The Graham Number: How to Use Benjamin Graham's Valuation Formula
The Graham Number is a simple valuation formula that calculates the maximum price a defensive investor should pay for a stock, based on two fundamental inputs: earnings per share (EPS) and book value per share (BVPS). Developed by Benjamin Graham and popularized through his book The Intelligent Investor, the formula distills decades of Graham's thinking about defensive stock selection into a single, calculable upper bound on price. Stocks trading below their Graham Number are, by Graham's standard, potentially undervalued. Stocks above it are, at minimum, not cheap.
The Formula
Graham Number = √(22.5 × EPS × BVPS)
The constant 22.5 comes from Graham's view that a defensively purchased stock should not exceed a P/E ratio of 15 and a P/B ratio of 1.5. Multiplied together: 15 × 1.5 = 22.5.
The formula is the geometric mean of two valuations:
- A price justified by earnings at a 15x P/E: Price₁ = 15 × EPS
- A price justified by book value at a 1.5x P/B: Price₂ = 1.5 × BVPS
The Graham Number is the square root of their product: √(Price₁ × Price₂) = √(15 × EPS × 1.5 × BVPS) = √(22.5 × EPS × BVPS).
This mathematical structure means the Graham Number places equal weight on earnings and asset value, which reflects Graham's belief that a sound stock purchase requires both earnings power and asset backing.
Historical Context
Graham developed his valuation principles during a period shaped by the Great Depression and the corporate accounting scandals of the early 20th century. His primary concern was not finding the fastest-growing businesses but protecting investors from permanent capital loss. The 15x P/E and 1.5x P/B limits were Graham's way of ensuring that investors did not pay speculative premiums for either earnings or assets.
The formula as a distinct named concept — "the Graham Number" — was largely popularized by later commentators rather than Graham himself using those exact words. But the mathematical constraints Graham described in The Intelligent Investor Chapter 14 (on the defensive investor's stock selection criteria) are the direct source of the formula.
Graham's era featured much lower average P/E multiples than modern markets. The S&P 500 averaged P/E multiples of 10-15 for much of Graham's career. Today, with P/E ratios on the S&P 500 frequently running 20-28x, the Graham Number will classify most large-cap US stocks as overvalued by construction. This does not invalidate the formula — it reflects a genuine change in market valuations driven by lower interest rates, higher corporate profit margins, and the shift toward capital-light businesses.
Worked Examples
Example 1: Procter & Gamble (PG)
- EPS (trailing twelve months): $6.02
- BVPS: $18.87
Graham Number = √(22.5 × $6.02 × $18.87) = √(22.5 × $113.60) = √($2,556) = $50.56
At a recent price near $170, PG trades at more than 3x its Graham Number. By Graham's standard, P&G is not a defensive bargain at current prices. This is partly because P&G's book value is artificially low — intangible assets like brand value and goodwill from acquisitions either do not appear on the balance sheet or appear there in ways that may not reflect true economic value.
Example 2: JPMorgan Chase (JPM)
- EPS (trailing twelve months): $18.22
- BVPS: $115.80
Graham Number = √(22.5 × $18.22 × $115.80) = √(22.5 × $2,110) = √($47,475) = $217.89
At a recent price near $235, JPM trades modestly above its Graham Number. The gap is relatively small, and financial stocks are a reasonably good fit for the formula since bank earnings and book value have a more direct relationship than in capital-light businesses.
Example 3: A Hypothetical Discount Retailer
- EPS: $3.50
- BVPS: $22.00
- Current price: $45.00
Graham Number = √(22.5 × $3.50 × $22.00) = √(22.5 × $77) = √($1,732.50) = $41.63
This stock is trading approximately 8% above its Graham Number ($45 vs. $41.63). Not dramatically expensive, but also not a margin-of-safety purchase by Graham's standards.
Calculating Discount or Premium
Once you have the Graham Number, you can calculate the Graham Number margin of safety the same way you would any intrinsic value estimate:
Graham Number MOS% = (Graham Number − Current Price) / Graham Number × 100
For the discount retailer above: ($41.63 − $45.00) / $41.63 = −8.1%. The stock is trading at an 8% premium to Graham's upper bound.
