# Graham number

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Not to be confused with [Benjamin Graham formula](/source/Benjamin_Graham_formula).

This article is about the investing term named after Benjamin Graham. For the large number named after Ronald Graham, see [Graham's number](/source/Graham's_number).

The **Graham number** or **Benjamin Graham number** is a figure used in [securities](/source/Securities) investing that measures a [stock](/source/Share_capital)'s so-called fair value.[1] Named after [Benjamin Graham](/source/Benjamin_Graham), the founder of [value investing](/source/Value_investing), the Graham number can be calculated as follows:

\sqrt{22.5\times(\text{earnings per share})\times(\text{book value per share})}

The final number is, theoretically, the maximum price that a [defensive investor](/source/Defensive_investing) should pay for the given stock. Put another way, a stock priced below the Graham number would be considered a good value, if it also meets a number of other criteria.

The number represents the [geometric mean](/source/Geometric_mean) of the maximum that one would pay based on earnings and based on book value. Graham writes:[2]

Current price should not be more than 11⁄2 times the book value last reported. However a multiplier of earnings below 15 could justify a correspondingly higher multiplier of assets. As a rule of thumb we suggest that the *product* of the multiplier times the ratio of price to book value should not exceed 22.5. (This figure corresponds to 15 times earnings and 11⁄2 times book value. It would admit an issue selling at only 9 times earnings and 2.5 times asset value, etc.)

— [Benjamin Graham](/source/Benjamin_Graham), *[The Intelligent Investor](/source/The_Intelligent_Investor), chapter 14*

## Derivation

The constant 22.5 in the formula is derived from Graham's two criteria for defensive stock selection:[2]

1. The [price-to-earnings ratio](/source/Price-to-earnings_ratio) (P/E) should not exceed 15
1. The [price-to-book ratio](/source/Price-to-book_ratio) (P/B) should not exceed 1.5

The product of these two maximum multiples is 15 x 1.5 = 22.5. Since:

- \text{P/E} \times \text{P/B} = \frac{\text{Price}}{\text{EPS}} \times \frac{\text{Price}}{\text{BVPS}} = \frac{\text{Price}^2}{\text{EPS} \times \text{BVPS}}

Setting this product equal to 22.5 and solving for Price yields the Graham number formula:[3]

- \text{Price} \leq \sqrt{22.5 \times \text{EPS} \times \text{BVPS}}

This derivation shows that the Graham number simultaneously enforces both the P/E and P/B constraints in a single metric.

## Alternative calculation

Earnings per share is calculated by dividing *net income* by *shares outstanding*. Book value is another way of saying *[shareholders' equity](/source/Shareholders'_equity)*. Therefore, book value per share is calculated by dividing *equity* by *shares outstanding*. Consequently, the formula for the Graham number can also be written as follows:

\sqrt{15 \times 1.5 \times \left(\frac{\text{net income}}{\text{shares outstanding}}\right) \times \left(\frac{\mathrm{shareholders'\ equity}}{\text{shares outstanding}}\right)}

## Practical example

Consider a company with trailing twelve-month [earnings per share](/source/Earnings_per_share) of $5.00 and a [book value per share](/source/Book_value_per_share) of $30.00. The Graham number would be:

- \sqrt{22.5 \times 5.00 \times 30.00} = \sqrt{3375} \approx 58.09

Under Graham's framework, a defensive investor should consider paying no more than approximately $58.09 per share for this stock. If the stock is trading at $45, the stock would be trading below its Graham number, suggesting it may be undervalued by this metric. If it is trading at $75, it would exceed the Graham number, indicating the stock may be overvalued relative to its earnings and book value.[3]

## History

The Graham number was first mentioned in Benjamin Graham's famous 1949 book, *[The Intelligent Investor](/source/The_Intelligent_Investor)*.[3] Graham's defensive investment strategy mainly focused on a "[margin of safety](/source/Margin_of_safety_(financial))" and reducing losses as opposed to maximizing gains. The Graham number was developed based on this concept to quickly [value a stock](/source/Stock_valuation).[3]

Graham himself never gave a specific formula or equation. The Graham number was derived from guidelines he laid down in the book.[4] The formula has since become widely used by [value investors](/source/Value_investing) as a quick screening tool to identify potentially undervalued stocks.[1]

## Limitations

The Graham number has several limitations that investors should consider:[3][4]

- **No growth consideration**: The formula does not account for future [earnings growth](/source/Earnings_growth), making it unsuitable for evaluating [growth stocks](/source/Growth_stock), particularly in sectors such as technology where much of a company's value derives from expected future earnings.
- **Requires positive values**: The equation requires both positive [earnings per share](/source/Earnings_per_share) and positive [book value per share](/source/Book_value_per_share). Companies with negative earnings or negative equity produce an undefined result under the square root, making the metric inapplicable.
- **Sector limitations**: The metric is most applicable to industrial and manufacturing companies. It is less useful for [financial institutions](/source/Financial_institution), [REITs](/source/Real_estate_investment_trust), and asset-light businesses where [book value](/source/Book_value) may not reflect the company's true economic value.[1]
- **Backward-looking**: The formula uses historical financial data and does not incorporate forward-looking estimates or qualitative factors such as management quality or competitive advantage.
- **Single-point estimate**: The Graham number produces a single value and does not account for the range of possible fair values that more sophisticated methods such as [discounted cash flow](/source/Discounted_cash_flow) analysis can provide.

Despite these limitations, the Graham number remains a popular initial screening tool among value investors due to its simplicity and its direct connection to Benjamin Graham's investment philosophy.[2]

## See also

- [Altman Z-score](/source/Altman_Z-score)
- [Beneish M-score](/source/Beneish_M-score)
- [Piotroski F-score](/source/Piotroski_F-score)
- [Ohlson O-score](/source/Ohlson_O-score)
- [Fundamental analysis](/source/Fundamental_analysis)
- [Magic formula investing](/source/Magic_formula_investing)
- [Value investing](/source/Value_investing)
- [Benjamin Graham](/source/Benjamin_Graham)
- [The Intelligent Investor](/source/The_Intelligent_Investor)
- [Margin of safety](/source/Margin_of_safety_(financial))
- [Price-to-earnings ratio](/source/Price-to-earnings_ratio)
- [Price-to-book ratio](/source/Price-to-book_ratio)

## References

1. [Investopedia: Definition of 'Graham Number'](https://www.investopedia.com/terms/g/graham-number.asp)

1. Graham, Benjamin & [Jason Zweig](/source/Jason_Zweig) (1986-01-01 [1949]). ["14"](https://archive.org/details/harrypotterhalfb00rowl_0/page/349). *The Intelligent Investor*. 1986 ed. [HarperCollins](/source/HarperCollins). p. [halfb00rowl_0/page/389 389](https://archive.org/details/harrypotter). ISBN 0-06-055566-1.

1. ["How to Use the Graham Number to Value Stocks"](https://stablebread.com/graham-number/). 2024-06-29. Retrieved 2026-01-02.

1. ["Graham Number: Classic Screener for Defensive Investors"](https://einvestingforbeginners.com/graham-number-daah/). *Investing for Beginners 101*. 2021-01-26. Retrieved 2026-01-02.

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