Where the formula comes from
In The Intelligent Investor, Graham set out tests for a defensive investor: someone who wants a reasonable result without the time to do deep work on each company. Two of those tests concerned price. The investor should not pay more than 15 times average earnings over the past three years, and should not pay more than 1.5 times book value.
Graham added a release valve. A stock with a low P/E could carry a higher price-to-book ratio, and the reverse, so long as the P/E multiplied by the price-to-book ratio did not exceed 22.5. That figure is simply 15 times 1.5. A stock at 9 times earnings could trade at 2.5 times book and still pass, because 9 times 2.5 is 22.5.
The Graham Number rearranges that test to solve for price. If price divided by EPS, times price divided by book value per share, must be at most 22.5, then price squared must be at most 22.5 times EPS times book value per share. Take the square root and you have the maximum price.
The formula and its inputs
Graham Number = √(22.5 × EPS × book value per share)
Each input needs care, because small choices move the result.
| Input | What to use | Where to find it | Common error |
|---|---|---|---|
| Earnings per share | Average diluted EPS over 3 years (Graham's method) or trailing twelve months | Income statement in the 10-K and recent 10-Qs | Using one peak year or adjusted EPS from a press release |
| Book value per share | Common equity divided by diluted shares | Balance sheet, latest 10-Q or 10-K | Including preferred equity or noncontrolling interests |
| Share count | The same count for both inputs | Cover page or equity note | Mixing basic shares for one input and diluted for the other |
| 22.5 | 15 × 1.5, fixed | Graham's defensive investor tests | Changing it without saying so |
| Market price | Current quote | Any market data source | Comparing with a stale Graham Number after a new quarter |
Every figure except the price comes from the company's own filings, which are free on SEC EDGAR. If the difference between trailing and forward P/E is unfamiliar, read that first: a Graham Number built on forward estimates is a different and much less conservative test.
Worked example
Company A is a regional distributor. Its diluted EPS over the past three years was $2.10, $2.40 and $2.70, an average of $2.40. Its common equity is $360 million and it has 20 million diluted shares, so book value per share is $18.00.
- Multiply the inputs: 22.5 × $2.40 × $18.00 = 972.
- Take the square root: √972 is about $31.18.
- Compare with the price. If Company A trades at $26.00, it sits about 17% below its Graham Number.
Check the result against the original tests. At $26.00, the P/E on average earnings is about 10.8 and the price-to-book ratio is about 1.44. Multiplied together, that is about 15.6, well under 22.5. The stock passes.
Now change one input. Suppose $5.00 of Company A's book value per share is goodwill from an old acquisition. Using tangible book value of $13.00 instead, the number becomes √(22.5 × 2.40 × 13.00), about $26.50. The stock now sits only 2% below the ceiling. Same company, same price, very different picture.
Company B, a software business, shows the opposite problem. It earns $3.00 a share but has book value of only $4.00, because its main assets are code and customers that never appear on the balance sheet. Its Graham Number is √(22.5 × 3.00 × 4.00), about $16.43. At $45.00 the stock is far above the ceiling. That says the stock fails a test built for asset-heavy industrial companies, which is not the same as saying it is overpriced.
How to read the result
The gap between the price and the Graham Number is a rough version of a margin of safety: the cushion between what you pay and a conservative ceiling. Some screens rank stocks by that gap. Treat it as a sorting device rather than a valuation.
A few rules keep the reading honest:
- If the stock is below the number on trailing EPS but above it on three-year average EPS, earnings are probably at a peak, and the trailing figure flatters it.
- If the stock passes on reported book value but fails on tangible book value, the pass depends on goodwill and intangibles that may never be recovered.
- If the stock passes comfortably but carries heavy debt, the test has missed the risk, because neither EPS nor book value shows leverage directly.
- If the stock fails because book value is small relative to earnings, check whether the business simply does not need many assets before treating the fail as a warning.
Graham Number versus other Graham measures
Graham wrote several ways of setting a price, and they are often confused.
The Graham Number blends earnings and assets into a single ceiling for a defensive investor. The Graham formula is a separate growth formula that values a stock from current earnings and an expected growth rate; it can produce much higher figures and depends heavily on the growth guess. Net current asset value, or NCAV, is Graham's balance-sheet floor for deep-value bargains: current assets minus all liabilities. Our guide to net current asset value covers it in full.
These measures sit at different points on the spectrum. NCAV asks what the company would be worth if it stopped and collected its working capital. The Graham Number asks whether the price is reasonable for a stable, profitable company. The growth formula asks what the stock is worth if growth continues. A stock can look cheap on one and expensive on another, and that disagreement is usually the most useful finding.
Where this goes wrong
The Graham Number is a screen built for a particular kind of company in a particular era. It fails in predictable ways.
- It ignores debt. Two companies with the same EPS and book value get the same number even if one carries no debt and the other is heavily borrowed. Graham's full defensive test included balance-sheet strength checks that the number leaves out.
- It trusts book value. Goodwill, capitalized costs and deferred tax assets inflate book value without adding liquidation value. Write-downs can then erase the margin overnight. The price-to-book ratio explainer covers the same distortion.
- It penalizes asset-light businesses. Software, brands and service firms with high returns on little capital almost never pass. The test was not designed for them.
- It cannot handle losses. Negative EPS or negative equity makes the formula undefined. That excludes many special situations, such as turnarounds and companies emerging from restructuring, that need a different method.
- It rewards cyclical peaks. On trailing EPS, a commodity producer at the top of its cycle can look cheap just before earnings fall. Using three-year average earnings reduces this but does not remove it.
- It says nothing about why the stock is cheap. A low price relative to earnings and assets is also the profile of a value trap, where the business is shrinking and the numbers lag the decline.
Using it in a research process
The Graham Number works best at the start of research, as a way to narrow a long list. A reasonable sequence:
- Screen for stocks trading below their Graham Number on three-year average EPS.
- Recompute using tangible book value and drop stocks that only pass on goodwill.
- Check debt against equity and earnings, and drop stocks where leverage explains the discount.
- Read the latest 10-K for why earnings or assets might fall, and compare the price with what a buyer would pay for the assets, as covered in how to value a company below book.
Most stock screeners can run step one. The comparison of stock research tools for individual investors lists which ones show the Graham Number and which let you build the screen yourself. Dombey's published research applies balance-sheet checks of this kind before writing up a cheap stock; see the research archive.
The bottom line
The Graham Number is the square root of 22.5 times EPS times book value per share, a price ceiling derived from Graham's limits of 15 times earnings and 1.5 times book. It is quick to compute and useful for sorting a list of stable, asset-heavy companies. It ignores debt, trusts book value and fails on asset-light and loss-making businesses. Use it to decide which stocks deserve a closer look, then do the work on earnings quality, tangible assets and leverage that the formula leaves out.