How the Graham number turns two figures into a ceiling
Graham wanted a quick, conservative test that a defensiveinvestor could apply without forecasting the future. The Graham number does that by combining a company’s profitability and its asset backing into a single price cap: take its earnings per share and its book value per share, multiply them together with a constant, and take the square root. The square root deliberately tempers each input so neither high earnings nor a fat book value alone can justify an unlimited price. The result is not a precise valuation but a maximum — a level above which a cautious buyer is, by Graham’s standards, overpaying. For a forward-looking estimate that accounts for growth, pair it with anintrinsic value calculator.
The Graham number formula
Graham number = √( 22.5 × EPS × Book value per share )
The constant 22.5 = 15 × 1.5: a maximum price-to-earnings ratio of 15 multiplied by a maximum price-to-book ratio of 1.5. It therefore caps how much a defensive investor pays for earnings and for assets at the same time. Both EPS and book value per share must be positive for the result to be meaningful.
What makes this calculator different
- It computes the defensive ceiling. From EPS and book value per share it returns the Graham number — the maximum price Graham’s rules would sanction — rather than a vague “fair value.”
- It shows the margin of safety. Enter the current price and the tool compares it to the Graham number, so you can see at once whether you are buying below the ceiling and by how much.
- It explains the 22.5 cap. The constant is broken down as 15 × 1.5 — a P/E limit times a price-to-book limit — so the number is transparent rather than a black box.
- It flags when the method doesn’t apply. For loss-making or negative-equity companies, where EPS or book value is not positive, the calculator tells you the Graham number is undefined instead of returning a misleading figure.
Frequently asked questions
What is the Graham number and what is the formula?+
The Graham number is Benjamin Graham’s estimate of the maximum price a defensive investor should pay for a stock. It is computed directly from two per-share figures: earnings per share (EPS) and book value per share (BVPS). The formula is the square root of 22.5 × EPS × BVPS — written √(22.5 × EPS × BVPS). Because both inputs sit under the same root, the result blends profitability and asset backing into a single fair-value ceiling.
Where does the 22.5 come from?+
The 22.5 is the product of two valuation caps Graham proposed for defensive stocks: a maximum price-to-earnings ratio of 15 and a maximum price-to-book ratio of 1.5. Multiplying 15 × 1.5 gives 22.5. The constant is therefore not arbitrary — it encodes the joint limit that a conservative investor would tolerate on both earnings and assets at once, so a stock priced above its Graham number breaches at least one of those ceilings.
What is a margin of safety?+
A margin of safety is the gap between a stock’s estimated value and the price you actually pay for it. In Graham’s framework, buying below the Graham number builds in that cushion: the further the market price sits beneath the calculated ceiling, the larger your protection against errors in the inputs or in your own judgement. The idea is to avoid paying full estimated value, leaving room for the analysis to be wrong and still come out ahead.
What are the Graham number’s limitations?+
The Graham number ignores growth entirely — it treats a fast-growing company and a stagnant one identically if their EPS and book value match. It also ignores intangible assets such as brands, software, and intellectual property, which barely register in book value. As a result it is poorly suited to asset-light businesses and fast-growing firms, where it tends to flag almost everything as overpriced. It is a blunt screen, not a complete valuation.
When doesn’t the Graham number apply?+
The formula needs both a positive EPS and a positive book value per share, because you cannot take the square root of a negative product in a meaningful way. That rules out loss-making companies and firms with negative equity, for which the Graham number is undefined or misleading. In those cases the calculator flags that the method does not apply rather than returning a figure you should trust.
Disclaimer: This calculator is foreducation and illustration only. The Graham number is a simple rule of thumb that ignores growth, intangibles, and business quality, and it does not apply to loss-making or negative-equity firms; its output is not a tradeable valuation and real fair values will differ. Nothing here is investment, tax, or trading advice.