. Mixing trailing EPS for one stock with averaged EPS for another turns the comparison into noise.

Recompute when the numbers change. Earnings and book values print every quarter. A stock that passed the screen in January can fail it by October after two weak quarters erode both inputs. Set a routine — quarterly for watchlists, annually at minimum — and let the ceiling move with the fundamentals instead of anchoring on a number you computed a year ago.

Remember, too, that Graham's defensive investor ran more tests than this one: adequate company size, a strong current ratio, a long record of uninterrupted dividends, and stable earnings growth across a decade. The Graham Number is one gate in that gauntlet, not the whole gauntlet. A stock that clears it has earned an afternoon of your research; nothing more is promised.

What the Formula Misses​

Every formula has a shape of company it was built for, and the Graham Number was built for profitable, asset-heavy, slow-growing businesses — the railroads and manufacturers of Graham's era. Know the blind spots before you trust a ceiling it gives you.

Growth​

The formula has no growth term. A company compounding earnings at 15 percent a year will almost always trade above its Graham Number, because the market is pricing future earnings the formula cannot see. As a rule of thumb, once expected earnings growth runs into double digits, the number systematically understates value — which is why growth investors ignore it entirely.

Graham knew this, and he wrote a second formula for growth stocks: V = EPS × (8.5 + 2g), where 8.5 is the P/E he considered fair for a no-growth company and g is the expected annual growth rate over the next seven to ten years. In 1974 he revised it to adjust for interest rates: V* = EPS × (8.5 + 2g) × 4.4 ÷ Y, where 4.4 was the average high-grade corporate bond yield of his day and Y is the current one. If you find yourself valuing growers rather than cigar butts, that formula — not the Graham Number — is the Graham tool for the job.

Negative earnings or negative book value​

The formula needs positive EPS and positive BVPS, because the square root of a negative product is meaningless. Loss-making companies fail by construction, and so do companies with negative shareholder equity — a group that includes firms stuffed with debt-funded buybacks as well as genuinely distressed ones. Exclusion here is a feature, not a bug: Graham's defensive investor simply did not buy companies without earnings and equity to measure.

Temporarily depressed earnings​

This is the mirror image of the peak-earnings problem, and it is the more expensive mistake. A solid cyclical company in a recession year prints tiny EPS, the Graham Number collapses, and the screen rejects the stock at exactly the moment it may be cheapest. Averaged or normalized earnings are the fix — never run the formula on a trough year alone and call the result a ceiling.

Asset-light businesses​

Book value understates the worth of companies whose assets never reach the balance sheet. Software firms expense their R&D, consumer brands carry internally built trademarks at zero, and pharmaceutical pipelines appear only after acquisition. For these businesses the BVPS input is structurally too small, so the ceiling comes out structurally too low. The formula fits manufacturers, retailers, and distributors far better than it fits technology and pharma.

Debt, quality, and cash​

The number sees earnings and equity and nothing else: not leverage, not cash conversion, not customer concentration, not management quality. Two companies can share a Graham Number while one funds itself with equity and the other with floating-rate debt. Pair the screen with a balance-sheet check — the current ratio, debt to equity, and whether reported earnings actually turn into operating cash flow — before any candidate graduates from your watchlist to your portfolio.

Tracking Your Graham Ceilings in Your Own Books​

Here is where your bookkeeping earns its keep. The two inputs to the Graham Number come from the same two statements your own ledger produces every month: earnings from the income statement, equity from the balance sheet. If you keep plain-text books, you can record each stock purchase with its cost basis and log market prices over time, so your ledger — not your memory — tracks whether the market ever dipped below your ceiling.

A purchase entry with cost basis looks like this:

2026-03-14 * "Brokerage" "Buy 50 shares ACME below Graham ceiling"
  Assets:Brokerage:ACME   50 ACME {42.00 USD}
  Assets:Brokerage:Cash  -2,100.00 USD
  Expenses:Commissions      4.95 USD
  Assets:Brokerage:Cash     -4.95 USD
 
2026-10-29 price ACME  46.20 USD

The {42.00 USD} cost lot preserves what you actually paid, the price directive records where the market stands, and a dashboard like Fava turns the two into an unrealized-gain chart with no spreadsheet maintenance. When fresh earnings print, recompute the ceiling, add a new price line, and the comparison updates itself. The bookkeeping documentation walks through price directives and investment accounts in detail if you have not tracked holdings this way before.

This habit also enforces the discipline the formula assumes. Writing down your ceiling before you buy — as a comment on the entry, or in the investment journal alongside it — commits you to Graham's side of the trade. Months later, when the price has drifted above the ceiling and you are tempted to average up, the ledger shows you the line you drew and asks what changed: the company's earnings, or just your enthusiasm.

Common Mistakes to Avoid​

• Annualizing one hot quarter. Multiplying a single great quarter by four bakes seasonality and one-time gains into a ceiling that should rest on durable earnings. Use trailing twelve months at minimum, averaged years when earnings swing.
• Using basic instead of diluted EPS. Ignoring convertible claims overstates the ceiling for exactly the companies — acquisitive issuers, option-heavy tech firms — where the difference bites hardest.
• Running it on banks and insurers. For financial firms, book value and earnings mean something structurally different than for industrials, and Graham's 15 × 1.5 limits were never calibrated on them. Use bank-specific tools — price to tangible book, return on tangible equity — instead.
• Treating the ceiling as a target. A stock trading below its Graham Number is eligible for research, not destined to rise. Some cheap stocks are cheap because the business is deteriorating; the screen cannot tell a value from a value trap.
• Forgetting the rest of the checklist. Size, financial strength, dividend history, earnings stability — Graham's defensive investor demanded all of them. A micro-cap with a great Graham Number and a debt-laden balance sheet fails the philosophy even as it passes the formula.

Your Next Sixty Seconds​

Pick one stock you already own. Pull its trailing EPS and latest book value per share, multiply, take the square root, and compare the result with today's price. If the price sits above your number, you do not have to sell — but you should know exactly why you are paying more than Graham's defensive ceiling, and what you believe that he would have wanted proven first. Write the ceiling in your ledger next to the position, and let every future buy decision argue with the number you computed today.