Value investing · Benjamin Graham
Graham Number: Formula, Calculation, and Value Investing Screen
The Graham Number gives you a conservative fair-value ceiling in one calculation. Derived from Benjamin Graham's twin rules — no more than 15x earnings, no more than 1.5x book value — it distills a full valuation framework into a single number you can compare directly to any stock's market price. This guide covers the formula, the 22.5 constant, a worked Macy's example, and exactly when the formula breaks down.
The Graham Number is a conservative fair-value ceiling derived from Benjamin Graham's rule: a stock should not trade above 15x earnings or 1.5x book value.The Graham Number is a conservative fair-value ceiling derived from Benjamin Graham's rule: a stock should not trade above 15x earnings or 1.5x book value. Formula: Graham Number = square root of (22.5 x EPS x BVPS). A stock trading below its Graham Number passes this classic value screen.
The Graham Number Formula
Graham Number = square root of (22.5 x EPS x BVPS). Each component maps to one of Graham's valuation rules for defensive stocks.
- 22.5 (the constant)
- Graham set a 15x P/E ceiling and a 1.5x P/B ceiling for defensive stocks. Combined: 15 x 1.5 = 22.5. The constant encodes both constraints simultaneously.
- EPS
- Diluted trailing-12-month earnings per share. Use diluted EPS to account for stock options, convertibles, and warrants.
- BVPS
- Book value per share = stockholders equity divided by diluted shares outstanding. See the book value per share guide for how to find and verify this figure from the balance sheet.
- sqrt( )
- The square root normalizes the units. EPS is in dollars per share; BVPS is in dollars per share; multiplying them gives dollars squared per share squared. The square root returns the result to dollars per share — a price.
The Graham Number is not a discounted cash flow model. It does not project future earnings or apply a discount rate. It is a conservative mechanical screen that rules out stocks where both earnings and book value are too expensive relative to Graham's defensive thresholds. For a more comprehensive valuation, pair it with the intrinsic value guide which covers the full DCF approach.
Worked Example: Macy's Inc. (M) FY2024
Macy's is an asset-heavy retailer — a business type for which the Graham Number was designed. Using approximate FY2024 figures: EPS of approximately $2.50 and BVPS of approximately $23.
- Step 1: Gather inputs
- EPS = $2.50 | BVPS = $23.00
- Step 2: Multiply EPS x BVPS x 22.5
- $2.50 x $23.00 x 22.5 = $1,293.75
- Step 3: Take the square root
- sqrt($1,293.75) = approximately $35.98
- Graham Number result
- $35.98 — if Macy's trades below this, it passes the Graham screen
This is a conservative floor estimate, not a precise price target. The Graham Number tells you a price above which Graham would consider the stock too expensive on combined earnings and book value grounds. It does not say the stock is a buy at $35.97 — only that at prices above $35.98, it fails both his P/E and P/B rules simultaneously. Figures are approximate illustrative values.
How to Interpret the Result
When a stock's market price is below its Graham Number, it passes Graham's classic dual-condition screen: the market is not paying more than 15x earnings or more than 1.5x book value. This is a necessary condition for Graham's definition of a defensively valued stock — it is not a sufficient condition for investment quality. A stock can trade below its Graham Number because earnings are depressed, because book value is impaired, or because the business faces genuine structural deterioration. The screen filters out the clearly overvalued; it does not filter out the fundamentally impaired.
When a stock trades above its Graham Number, it fails at least one of his two price rules. That does not mean it is uninvestable — most high-quality growth companies consistently trade above their Graham Number by design. The Graham Number is a tool for conservative, asset-focused value investing, not a universal valuation standard. Pair any Graham Number finding with qualitative analysis of the business, an examination of the margin of safety relative to intrinsic value, and a review of the P/E ratio in sector context.
When the Formula Breaks
Negative EPS. The square root of a negative number is undefined in real arithmetic. If a company is running at a loss, the product 22.5 x EPS x BVPS is negative and the formula produces no result. Graham's formula assumes a profitable business; it has nothing to say about loss-making companies.
Negative BVPS. Companies with aggressive share buyback programs or large accumulated goodwill and intangible write-downs can carry negative stockholders equity — meaning BVPS is negative. This also makes the product negative and the formula undefined. This is increasingly common among mature technology and consumer companies that have returned capital aggressively. The book value per share guide covers how to identify negative book value situations.
Growth companies. Graham designed this formula for defensive value stocks — businesses with stable, asset-backed earnings and modest growth expectations. Applying a 15x P/E ceiling to a company growing earnings at 25% per year produces a Graham Number far below the market price by design. The PEG ratio guide covers a better framework for growth-oriented valuation where earnings growth rate is a core input.
Financial companies. Banks and insurers have structurally different balance sheets where book value means something different from industrial companies. Leverage is a business input for a bank, not a risk indicator. P/B ratios that would look expensive for a manufacturer are normal for a well-run bank. The Graham Number should not be applied to financial sector companies without significant adjustment.
Sector Applicability
The Graham Number works best where both earnings and tangible book value are meaningful and relatively stable. It performs poorly in sectors where intangibles dominate value or where leverage is a business input rather than a risk indicator.
| Sector Type | Applicability |
|---|---|
| Manufacturing | Works well — tangible assets, stable earnings multiples near Graham thresholds |
| Retail | Works well — inventory and real estate anchor book value; earnings cycles create screen entry points |
| Energy | Works well for E&P and midstream — reserve-backed book value; watch for negative EPS at cycle troughs |
| Utilities | Works well — regulated asset base, predictable earnings; often trade near Graham Number by nature |
| Technology / SaaS | Poorly suited — high intangibles, low book value, growth-driven multiples far above 15x; use PEG or DCF instead |
| Biotech | Poorly suited — often pre-profit; negative EPS makes formula undefined; value is pipeline, not book |
| Financial (Banks / Insurers) | Needs adjustment — P/B means something different; leverage is a business input; use sector-specific P/B benchmarks |