Graham Number calculator
The Graham Number is the price at which a company sits exactly on two of Benjamin Graham's ceilings for a defensive buyer at the same time. It is not an estimate of what a business is worth. It is a screening threshold, and knowing which threshold is the whole of understanding it.
The formula
Graham Number = sqrt(22.5 x earnings per share x book value per share)
Both inputs are per share and both are filed. Earnings per share comes from the bottom of the income statement, book value per share from shareholders equity divided by the share count. The result is a price per share in the same currency.
Illustrative inputs The calculator loads with earnings of 4 a share, book value of 25 a share and a price of 60. Invented round numbers, chosen so the square root comes out at 47.43 and can be checked on any calculator. They are not any company's filed accounts and they are not a view on any security.
Two filed figures, and your price
Diluted, from the bottom of the income statement, for the most recent full year. Graham used an average of several years and this figure is one year, which is a real difference and is discussed below.
Total shareholders equity from the balance sheet, divided by the diluted share count. Exclude minority interests, which are equity somebody else owns. Some readers use tangible book, which removes goodwill and gives a smaller and more conservative number.
Whatever the shares cost right now. This is the one input with no document behind it, and it is the only one on this page that changes between the moment you read it and the moment you act on it.
| Step | Value |
|---|---|
| The constant, 15 times 1.5 | 22.50 |
| That constant times earnings per share times book value per share | 2,250 |
| The square root of it | 47.43 |
| Graham Number | 47.43 |
| Measure | Value |
|---|---|
| Price to earnings at your price | 15.00 |
| Price to book at your price | 2.40 |
| The two multiplied together | 36.00 |
| The ceiling those two have to stay under | 22.50 |
| Your price over the Graham Number | 1.26 |
The constant is 15 times 1.5
It is not fitted to anything and it is not a constant of nature. In the chapter of The Intelligent Investor setting out stock selection for the defensive investor, Graham gives two price limits: no more than 15 times earnings, and no more than 1.5 times book value. He then says the two can be traded against each other as long as their product stays under 22.5.
That product is the whole formula. Price to earnings is price over earnings per share, price to book is price over book value per share, so multiplying them gives price squared over the product of the two per-share figures. Set that equal to 22.5 and solve for price, and the square root falls out. The Graham Number is not a valuation method that happens to use a root; it is the price at which the two ceilings are met exactly, written the other way round.
The calculator prints that product next to the constant for whatever price you entered, which is the fastest way to see what the formula is doing. At 60 the example company is on 15.00 times earnings and 2.40 times book, and the product of those is 36.00 against a ceiling of 22.5.
What the test was built to find
The defensive investor Graham described was buying a diversified list of large, financially conservative companies and holding them without following each one closely. The two ceilings sit inside a longer set of criteria that also asks for adequate size, a strong current ratio, an uninterrupted dividend record and earnings growth over the previous decade. Lifted out of that list, the Graham Number is one leg of a stool, and it was never meant to carry the weight on its own.
It also matters that the price ceilings were written for a market of industrial companies whose assets were mostly on the balance sheet. Book value then was a reasonable proxy for the productive assets. That is the assumption the measure lives or dies on, and it is the one that has weakened most since.
One difference between this page and the original worth stating plainly: Graham measured the earnings ceiling against an average of several years, not against the last one. This calculator takes a single earnings per share figure, because that is what the product stores and what a reader has in front of them. Averaging three years yourself and entering that instead is closer to the original test, and it changes the answer at any company with a cyclical year in the window.
The formula returns nothing more often than it returns a number
A negative earnings per share and a negative book value per share both take the formula out of the domain where it means anything, and the page prints n/m rather than n/a because those are different claims. Not available means we could not get the figure. Not meaningful means we have the figures and the measure does not apply to them. Fifteen times a loss is not a price ceiling; it is not anything.
The negative book value case is the one that catches people. A company can earn well, owe little and still report equity below zero, because sustained buybacks above book value reduce reported equity without touching the business. The measure returns nothing for such a company, and the reason has nothing to do with its quality. This is why the product stores n/m with a note rather than a number, and why a screen sorted on the Graham Number quietly excludes a category of company rather than ranking it last.
It stops applying for a second reason where the arithmetic still works. At a company whose value is research, brands or software, the spending that built the advantage was expensed as it happened rather than capitalised, so almost none of it appears in book value. The formula returns a small number, correctly, about a balance sheet that does not describe the business.
The same figure, across the filings
The product computes this from filed accounts for every company it covers, using diluted earnings per share and equity over the diluted share count, and it stores n/m with the reason wherever either input is not positive. Each stored figure expands into the two statement lines behind it with the fiscal year and the filing date, so the number can be checked rather than trusted. It is a subscription and it wants a card for the trial, which is worth saying on a page that has just done the arithmetic for nothing. What it costs.
- Intrinsic value calculator runs this alongside the two other models the product implements, so you can see how far apart they land.
- Methodology states which figures the product scores on and what it stores when one of them is not meaningful.
What this leaves out
This is arithmetic on two figures and a price you supply. It is not a valuation, not a view on any security, and not advice. A price below the Graham Number is a statement about two ratios and nothing else.
The number moves with accounting policy as much as with the business. Goodwill from an acquisition raises book value and therefore raises the Graham Number, while the research that built an equivalent advantage internally raises neither.
Banks, insurers and property companies carry book values that mean something different from an industrial company's, and the one and a half times ceiling was not written with them in mind.
A single year of earnings is a fragile input. One large write-down, one disposal gain or one unusually good year moves the answer by more than most of what the business did, and the original test used a multi-year average for exactly that reason.
Nothing you type here is sent anywhere. The arithmetic runs in your browser and no input is stored, logged or transmitted.