You can run this calculation automatically using the ValueMarkers margin of safety calculator, which includes Graham Number as one of the intrinsic value inputs.
What the Formula Does Well
Simplicity and discipline. The Graham Number can be calculated in 30 seconds from publicly available financial statements. It creates an objective upper bound that prevents investors from rationalizing purchases at high valuations. When a stock trades at 5x its Graham Number, no amount of qualitative optimism should override that warning signal.
Combines earnings and assets. Most simple valuation ratios look at either earnings (P/E) or assets (P/B) in isolation. The Graham Number requires both. A company with high earnings but a tiny book value (which might indicate aggressive intangibles or significant debt) will have a lower Graham Number than one with the same earnings and solid asset backing.
Effective for banks and financial stocks. Financial companies — banks, insurance companies, asset managers — have balance sheets where book value is relatively meaningful. Book value for a bank is a reasonable proxy for the value of its loan book minus liabilities. The Graham Number tends to work better here than for technology or consumer brands companies.
Works well as a screener. The formula is most useful as a first-pass screen to eliminate the clearly overvalued and flag potential candidates for deeper analysis. A stock trading below its Graham Number is worth investigating. It is not automatically a buy.
Limitations and Weaknesses
Not designed for growth stocks. Graham's 15x P/E cap was intended for businesses with modest, predictable earnings growth — his "defensive" category. High-growth businesses may rationally deserve P/E multiples of 25, 35, or higher based on the present value of future earnings streams. Applying the Graham Number to Amazon, Alphabet, or any fast-growing software company will generate misleadingly low valuations.
Book value is less meaningful for intangible-heavy businesses. A software company may have $1 in book value per share but generate $10 in free cash flow per share. The Graham Number would be extremely low for this company not because it is undervalued but because the formula cannot handle businesses whose primary value lies in intellectual property, customer relationships, and network effects that do not appear on the balance sheet.
Goodwill distortion. Companies that grow through acquisitions accumulate goodwill on the balance sheet, which inflates BVPS. This can make acquisition-heavy companies appear cheaper by the Graham Number than they really are. Before using BVPS in the formula, check how much of book value consists of goodwill and intangibles — if it is more than 50%, consider using tangible book value per share instead.
Does not account for debt levels. Two companies with identical EPS and BVPS can have very different risk profiles if one carries substantial debt. A highly leveraged company might trade below its Graham Number not because it is a bargain but because the market is pricing in bankruptcy risk. Always check the balance sheet before treating a below-Graham-Number stock as an opportunity.
Backward-looking earnings. The formula uses trailing EPS. If a company's earnings are at a peak (cyclical industries like steel, semiconductors, or shipping), the Graham Number will overstate fair value. Conversely, if earnings have been temporarily depressed by one-time charges, the Graham Number understates it. Normalize earnings before applying the formula in cyclical or recently-disrupted businesses.
The constants may need updating. Graham chose 15x P/E and 1.5x P/B based on the market conditions of his era. Some analysts argue that with AAA bond yields near 5% rather than the 4-6% range of Graham's era, the appropriate P/E multiple is somewhat lower, and the formula's constant should be adjusted accordingly.
How to Apply the Graham Number Correctly
The Graham Number is most useful as one input among several, not as a standalone buy decision.
Step 1: Normalize earnings. Before calculating EPS, verify it reflects the company's sustainable earnings power. Strip out one-time gains and charges. For cyclical businesses, average earnings across the full cycle.
Step 2: Check tangible book value. Calculate tangible book value per share (BVPS minus goodwill and other intangibles). Consider running the formula with both versions and using the lower result.
Step 3: Calculate the Graham Number. Apply the formula: √(22.5 × normalized EPS × BVPS).
Step 4: Compare to current price. A stock trading at 70-80% of its Graham Number (a 20-30% discount) is where Graham would start paying closer attention. A stock at 50% of its Graham Number is an unusual situation worth serious investigation.
