Graham Number Calculator
A fair-value ceiling from earnings and book value — √(22.5 × EPS × BVPS), Benjamin Graham style.
Graham Number
Live tool22.5 = a 15 P/E cap × a 1.5 P/B cap, Graham’s defensive-investor limits. A screen, not a verdict — book-value-light businesses score low here regardless of quality.
How it works
Benjamin Graham gave defensive investors two price caps: pay no more than 15 times earnings and no more than 1.5 times book value. The Graham Number folds both caps into a single ceiling — the square root of 22.5 (that is 15 × 1.5) times earnings per share times book value per share. At any price at or below that ceiling, the product of the stock’s P/E ratio and its P/B ratio is 22.5 or less, which is the combined test Graham actually proposed — a stock may run slightly over one cap if it sits under the other by enough.
Enter diluted trailing-twelve-month EPS and book value per share; add the current price if you want the premium or discount versus the ceiling. When EPS or book value is zero or negative the calculator says plainly that no Graham Number exists — the formula would need the square root of a non-positive number, and a company without earnings or without positive equity fails the defensive screen outright. You get the honest verdict, never a fake $0.00 or a NaN.
The formula
Graham Number = √(22.5 × EPS × BVPS), where EPS is diluted trailing-twelve-month earnings per share and BVPS is book value per share. Defined only when both inputs are positive.
Where 22.5 comes from: 15 (max P/E) × 1.5 (max P/B) = 22.5. At the ceiling price, implied P/E × implied P/B = 22.5 exactly — the calculator shows both implied multiples so you can see which cap is doing the work.
Premium / discount = (price − Graham Number) ÷ Graham Number × 100, shown only when a price above $0 is entered. Negative means the stock trades below the ceiling.
Worked example
Inputs: diluted EPS = $6.00; book value per share = $20.00; current price = $45.00.
- Product: 22.5 × 6.00 × 20.00 = 2,700.
- Graham Number: √2,700 = $51.96 (51.9615 before rounding).
- Implied multiples at the ceiling: P/E = 51.96 ÷ 6.00 = 8.66x; P/B = 51.96 ÷ 20.00 = 2.60x. Check: 8.66 × 2.60 ≈ 22.5 ✓.
- Premium/discount: (45.00 − 51.96) ÷ 51.96 × 100 = −13.40% — the stock trades 13.40% below its Graham Number.
The no-real-value case.EPS = −$2.00, BVPS = $20.00: the product is 22.5 × (−2) × 20 = −900, and √(−900) has no real answer. The calculator reports that no Graham Number exists — a money-losing company fails Graham’s defensive test, and that verdict is the output.
FAQ
What is the Graham Number?
The Graham Number is a fair-value ceiling from Benjamin Graham’s defensive-investor test: the square root of 22.5 times earnings per share times book value per share. A stock with $6.00 diluted EPS and $20.00 book value per share has a Graham Number of √(22.5 × 6 × 20) = √2,700 ≈ $51.96.
Where does the 22.5 come from?
Graham capped a defensive purchase at a P/E of 15 and a price-to-book of 1.5. Multiplying the two caps gives 15 × 1.5 = 22.5. Any price at or below the Graham Number satisfies the combined test — a stock can run slightly over one cap if it is under the other by enough.
What if EPS or book value is negative?
Then the Graham Number does not exist — the formula would take the square root of a negative product, which has no real answer. That is a verdict, not a bug: a company losing money or carrying negative equity fails Graham’s defensive screen outright, so the calculator says so instead of printing a number.
Which EPS and book value should I use?
Diluted EPS over the trailing twelve months, and book value per share from the latest quarterly balance sheet (total shareholders’ equity ÷ diluted shares). Basic EPS overstates the input for companies with heavy option or convertible issuance.
Is a stock trading below its Graham Number automatically a buy?
No. It is a screen, not a verdict. The formula leans on book value, so it flatters asset-heavy businesses like banks and insurers and penalizes asset-light ones — a software firm earning $6.00 per share on $3.00 of book value gets a Graham Number of just √(22.5 × 6 × 3) ≈ $20.12 even if its cash flow justifies far more.
How is the Graham Number different from a DCF value?
The Graham Number looks backward at two reported figures — earnings and book value — and applies fixed 15x and 1.5x caps. A DCF looks forward, projecting free cash flow and discounting it at your required return. A $51.96 Graham Number and a $70 DCF value can both be true; they answer different questions.
Continue your analysis
Your numbers ride along — the next tool opens pre-filled.
Educational use only — nothing here is investment, tax, or legal advice. The Graham Number is a 1970s-era screening ceiling, not an intrinsic-value estimate: it leans on book value, so it flatters asset-heavy businesses and penalizes asset-light ones, and it ignores growth, cash flow, and debt quality entirely. A stock below its Graham Number is a candidate for further work, not a buy signal. US markets / USD framing throughout.