Skip to content

Graham number calculator

By Jude Wallis

The Graham number is the square root of 22.5 times earnings per share times book value per share. $2 of EPS and $20 of book value gives a product of 900 and a Graham number of $30 a share.

Graham number

$30.00

Square root of 22.5 times EPS times book value per share.

Graham number
$30.00
$
$

Put this on a class page: one iframe, free, for Google Sites, Canvas, WordPress or Notion.

On this page

The formula

G=22.5×EPS×BVPSG=\sqrt{22.5\times\text{EPS}\times\text{BVPS}}

EPS is earnings per share and BVPS is book value per share. The constant 22.5 is a P/E of 15 multiplied by a price to book of 1.5.

Where 22.5 comes from

It is two limits multiplied together. Graham suggested paying no more than 15 times earnings and no more than 1.5 times book value, and 15×1.5=22.515 \times 1.5 = 22.5. Taking the square root of the product allows one limit to be exceeded if the other is comfortably met.

So the number is not a valuation model. It is a pair of screening rules combined into a single ceiling, which is why it produces a price rather than a range.

The square root is doing something specific

A geometric mean punishes imbalance. With $2 of EPS and $20 of book value the product is 900 and the root is $30. In the second example, $3 of EPS against $12 of book value gives 810 and $28.46: higher earnings, lower book value, and a slightly lower ceiling.

A company with strong earnings and almost no book value scores poorly here whatever its profits, which is deliberate. The rule was built for asset backed businesses where book value means something.

What it screens for, and what it misses

The method suits stable, asset heavy companies with real book values: manufacturers, utilities, banks. It has little to say about a software business whose main assets are people and code, because book value understates them by construction.

Used as a first filter on the right kind of company it is fast and hard to argue with. The price to book calculator and the P/E calculator show the two limits separately.

What the number represents

A ceiling price for one share, derived from two per share figures and one constant. Compare it to the market price: below the Graham number passes the screen, above it does not. Book value is the input most worth checking first, since accounting choices move it. This is educational material, not financial advice.

Worked examples

\$2 of EPS and \$20 of book value

A company earns $2 per share with $20 of book value per share. What is the Graham number?

  1. Multiply: 22.5×2×20=90022.5 \times 2 \times 20 = 900.
  2. Take the square root: 900=30\sqrt{900} = 30.

The product is 900 and the Graham number is $30 a share.

Higher earnings, lower book value

A second company earns $3 per share with $12 of book value per share.

  1. Multiply: 22.5×3×12=81022.5 \times 3 \times 12 = 810.
  2. Square root: 810=28.46\sqrt{810} = 28.46.

The product is 810 and the Graham number is $28.46, slightly below the first company despite higher earnings.

Reading it as an intrinsic value

$30 is a ceiling from two screening limits, not an estimate of what the business is worth. A share trading below it has passed a filter, which is the beginning of the analysis rather than the end of it.

Common questions

Why 22.5 rather than some other constant?

It is a P/E limit of 15 times a price to book limit of 1.5, combined into one number.

Does it work for asset light companies?

Poorly, because book value understates businesses whose value sits in people and software rather than in assets on the balance sheet.

Is this financial advice?

No. It is educational material for the Graham number 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.