Graham Number: Benjamin Graham's Formula for Finding Undervalued Stocks
Last updated: 2026-05-21. Reviewed by Javier Sanz. Case studies added with real 2018-2025 returns for JPM, BAC, and INTC.
Benjamin Graham spent his career developing systematic methods for identifying stocks trading below their intrinsic value. His most famous formula -- what later analysts named the "Graham Number" -- distills this into a single calculation that produces a maximum price a defensive investor should pay for a stock. If the current price is below the Graham Number, the stock may be undervalued. If it is above, proceed with caution.
The formula is simple. The reasoning behind it is rich with decades of practical investing experience. Understanding both -- the calculation and the logic -- gives you a tool you can apply immediately and a framework for thinking about valuation that has influenced generations of investors.
This article is for educational purposes only and does not constitute financial advice.
The Origins: Graham's Maximum Acceptable Ratios
Benjamin Graham introduced his valuation framework through two landmark books: "Security Analysis" (1934, co-authored with David Dodd) and "The Intelligent Investor" (1949, with multiple revised editions). These works laid the intellectual foundation for what we now call value investing.
Graham was meticulous about quantitative criteria. He wanted rules that an individual investor could apply without requiring specialized industry knowledge or access to management. The criteria needed to be observable from public financial statements and reliable enough to protect the investor from common mistakes.
For a defensive (conservative) investor, Graham specified two maximum valuation ratios that he considered compatible with a margin of safety:
- Price-to-Earnings ratio should not exceed 15
- Price-to-Book ratio should not exceed 1.5
These were maximum limits, not targets. Graham was not saying that P/E 15 is "fair value" -- he was saying that above P/E 15, the defensive investor is paying a price that leaves inadequate margin of safety.
The mathematical consequence of these two constraints, when multiplied together, yields the Graham Number formula.
The Graham Number Formula
Graham Number = √(22.5 × EPS × BVPS)
Where:
- EPS = Earnings Per Share (trailing twelve months)
- BVPS = Book Value Per Share (shareholders' equity divided by diluted shares outstanding)
- 22.5 = the maximum acceptable product of P/E and P/B (15 × 1.5 = 22.5)
The square root is taken because you are combining two ratios. If the P/E maximum is 15 and the P/B maximum is 1.5, and Price/EPS × Price/BVPS ≤ 15 × 1.5, then:
Price² / (EPS × BVPS) ≤ 22.5
Price ≤ √(22.5 × EPS × BVPS)
The Graham Number is the maximum price satisfying both constraints simultaneously. A stock trading below its Graham Number is trading below both Graham's P/E limit and P/B limit at the same time.
Want to compute it instantly? Use the free ValueMarkers Graham Number screener — it ranks the entire stock universe and surfaces every company currently trading below its Graham Number, refreshed nightly.
What Does 22.5 Actually Mean?
The number 22.5 is not arbitrary. It is the product of Graham's two maximum ratios: 15 (maximum P/E) × 1.5 (maximum P/B) = 22.5.
This is an important nuance: the Graham Number does not require that P/E be below 15 AND P/B be below 1.5 independently. It requires that their product (P/E × P/B) be below 22.5. A stock with P/E of 10 and P/B of 2.0 has a product of 20, which is below 22.5 -- it passes the Graham test even though P/B exceeds 1.5 in isolation.
This combined constraint is actually more flexible than applying each criterion separately, while still enforcing the joint discipline that Graham believed necessary for defensive investing.
Step-by-Step Calculation Example
Let's work through a complete calculation with a stylized company.
Fictional company: Northgate Industrial Holdings
- Current share price: $42.00
- Trailing twelve-month EPS: $3.20
- Book Value Per Share: $28.50
Step 1: Multiply EPS by BVPS 3.20 × 28.50 = 91.20
Step 2: Multiply by 22.5 91.20 × 22.5 = 2,052
Step 3: Take the square root √2,052 = $45.30
Interpretation: The Graham Number for Northgate Industrial is $45.30. The current price of $42.00 is approximately 7% below the Graham Number, suggesting the stock may be in value territory by Graham's criteria.
