What it means
Graham argued that a defensive investor should not pay more than about 15 times earnings, nor more than about 1.5 times book value, and that the two limits could be traded off against each other. Multiplying those two limits gives 22.5, and the Graham Number is simply the square root of 22.5 multiplied by earnings per share and by book value per share.
The square root is needed because the product of an earnings multiple and a book multiple produces a squared price. The reason it endures is that it forces attention onto two things a company cannot easily dress up in a presentation: what it actually earns per share and what the balance sheet says each share is backed by.
It cannot be moved by a compelling story about future markets, which is precisely the discipline it was designed to impose. Used properly it is a screen that decides what deserves further work, not a target price.
Applying it is straightforward. Take earnings per share from the income statement, ideally averaged across several years so a single unusual year does not distort things, and book value per share from shareholders' equity divided by the shares in issue.
Multiply both by 22.5, take the square root, and compare the result with the current share price. The limitations are significant and should be stated plainly.
The formula assumes book value means something, which is true for banks, insurers, property companies and manufacturers but far less true for software, pharmaceutical or brand-driven businesses whose real assets are intangible and often not on the balance sheet at all. It also breaks down entirely if earnings or book value are negative, since you cannot take the square root of a negative product.
Practitioners therefore treat it as one input among several. Common adjustments include using a three-year or five-year average earnings figure, excluding one-off gains, and checking whether the book value is inflated by goodwill from past acquisitions.
A share passing the Graham test still needs a look at debt levels, cash generation and whether the business is in structural decline.
In practice
Real-world examples.
Example
A private investor screens 400 listed industrial companies and keeps only the 23 trading below their Graham Number. That shortlist becomes the week's research list rather than a buy list, because each name still needs a look at debt and cash flow.
Example
An investment club compares two regional banks. Both trade at similar earnings multiples, but one has a book value per share 30% higher, so its Graham Number is meaningfully above its share price while the other's is not.
Example
An analyst tries to apply the formula to a fast-growing software company with negative book value after years of buybacks. The calculation fails outright, which correctly signals that this particular tool is the wrong one for that business.
Formula
Calculation
Graham Number = the square root of (22.5 x Earnings Per Share x Book Value Per Share)
Consider Ridgeway Industrial, a manufacturer of pumps and valves. It reports earnings per share of $4.00 and book value per share of $40.00, and its shares currently trade at $48.00.
22.5 x $4.00 x $40.00 = 3,600
Graham Number = the square root of 3,600 = $60.00
The formula says a defensive investor should pay no more than $60.00 a share. At the market price of $48.00 the share trades below that ceiling, and the margin of safety is:
($60.00 - $48.00) / $60.00 = $12.00 / $60.00 = 0.20, or 20%
As a sanity check, the two underlying limits hold: at $48.00 the price to earnings ratio is 12.0 and the price to book ratio is 1.2, both comfortably inside Graham's caps of 15 and 1.5. Had the shares traded at $75.00 instead, the price would sit 25% above the Graham Number and the screen would reject it.Case study
Seen in the real world.
Thornbury Value Partners is a fictional investment club invented to illustrate the sensible and foolish uses of this measure. The club screened a list of mid-sized engineering companies and found Calder Forge, another invented company, with earnings per share of $3.00, book value per share of $30.00 and a share price of $34.00.
The Graham Number came to the square root of 22.5 x $3.00 x $30.00, which is the square root of 2,025, or $45.00. At $34.00 the share sat roughly 24% below that ceiling, and two members wanted to buy immediately on the strength of the number alone.
A third member did the follow-up work. Calder Forge's earnings had come from a single one-off contract, the three-year average earnings per share was closer to $1.20, and on that basis the Graham Number fell to the square root of 22.5 x $1.20 x $30.00, which is the square root of 810, or about $28.46, well below the market price. The illustrative moral is that the formula is only ever as good as the earnings figure fed into it.
Watch out
Common mistakes.
- Using a single year's earnings per share. One unusually good or bad year swings the result badly, which is why an average across three to five years is safer.
- Applying the formula to asset-light businesses. Software, media and brand-led companies carry little book value, so the calculation systematically calls them expensive.
- Treating the result as a fair value or price target. It is a maximum price for a cautious buyer, not an estimate of what the business is worth.
Questions
People also ask.
Where does the number 22.5 come from?
It is 15 multiplied by 1.5, the price to earnings and price to book limits Graham suggested for a defensive investor.
What if earnings or book value are negative?
The formula cannot be used, because multiplying a negative figure gives a product with no real square root, and that itself is a useful signal.
Is a share below its Graham Number automatically a buy?
No, it has only passed a first screen; debt, cash generation, competitive position and the quality of the reported earnings all still need checking.
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