Graham Number

What is Graham Number?

Benjamin Graham's estimate of the maximum fair price for a defensive stock, calculated as the square root of 22.5 times EPS times book value per share.

Overview

The Graham number is an estimate of the highest price a defensive investor should pay for a stock, calculated as the square root of 22.5 times earnings per share times book value per share. It comes from the valuation limits Benjamin Graham set out for conservative investors in The Intelligent Investor.

Graham did not use the name himself; the label was attached to his rule of thumb later. The formula combines two tests in one figure: a cap on the price to earnings ratio and a cap on the price to book ratio. A share price below the Graham number passes the combined test; a price above it does not.

Alternative Names: Graham Formula, Benjamin Graham Number, Graham Fair Value

Formula

Graham Number = √(22.5 × EPS × Book Value Per Share)

Graham Upside = (Graham Number − Share Price) ÷ Share Price × 100

Where:

EPS: Trailing twelve month diluted earnings per share: net income over the last four quarters divided by the average diluted share count
Book Value Per Share: Shareholders' equity from the most recent balance sheet divided by shares outstanding. See book value per share
22.5: Graham's maximum P/E of 15 multiplied by his maximum P/B of 1.5

Where 22.5 Comes From

Graham suggested that a defensive investor should not pay more than 15 times earnings or more than 1.5 times book value. He also allowed a trade-off: a stock with a lower P/E could justify a higher P/B, as long as the product of the two did not exceed 15 × 1.5 = 22.5. Setting P/E × P/B equal to 22.5 and solving for price gives the formula:

(Price ÷ EPS) × (Price ÷ BVPS) = 22.5, so Price² = 22.5 × EPS × BVPS, and Price = √(22.5 × EPS × BVPS)

How FinSpry calculates it: FinSpry applies the formula with TTM diluted EPS and the latest book value per share, and computes it only when both are positive. A company with a net loss or negative shareholders' equity has no Graham number, because the square root of a negative product is undefined and the idea of a fair multiple of losses makes no sense. FinSpry also shows Graham upside, the percentage gap between the Graham number and the latest closing price. Graham himself recommended average earnings over the past three years rather than a single trailing year, so the result can differ from versions that use multi-year averages.

Calculation Example

Here is the calculation for a hypothetical company:

Example Company - Financial Data:

TTM Diluted EPS	$4.00
Book Value Per Share	$25.00
Current Share Price	$40.00

Step 1: Graham Number

22.5 × $4.00 × $25.00 = 2,250

Graham Number = √2,250 ≈ $47.434

= $47.43

Step 2: Graham Upside

($47.434 − $40.00) ÷ $40.00 × 100

= +18.59%

Interpretation: The Graham number is about 18.6% above the current price, so the stock passes Graham's combined valuation test. At a price equal to the Graham number, the P/E would be 11.86 ($47.43 ÷ $4.00) and the P/B would be 1.90 ($47.43 ÷ $25.00). The P/B is above 1.5, but the low P/E offsets it: before rounding, the product of the two is exactly 22.5.

If the Price Were Higher:

At $55.00, Graham upside = ($47.434 − $55.00) ÷ $55.00 × 100 = −13.76%, so the stock would fail the test.

How to Interpret

The Graham number is a ceiling, not a target. Graham intended it as a maximum price for a stable, established company, not as a forecast of where the stock will trade.

Reading Graham Upside:

Positive Upside: Price Below the Graham Number

The stock meets Graham's combined earnings and asset test. The larger the gap, the bigger the cushion, which Graham called a margin of safety. Check that earnings are stable and not temporarily inflated.

Near Zero: Price Close to the Graham Number

The stock is priced right at Graham's limit. It neither offers a margin of safety nor looks expensive by this measure.

Negative Upside: Price Above the Graham Number

The market values the company above what Graham's defensive criteria allow. This is normal for growing companies and for businesses whose value lies mostly in brands, software or other assets that do not appear on the balance sheet.

Why It Matters

Simple and Transparent: It needs only two inputs from published financial statements and involves no growth forecasts.
Combines Earnings and Assets: Requiring both positive earnings and positive book value screens out companies that are profitable on paper but have weak balance sheets, and vice versa.
A Discipline Check: It gives a fixed reference point against which a share price can be judged, independent of market sentiment.

Limitations

No Growth Credit: The formula assigns the same value to a company whose earnings are rising quickly as to one whose earnings are flat. For a growth-aware estimate, see the Peter Lynch fair value.
Book Value Can Mislead: Share buybacks, write-downs and intangible assets that are not recorded on the balance sheet can make book value very low, pushing the Graham number down for companies that are financially strong.
Undefined for Losses or Negative Equity: Many companies, including some large and established ones with negative equity from buybacks, have no Graham number at all.
Single-Year Earnings: Using TTM EPS makes the figure sensitive to one strong or weak year, which Graham's multi-year average was meant to smooth.
Fixed Multiples: The 15 and 1.5 limits were set decades ago and do not adjust for interest rates or industry norms.

Graham paired these valuation limits with other requirements for defensive investors, including adequate size, a strong financial condition, an uninterrupted dividend record and steady earnings growth. The Graham number covers only the price test.

Related Financial Ratios

These related metrics provide additional insights for comprehensive financial analysis:

Peter Lynch Fair Value

A fair value estimate based on earnings growth and dividend yield rather than book value.

Price to Earnings Ratio (P/E)

One half of Graham's test. He capped it at 15 for defensive investors.

Price to Book Ratio (P/B)

The other half of the test. Graham capped it at 1.5, or higher when the P/E is low.

Book Value Per Share

Shareholders' equity per share, one of the two inputs to the formula.

Use This Metric

The Graham number and Graham upside appear on each stock's statistics page. To apply Graham's limits across the market, screen by P/E and P/B ratio.

Screen by P/E and P/B

Is the stock cheap or expensive?

Explore all Valuation Ratios & Multiples

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