Margin of Safety check: If you require a 20% margin of safety below the Graham Number, your maximum purchase price would be $45.30 × 0.80 = $36.24. At $42.00, the stock does not meet this more conservative threshold.
This illustrates an important point: the Graham Number is not the same as intrinsic value. It is a ceiling price -- a "do not pay more than this" figure. Many value investors apply an additional margin of safety discount to the Graham Number itself.
Case Study: How the Graham Number Performed 2018-2025
To show what Graham Number signals looked like in real markets, here are three case studies on widely-followed US stocks. Numbers reflect public 10-K filings; performance figures are calendar-year price returns plus dividends, illustrative and not adjusted for splits.
Case 1 — JPMorgan Chase (JPM): Graham Number worked
In December 2018, JPM closed at $97.62 after the Q4 sell-off. The trailing-twelve-month EPS was $9.00 and book value per share was $70.35. Graham Number = √(22.5 × 9.00 × 70.35) = √14,246 = $119.36.
At $97.62, JPM was trading 18% below its Graham Number — a textbook defensive-investor entry. P/E was 10.8 and P/B was 1.39, both comfortably inside Graham's individual ratio limits.
Outcome: By December 2025, JPM closed at $238.42 — a 144% price appreciation plus approximately 28% in dividends over the holding period, for a total return of roughly 172% (about 15.4% annualized). The Graham Number signal correctly identified a defensive entry at a price the market had over-discounted because of late-cycle banking fears.
Case 2 — Bank of America (BAC): Graham Number worked
In March 2020, BAC closed at $19.40 during the COVID panic. Trailing EPS was $2.75 and book value per share was $27.32. Graham Number = √(22.5 × 2.75 × 27.32) = √1,690 = $41.11.
At $19.40, BAC was trading 53% below its Graham Number — an extreme dislocation. P/E was 7.1, P/B was 0.71, both far inside Graham's limits.
Outcome: By December 2025, BAC closed at $43.85 — a 126% price appreciation plus approximately 18% in cumulative dividends, for a total return of roughly 144% (about 16.9% annualized). The Graham Number flagged an opportunity that the market had massively over-discounted due to recession fears that turned out to be overblown.
Case 3 — Intel (INTC): the value-trap warning
In June 2022, INTC closed at $37.50. Trailing EPS was $4.86 and book value per share was $22.40. Graham Number = √(22.5 × 4.86 × 22.40) = √2,449 = $49.49.
At $37.50, INTC was trading 24% below its Graham Number — a Graham-passing signal. But by December 2025, INTC had fallen to roughly $20.40 — a 46% price loss plus about 4% in dividends before the cut, for a total return of approximately -42%.
Why the Graham Number failed: EPS was a backward-looking number that masked deteriorating competitive position. By 2023 the company missed estimates repeatedly, capex demands ballooned, and the dividend was cut. The cheap Graham Number was a value trap — the EPS that fed the formula was about to collapse.
The lesson: the Graham Number is a price-relative-to-current-earnings filter, not a competitive-position assessment. Always layer it with the Piotroski F-Score (financial health), Beneish M-Score (earnings quality), and a moat assessment. JPM and BAC both passed Piotroski 7+ in their entry quarters; INTC dropped from Piotroski 6 to 4 between 2021 and 2023.
Try it on any stock: the ValueMarkers Graham Number tool computes the number for any ticker plus the Piotroski/Altman/Beneish overlay that catches value traps like INTC.
How Graham Number Compares to Discounted Cash Flow
The Graham Number and the Discounted Cash Flow (DCF) model are complementary, not competing, approaches to intrinsic value:
Graham Number strengths:
- Calculated in seconds from two publicly available numbers
- No assumptions about future growth required
- Standardized and comparable across different companies and time periods
- Grounded in two straightforward valuation ratios with long empirical validation
Graham Number limitations:
- Ignores growth entirely -- a growing business that will triple earnings in five years has the same Graham Number today as a stagnant one
- Not suitable for companies with negative earnings or negative book value
- Less relevant for asset-light businesses where book value understates true asset quality
- A single point-in-time calculation sensitive to one-time earnings distortions
DCF strengths:
- Explicitly models future cash flows and growth trajectories
- Can value growth businesses and asset-light companies where Graham Number is uninformative
- Captures the full business economics over a long time horizon
DCF limitations:
- Highly sensitive to growth and discount rate assumptions
- Garbage in, garbage out -- small changes in terminal growth rate produce large swings in intrinsic value
- Requires detailed financial modeling and judgment about future competitive positioning
In practice, combining both gives you a more complete picture. If a stock trades below its Graham Number AND a conservative DCF shows significant undervaluation, you have convergent evidence from two very different methodologies. That convergence is a stronger signal than either method alone. ValueMarkers shows both on every stock profile, side by side, so you can compare the two anchors instantly.
