Graham Number Calculator
Enter the earnings per share (EPS) and book value per share (BVPS) of any stock to calculate its Graham Number, the maximum price Benjamin Graham considered reasonable to pay. Optionally add the current market price to see the margin of safety and a buy/hold/avoid signal. Adjust the P/E and P/B multipliers to stress-test beyond Graham's original 15 and 1.5 defaults. Results update instantly as you type.
Formula
Worked example
A company with EPS of $5.00 and BVPS of $30.00: Graham Number = sqrt(22.5 x 5.00 x 30.00) = sqrt(3375) = $58.09. If the stock trades at $40.00, the margin of safety is (58.09 - 40.00) / 58.09 = 31.1%. The P/E is 40/5 = 8.0 and the P/B is 40/30 = 1.33; their product is 10.7, well below 22.5.
What is the Graham Number?
The Graham Number is a simple formula developed by Benjamin Graham, the father of value investing and mentor to Warren Buffett, to estimate the maximum price a conservative investor should pay for a stock. It combines two fundamental per-share metrics: earnings per share (EPS) and book value per share (BVPS). The formula is the square root of 22.5 times the product of those two figures. The constant 22.5 comes from Graham's view that a stock should trade at no more than 15 times earnings and no more than 1.5 times book value simultaneously; 15 multiplied by 1.5 equals 22.5. If the current market price is below the Graham Number, the stock may be undervalued and worth further investigation.
Graham's dual-ratio test
Beyond the single Graham Number formula, Benjamin Graham applied a dual-ratio test in his book "The Intelligent Investor": the P/E ratio should be at most 15, the P/B ratio at most 1.5, and crucially their product must not exceed 22.5. This calculator shows all three checks. A stock can pass the Graham Number screen while still failing the product rule if, for example, the P/E is very low (e.g. 5) but the P/B is unusually high (e.g. 6), which would push the product to 30. The product rule is therefore the stricter combined test and should take precedence.
Margin of safety and how to interpret it
Margin of safety is the gap between the Graham Number and the current market price, expressed as a percentage of the Graham Number. A margin of safety of 33% or more is the classic threshold: it means you could be wrong about intrinsic value by up to a third and still not lose money. A negative margin of safety simply means the stock is priced above the Graham Number and, by Graham's standards, offers no cushion. Keep in mind that the Graham Number itself is an estimate based on two inputs, both of which carry uncertainty, so the margin of safety is your buffer against estimation errors, not a guarantee.
Adjusting the P/E and P/B multipliers
The calculator lets you change the P/E and P/B multipliers away from Graham's original 15 and 1.5. Analysts sometimes raise the P/E multiplier for high-quality businesses with durable competitive advantages, or lower it for cyclical or financially stressed companies. Lowering the P/B multiplier is appropriate for companies with large goodwill balances or other intangibles that may overstate book value. Any change you make is reflected immediately in the Graham Number, the implied ratios, and the margin of safety, allowing you to stress-test your valuation assumption.
Limitations of the Graham Number
The Graham Number was designed for mature, asset-heavy businesses such as manufacturers, utilities, and financial companies. It does not work well for technology or asset-light firms where book value is low relative to earning power, because a small BVPS drags the Graham Number down even when the company is highly profitable. It also ignores growth, competitive moats, free cash flow generation, and management quality. Graham himself never intended it to be used in isolation: it is a starting screen to find candidates worth deeper analysis, not a substitute for full due diligence including a discounted cash flow valuation.
Graham's Dual-Ratio Criteria
| Criterion | Graham Limit | Purpose |
|---|---|---|
| Price-to-Earnings (P/E) | <= 15 | Limits the earnings multiple paid |
| Price-to-Book (P/B) | <= 1.5 | Ensures assets back the purchase price |
| P/E x P/B product | <= 22.5 | Combined sanity check (15 x 1.5) |
| Graham Number formula | sqrt(22.5 x EPS x BVPS) | Maximum intrinsic value estimate |
| Margin of safety target | >= 33% | Buffer against estimate error (classic rule) |
Benjamin Graham required both conditions to hold simultaneously. The product rule (P/E x P/B <= 22.5) is the compact form of the same requirement.
Frequently asked questions
What is the Graham Number formula?
The Graham Number equals the square root of (22.5 times EPS times BVPS). The 22.5 constant is Graham's maximum P/E ratio (15) multiplied by his maximum P/B ratio (1.5). For example, a stock with EPS of $5.00 and BVPS of $30.00 has a Graham Number of sqrt(22.5 x 5 x 30) = sqrt(3375) = $58.09.
What EPS figure should I use?
Use trailing twelve-month (TTM) diluted EPS attributable to common shareholders. Avoid using earnings from a period that contained large one-off items (asset sales, write-offs, insurance payouts) that distort the underlying profitability. Some analysts use a 3- or 5-year average EPS to smooth cyclical swings.
Should I use reported BVPS or tangible BVPS?
For a more conservative estimate, use tangible book value per share, which excludes goodwill and other intangible assets. Reported BVPS can overstate the hard asset base for companies that have made acquisitions, because goodwill reflects a premium paid over fair value and may never be recoverable in a liquidation. Graham himself preferred tangible assets.
What margin of safety does Graham recommend?
Graham advocated buying at a significant discount to intrinsic value to protect against estimation errors and market volatility. A classic rule of thumb is a margin of safety of at least one-third (33%), meaning the stock price should be no more than two-thirds of the calculated intrinsic value. The margin of safety is intentionally a conservative buffer, not an exact science.
Does the Graham Number work for technology stocks?
Generally no. Technology and asset-light companies often have low book values relative to their earning power, which pulls the Graham Number artificially low. Similarly, the formula produces no result for companies with negative EPS or negative book value. For high-growth or asset-light businesses, a discounted cash flow (DCF) model or a price-to-earnings-growth (PEG) ratio analysis is more appropriate.
What does a negative margin of safety mean?
A negative margin of safety means the current market price is higher than the Graham Number. By Graham's standards the stock offers no margin of safety at that price. This does not necessarily mean the stock is a bad investment; it may be that the market is pricing in growth or quality that the Graham Number formula does not capture. It simply means the price fails Graham's conservative screen.