Step 5: Do the qualitative work. Why is the stock cheap? Is it a cyclical downturn (opportunity) or structural deterioration (trap)? Is the balance sheet sound? Does the business earn above its cost of capital? Does management allocate capital intelligently? The Graham Number identifies candidates — it does not do the investment research.
Step 6: Apply a margin of safety. The Graham Number is already Graham's upper-bound price — it is not intrinsic value; it is the maximum he thought a defensive investor should pay. For a genuine margin of safety, look for stocks trading at 70% or less of the Graham Number.
Graham Number vs. Other Valuation Methods
| Method | Inputs | Best For | Limitation |
|---|---|---|---|
| Graham Number | EPS, BVPS | Defensive/value stocks, banks | Growth stocks, intangibles-heavy businesses |
| DCF | FCF, growth rate, discount rate | Any business with predictable cash flows | Sensitivity to assumptions |
| Earnings Power Value (EPV) | Normalized earnings, discount rate | Stable businesses; ignores growth | Does not capture growth value |
| P/E relative | EPS, sector P/E | Quick comparisons within sectors | Ignores assets, debt |
| P/B relative | BVPS, sector P/B | Asset-heavy businesses | Ignores earnings quality |
For most individual investors, the most robust approach is to cross-check the Graham Number with at least one cash-flow-based method (DCF or EPV). When both point to undervaluation, the case is stronger. When they diverge, investigate why.
Practical Screening with Graham Number
The most efficient use of the Graham Number is as a screener to reduce a large universe of stocks to a manageable shortlist. Starting from 50,000+ global stocks, filter for:
- Graham Number discount of 20%+ (current price ≤ 80% of Graham Number)
- Positive EPS for each of the last five years
- No dividend cuts in the last three years
- Debt/equity ratio below 1.0x
- Current ratio above 1.5x (Graham's own liquidity requirement)
This screen will produce a small number of candidates — typically 50-200 depending on market conditions. From there, apply DCF or EPV to confirm the valuation and do qualitative research to filter out value traps.
The ValueMarkers margin of safety calculator includes the Graham Number as one of the valuation inputs, letting you compare it side-by-side with DCF and EPV estimates for any covered ticker.
Frequently Asked Questions
What does the Graham Number tell you?
The Graham Number tells you the maximum price Benjamin Graham would consider paying for a stock based on its earnings and book value. A stock trading below its Graham Number may be undervalued by Graham's criteria; a stock above it is not a defensive bargain by that standard.
Is the Graham Number still relevant today?
Yes, but with context. The formula works best for stable, asset-backed businesses in traditional industries. It is not well-suited for high-growth technology companies or businesses where most value lies in intangible assets. Used as one input among several, alongside DCF and qualitative analysis, it remains a useful check against paying excessive prices.
What is a good Graham Number discount?
Graham considered a stock trading at or below its Graham Number to be defensively priced. For a genuine margin of safety, most value investors look for a 20-30% discount to the Graham Number — meaning the stock trades at 70-80 cents on the dollar relative to the formula's output.
Why is the Graham Number formula √(22.5 × EPS × BVPS)?
The 22.5 constant comes from multiplying Graham's two valuation limits: maximum P/E of 15 and maximum P/B of 1.5 (15 × 1.5 = 22.5). The square root gives the geometric mean of the two implied prices, weighting earnings-based and asset-based valuation equally.
Should I use earnings per share or free cash flow per share?
Graham's original formula uses earnings per share (net income / shares outstanding). Some practitioners substitute free cash flow per share for businesses where earnings are significantly distorted by non-cash charges. If EPS and FCF per share are similar, it makes little difference. If they diverge significantly, investigate why before using either figure.
Related ValueMarkers Resources
- Graham Number Calculator — Calculate Graham Number and MOS% for any ticker
- Graham Number Explained — Detailed explanation of Graham's formula
- Benjamin Graham Formula — Graham's complete valuation methodology
- Margin of Safety Calculator Guide — How to use margin of safety across multiple valuation methods
- Graham Number Glossary — Formal definition and benchmarks
Ready to apply the Graham Number to your watchlist?
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Related tools: Margin of Safety Calculator · Stock Screener · Methodology
Written by Javier Sanz, Founder of ValueMarkers. Published May 2026.