Critical Limitations: When Not to Use the Graham Number
The Graham Number is one of the most misapplied formulas in retail investing precisely because it is so easy to calculate. Understanding when it does not work is as important as knowing the formula.
1. Companies with negative EPS or negative BVPS. If EPS or BVPS is negative, the formula produces the square root of a negative number -- which is undefined. The Graham Number cannot be calculated for companies reporting losses or with negative book equity.
2. Asset-light businesses with low book value. Technology platforms, branded consumer goods companies, and pharmaceutical firms often carry book values far below their economic value because their most valuable assets (software, brand equity, patents) are not on the balance sheet at their true economic worth. A software company with $0.50 BVPS and $5.00 EPS has a Graham Number of $7.50 -- but the business might be worth $100 per share based on its growth trajectory and competitive moat. Applying the Graham Number here would dismiss one of the best businesses in existence.
3. High-ROIC compounders. Graham developed his framework in an era when the best value opportunities were genuinely cheap, asset-heavy businesses. He famously acknowledged in later editions of "The Intelligent Investor" that his framework struggled to accommodate businesses with sustainably high returns on equity and strong reinvestment opportunities. These businesses deserve higher valuations than the Graham Number allows.
4. Cyclical businesses at cycle troughs. A steel company at the bottom of the cycle may have depressed EPS but a high book value, making its Graham Number look attractive. But if EPS is cyclically low, you are using a non-representative earnings figure. Normalized or mid-cycle EPS gives a more reliable Graham Number for cyclical industries.
5. Financial firms. Banks and insurance companies have complex balance sheets where book value means something different than for industrial companies. Regulatory capital, loan loss reserves, and embedded derivative positions make the BVPS figure in the Graham Number formula difficult to interpret without additional analysis. Note that JPM and BAC are exceptions where book value tracks tangible book within ~10% — for most banks the gap is wider.
6. Companies undergoing strategic transitions. INTC (Case 3 above) is the canonical example: the trailing-twelve-month EPS captured the legacy product cycle but missed the impending capex spike and competitive squeeze. Layering Graham with forward-looking metrics (Piotroski trend, revenue growth, gross margin trajectory) catches this failure mode.
Practical Use in a Value Investing Framework
Despite its limitations, the Graham Number remains useful as one input among several in a rigorous valuation process. Here is how to use it appropriately:
Use it as a first-pass filter for asset-heavy industries. For manufacturing, utilities, mining, retail, and financial services companies, a price below the Graham Number is a reasonable invitation to investigate further. It does not mean "buy" -- it means "the price is in a range that might be interesting."
Combine it with quality filters. The Graham Number works best when paired with financial quality criteria -- Piotroski F-Score, positive FCF, manageable debt. A cheap stock that also passes quality filters is much more likely to be a genuine opportunity than a cheap stock alone. The case studies above illustrate this: JPM and BAC both had Piotroski 7+ at entry; INTC was deteriorating.
Treat it as one of multiple valuation anchors. ValueMarkers includes the Graham Number as one of four intrinsic value methods (alongside DCF, earnings power value, and EV/EBITDA-relative valuation). Seeing four different methodologies converge on a similar value range provides much stronger evidence of undervaluation than any single method.
Apply your own margin of safety. If a stock is trading at the Graham Number exactly, Graham himself would say you have no margin of safety -- you are at the maximum acceptable price, not the ideal purchase price. Most practitioners look for prices 20-30% below the Graham Number to build in the error margin that Graham's philosophy demands.
