The Graham Number vs the Graham Formula: Which to Use

Last updated October 29, 2026·6 min read

Benjamin Graham left investors two tools that share his name and almost nothing else. The Graham Number is a ceiling price built from earnings and book value. The Graham Formula is an estimate of intrinsic value built from earnings and growth. They answer different questions, they fail in different places, and using one where the other belongs produces confident nonsense. This guide separates them, runs both on Apple, and shows exactly where each one stops working.

The Graham Number: A Ceiling, Not a Value

Graham argued that a defensive investor should not pay more than a set combination of earnings and assets. His limits were a price-to-earnings ratio no higher than 15 and a price-to-book ratio no higher than 1.5. Multiply the two limits and you get 22.5. The Graham Number turns that product into a price:

Graham Number = square root of (22.5 × earnings per share × book value per share)

If the market price sits above that figure, at least one of Graham's two limits is breached. The number is a screen, a quick ceiling check. It says nothing about what the company will earn next year, and it treats book value as a meaningful anchor, which it is for some companies and is not for others.

The Graham Formula: A Value, With Growth Inside

The formula, from the revised edition of The Intelligent Investor, estimates intrinsic value directly:

Value = EPS × (8.5 + 2g) × 4.4 / Y

EPS is earnings per share. The 8.5 is the price-to-earnings ratio Graham assigned to a company with no growth. The g is the expected annual growth rate over the next seven to ten years, stated in percent. The final term adjusts for interest rates: 4.4 was the yield on AAA corporate bonds in Graham's era, and Y is that yield today, so the whole value falls when bond yields rise and rises when they fall. At a growth rate of 7 percent and a yield of 4.4 percent, the multiplier on earnings is the famous 22.5, the same constant as the ceiling above, arrived at from the opposite direction.

Both Tools, One Company

Apple's fiscal 2025 filings give earnings per share of $7.46 and total shareholders' equity of $73,733 million over about 14,681 million shares on the balance sheet date, which is book value of $5.02 a share.

The Graham Number: the square root of (22.5 × $7.46 × $5.02), which is the square root of $843, or about $29.03.

The Graham Formula, at the Studio's preset growth rate of 7 percent and a 4.4 percent AAA yield: $7.46 × (8.5 + 14) × 4.4 / 4.4, which is $7.46 × 22.5, or $167.85. The Studio prints $167.96 from the unrounded earnings figure; recomputing from the rounded $7.46 differs by a few cents, which is expected.

Apple traded at $342.58 on October 27, 2026. Both tools land far below the price, but for different reasons, and the reasons are the lesson.

Why the Number Breaks First

The Graham Number leans on book value, and Apple's book value has been dismantled on purpose. Decades of share buybacks have pushed Apple's retained earnings line to negative $14,264 million. Book value per share of $5.02 against a price of $342.58 is a price-to-book ratio of about 69.5, against Graham's limit of 1.5. The screen is not wrong about the arithmetic. It is answering a question from an era when industrial companies carried their worth in plant and inventory on the balance sheet. A company whose worth lives in a brand, an installed base, and services contracts carries almost none of it in book value, and buybacks shrink what little is recorded. For such companies the Graham Number is a museum piece: correct, and not about the company in front of you.

It still earns its keep where book value is real: asset-heavy businesses, and any screen meant to find statistically cheap stocks rather than to appraise one business.

Where the Formula Needs Watching

The formula's moving part is g, and small changes swing the answer hard. On Apple's earnings of $7.46, at a 4.4 percent yield:

• At zero growth, the value is $7.46 × 8.5, which is $63.41.
• At growth of 3.5 percent, the value is $7.46 × 15.5, which is $115.63.
• At growth of 7 percent, the value is $167.85.

The rate term matters just as much. At 7 percent growth with a 5.0 percent AAA yield instead of 4.4, the value falls to $147.71, because the 4.4 / Y term drops from 1.00 to 0.88. Graham built that term so rising bond yields would drag stock values down, and it still does. Treat any single output as the middle of a range driven by two honest disagreements: how fast earnings grow, and what bonds pay.

Which to Use, and When

Use the Graham Number as a first-pass screen for statistically cheap, asset-backed companies, and as a discipline check on any stock whose appeal is that it looks inexpensive against its own balance sheet. Do not use it on companies that return capital through heavy buybacks or carry their value in intangibles. The input it trusts most is the one those companies have dismantled.

Use the Graham Formula when you want a quick earnings-based appraisal of a profitable company and you are willing to state your growth assumption out loud, where it can be argued with. State the yield assumption beside it. A formula value without its two assumptions is a number hiding its authors.

Use neither as the final word on a company with negative earnings. Both tools require earnings above zero, and an honest calculator reports that state instead of printing a value. The free Graham Number calculator runs the screen on any ticker and shows both Graham tools side by side with their inputs, so the difference between a ceiling and a value stays visible. The models hub in this series places both tools among the full set of 31 models the Studio runs.

Sources

• Benjamin Graham, The Intelligent Investor, revised edition: the defensive investor price limits and the intrinsic value formula with the AAA yield adjustment.
• Apple Inc. Form 10-K for the fiscal year ended September 27, 2025: diluted earnings per share of $7.46, total shareholders' equity of $73,733 million, retained earnings of negative $14,264 million. Filings are public at SEC EDGAR
• Stock Valuation Studio print for Apple, October 27, 2026: Graham Formula value $167.96 at a preset growth rate of 7 percent and a 4.4 percent AAA yield; price $342.58.