How the Graham number works
By Jude Wallis
The Graham number is the highest price a defensive investor would pay under two of Benjamin Graham's limits at once. Take 22.5 times earnings per share times book value per share and square root it: $2 and $20 give a product of 900 and a ceiling of $30.
Graham number
$30.00
Square root of 22.5 times EPS times book value per share.
- Graham number
- $30.00
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In short
- The formula is the square root of 22.5 times EPS times book value per share: 22.5 times 2 times 20 is 900, and the root is $30.
- The 22.5 is a P/E limit of 15 multiplied by a price to book limit of 1.5.
- Different inputs move it less than you expect: $3 of EPS with $15 of book value gives $31.82.
- It is a screen for established, asset-backed companies, and it says nothing about growth.
- Negative earnings or negative book value put the formula outside its domain entirely.
Two limits multiplied into one number
Graham's defensive criteria included paying no more than 15 times earnings and no more than 1.5 times book value. Rather than applying them separately, the Graham number applies their product: 15 times 1.5 is 22.5, and the square root turns the product of two per-share figures back into a price.
With $2 of earnings and $20 of book value that is a ceiling of $30. A company can breach one of the two limits and still pass, provided the other is low enough to pull the product back under the line, which is a deliberately more forgiving test than applying both separately.
What the two inputs actually contain
Earnings per share is a flow, and it is the input most easily distorted by a single year. A restructuring charge, a disposal gain or an unusual tax item can move it enough to change the ceiling substantially, which is why Graham favoured averaged earnings over several years.
Book value per share is a stock figure from the balance sheet, and it is an accounting number rather than a market one. Property carried at decades-old cost understates it; goodwill from an expensive acquisition can flatter it. Book value and how earnings per share works cover the two inputs on their own terms.
Where the screen breaks down
The formula assumes value shows up on the balance sheet. For a software company, an asset manager or a consultancy, most of what produces the earnings is not carried there at all, so book value per share is tiny and the ceiling comes out far below any plausible price.
That is not the formula misfiring so much as being asked the wrong question. It was built for capital-heavy, established businesses with steady earnings. Applied outside that, it rejects almost everything, which makes it useless as a filter rather than conservative.
Using the ceiling
Read it as one screen among several, and compare it with the actual quote rather than treating it as a valuation. Graham number against market price sets the two next to each other, and the earnings yield calculator turns the price back into a return so the comparison is not purely a rule of thumb. The Graham number calculator computes the ceiling from the two per-share inputs, and how the margin of safety works covers the discipline it belongs to. This is educational material, not financial advice.
Worked examples
\$2 of EPS and \$20 of book value
A company earns $2 a share and has $20 of book value a share. What is its Graham number?
- Multiply the constant by the two inputs: 22.5 times 2 times 20 gives 900.
- Take the square root: $30.
The ceiling is $30 a share, which is 15 times earnings and 1.5 times book value at the same time.
Higher earnings, lower book value
A second company earns $3 a share with $15 of book value a share.
- The product is 22.5 times 3 times 15, which is 1012.5.
- The square root of 1012.5 is $31.82.
$31.82, barely above the first company, because the formula rewards the product of the two inputs rather than either alone.
Common questions
Is the Graham number a target price?
No. It is a maximum under two conservative limits, so a price below it has passed a filter and nothing more.
Which earnings figure should go in?
A representative one. Graham preferred a multi-year average, because a single year can be distorted by one-off items.
Why does it reject technology companies?
Their value is largely off the balance sheet, so book value per share is small and the ceiling comes out unrealistically low.
Is this financial advice?
No. It is educational material about a valuation screen.
Keep reading
This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.