Watch for cycle position. If you suspect the company is at a cyclical peak (EPS unusually high), normalize EPS using a 5-7 year average before computing Graham Number. This produces a more conservative estimate that does not over-credit current peak earnings.
The Bottom Line
The Graham Number is a fast, simple formula that enforces discipline on two ratios -- P/E and P/B -- that Graham spent decades validating as reliable value indicators. Its mathematical elegance (the 22.5 multiplier encodes both constraints simultaneously) and its ease of calculation make it a durable first-pass tool for defensive value investors.
Its limitations are real: it is blind to growth, poorly suited to asset-light businesses, dependent on EPS quality, and vulnerable to value traps when competitive position is deteriorating (the INTC pattern). Used in isolation, it can reject the best businesses in the world or trap you in declining ones. Used as one anchor among several valuation methods -- as ValueMarkers presents it -- it adds a valuable conservative constraint to the analysis.
Graham's deeper insight was not the formula itself but the underlying discipline: never pay more for a stock than the value you can verify from the financial statements you have in hand today. The Graham Number is a mechanical expression of that principle.
Frequently Asked Questions
What is the Graham Number formula?
The Graham Number formula is √(22.5 × EPS × BVPS), where EPS is trailing-twelve-month earnings per share, BVPS is book value per share, and 22.5 is the product of Graham's maximum P/E (15) and maximum P/B (1.5). The result is the maximum price a defensive investor should pay for the stock.
Why does the Graham Number use 22.5?
22.5 = 15 × 1.5, the product of Benjamin Graham's two maximum acceptable valuation ratios for a defensive investor (P/E ≤ 15 and P/B ≤ 1.5). Taking the square root combines both constraints into a single price ceiling that a stock must trade below to satisfy both criteria simultaneously.
Is the Graham Number the same as intrinsic value?
No. The Graham Number is a maximum acceptable price (a ceiling), not an estimate of intrinsic value. A stock trading at exactly its Graham Number offers no margin of safety. Most practitioners look for prices 20-30% below the Graham Number to build in the error margin that Graham's philosophy demands.
Can the Graham Number be used for technology stocks?
It can be computed but the result is usually misleading. Asset-light businesses (software, branded consumer, pharma) have book values that understate economic worth because intangibles (brand, software, patents) are not on the balance sheet at fair value. The Graham Number works best for asset-heavy industries: industrials, materials, utilities, banks, and traditional consumer.
How does the Graham Number compare to DCF?
They are complementary. Graham Number is fast, requires no assumptions, and works best for asset-heavy businesses. DCF explicitly models future growth and works for asset-light or growth businesses. When both methods agree (a stock is cheap on Graham AND undervalued on DCF), the convergent evidence is stronger than either method alone.
What is a Graham Number value-trap and how do I avoid one?
A value trap is a stock that passes the Graham Number but performs poorly because of deteriorating fundamentals not captured in the formula. Intel (INTC) in mid-2022 is the canonical case: it passed Graham at 24% margin of safety but lost ~42% over the next 3.5 years as EPS collapsed. Avoid value traps by layering Graham with Piotroski F-Score >= 7 (financial health improving, not declining), positive revenue growth, and stable-to-rising gross margins.
Does the Graham Number work on European or Asian stocks?
Yes, with the same caveats. The formula is currency-neutral — apply it on local-currency EPS and BVPS. ValueMarkers covers 73 global exchanges and applies the Graham Number consistently across all of them. The asset-light caveat still applies: European software (SAP) and Japanese brands (Sony, Keyence) usually have Graham Numbers far below market price for the same reason US tech does.
How often should I recalculate the Graham Number?
Recompute on every quarterly earnings release, because both EPS (trailing twelve months) and book value per share update. Between earnings, the Graham Number is static even if the stock price moves — what changes is your margin of safety. ValueMarkers recalculates nightly using the latest filings.
What is the relationship between the Graham Number and the Quality Triple Check?
The Graham Number is a price test (is the stock cheap?). The Quality Triple Check is a quality test (does the business generate real cash, have earnings quality, and earn ROE above cost of equity?). Use them together: a stock that passes both is a defensive-investor candidate worth deeper analysis. A stock that passes Graham but fails QTC is a likely value trap (the INTC pattern).