How the Altman Z-score works
In 1968 Edward Altman asked a blunt question: can published financial statements tell a failing company from a healthy one before the failure happens? Working from 33 bankrupt manufacturers matched against 33 survivors, he used multiple discriminant analysis — a statistical method that finds the weighted combination of variables that best separates two groups — and published the result in theJournal of Finance (vol. 23, no. 4, pp. 589–609). The five ratios that survived the winnowing each capture a different failure channel: working capital ÷ total assets measures liquidity, which drains away as losses mount;retained earnings ÷ total assets measures cumulative reinvested profit, punishing young and chronically unprofitable firms;EBIT ÷ total assets measures the raw earning power of the asset base and carries the heaviest weight;market value of equity ÷ total liabilities measures how far asset values can fall before liabilities exceed them, letting the market do the valuing; and sales ÷ total assetsmeasures how hard the assets work to generate revenue.
The three Z-score formulas
Z = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E
Z′ = 0.717A + 0.847B + 3.107C + 0.420D + 0.998E
Z″ = 6.56A + 3.26B + 6.72C + 1.05D
where A = working capital ÷ total assets, B = retained earnings ÷ total assets, C = EBIT ÷ total assets,D = equity ÷ total liabilities (market value of equity in Z; book value in Z′ and Z″), and E = sales ÷ total assets. Zone cutoffs: Z — safe above 2.99, grey 1.81–2.99, distress below 1.81; Z′ — safe above 2.90, grey 1.23–2.90, distress below 1.23; Z″ — safe above 2.60, grey 1.1–2.60, distress below 1.1.
Worked example
Take a public manufacturer with $10,000M in total assets: working capital of $1,200M, retained earnings of $2,500M, EBIT of $900M, sales of $8,000M, a market capitalization of $6,000M, and total liabilities of $4,000M. The original model weighs each ratio like this:
| Step | Amount |
|---|---|
| 1.2 × A = 1.2 × 0.12A = working capital $1,200M ÷ total assets $10,000M = 0.12 | 0.144 |
| + 1.4 × B = 1.4 × 0.25B = retained earnings $2,500M ÷ total assets $10,000M = 0.25 | 0.350 |
| + 3.3 × C = 3.3 × 0.09C = EBIT $900M ÷ total assets $10,000M = 0.09 | 0.297 |
| + 0.6 × D = 0.6 × 1.5D = market value of equity $6,000M ÷ total liabilities $4,000M = 1.5 | 0.900 |
| + 1 × E = 1 × 0.8E = sales $8,000M ÷ total assets $10,000M = 0.8 | 0.800 |
| = Z-score of 2.491 — grey zonebetween the 1.81 distress cutoff and the 2.99 safe cutoff, the model declines a verdict either way | 2.491 |
Computed with this calculator's default settings — open the tool above and you'll see the same numbers, then swap in figures from any company's 10-K.
Three variants, and when each one applies
The original Z was estimated on publicly traded manufacturers, so its D ratio needs a market capitalization. Altman later re-derived the model twice for firms that fall outside that sample. Theprivate-firm Z′ swaps market equity for book equity and re-estimates every coefficient — which is why the weights change rather than just the input. The non-manufacturer Z″goes further and drops the sales-to-assets ratio entirely: asset turnover differs so much between, say, retailers and service firms that it said more about industry than about distress. Z″ is also the version Altman applied to emerging-market credits. None of the three applies to banks or insurers, whose deposit-funded, asset-opaque balance sheets were excluded from the sample by design.
What the Z-score can — and cannot — tell you
The Z-score is a screen, not a verdict. It was trained on data from 66 US manufacturers spanning 1946–1965 — mid-century balance sheets from a single sector — and it condenses everything into a linear formula that knows nothing about cash on hand, debt maturities, covenants, or management. Altman’s own later studies report that accuracy is strongest one to two years before failure and decays quickly beyond that, with false alarms common: many grey-zone and even distress-zone firms recover. Treat a low score as a reason to read the filings, not a forecast. It pairs naturally with ratio tools that unpack its components: theROA calculatorisolates the earning-power ratio at the heart of the model, theDuPont analysis calculatordecomposes returns into margin, turnover, and leverage, and theDSCR calculatorgives the cash-flow view of debt coverage that lenders actually underwrite against.
Frequently asked questions
What is the Altman Z-score?
The Altman Z-score is a bankruptcy-prediction score published by NYU professor Edward Altman in 1968 in the Journal of Finance. Using a statistical technique called multiple discriminant analysis, Altman studied 66 manufacturing companies — 33 that went bankrupt and 33 that survived — and found the weighted combination of five balance-sheet and income-statement ratios that best separated the two groups. The output is a single number: the higher the Z-score, the more a company’s financial profile resembles the survivors; the lower, the more it resembles firms that failed within about two years of the measurement date.
What do the safe, grey, and distress zones mean?
The zones translate the raw score using Altman’s published cutoffs. For the original public-company model, a Z above 2.99 is the safe zone — the territory of firms that did not fail in the sample. A Z below 1.81 is the distress zone, resembling companies that went bankrupt within roughly two years. Between 1.81 and 2.99 lies the grey zone — Altman’s “zone of ignorance” — where the model misclassified firms most often and offers no verdict. The private-firm Z′ uses 2.90 and 1.23; the non-manufacturer Z″ uses 2.60 and 1.1. A distress-zone score is a flag for deeper analysis, not a bankruptcy prediction by itself.
Which variant should I use?
Use the original Z for publicly traded manufacturers — its equity ratio needs a market capitalization. Use Z′ for privately held manufacturers: Altman re-estimated every weight with book value of equity, since private firms have no market price. Use Z″ for non-manufacturers and emerging-market companies: it drops the sales-to-assets ratio entirely, because asset turnover varies so much across industries that it distorted comparisons, and it also uses book equity. None of the variants apply to banks, insurers, or other financial companies. When in doubt, match the variant to how the company’s equity is valued and whether it actually manufactures things.
How accurate is the Altman Z-score?
On the original sample the model classified firms very accurately one year before bankruptcy, with accuracy falling off quickly at longer horizons — by four or five years out it was little better than chance. Altman’s own follow-up studies over later decades report that the model continued to catch most eventual bankrupts one to two years ahead on fresh samples, though with a meaningful rate of false alarms: plenty of grey- and distress-zone companies never fail. That asymmetry is why practitioners treat the Z-score as a screen that flags balance sheets worth investigating rather than a probability of default. Modern credit models add market signals and far larger samples.
Why are banks and financial firms excluded?
Altman built the model on manufacturers and explicitly left financial firms out of the sample, and the ratios show why. A bank’s balance sheet is leveraged by design — deposits are liabilities — so equity-to-liabilities looks alarming even at a perfectly healthy bank. Working capital is close to meaningless when nearly every asset and liability is a financial instrument, and sales-to-assets has no useful interpretation for a lender. Asset values at financial firms are also hard to judge from published statements, which makes the inputs themselves unreliable. Bank health is assessed instead with capital-adequacy, liquidity, and asset-quality measures built for that business model.
Sources
The official figures this page quotes are drawn from the primary sources above — check them (or a qualified professional) before relying on a result.
Primary source: Altman, E. I. (1968), “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy,”Journal of Finance, 23(4), 589–609. The Z′ and Z″ variants and their cutoffs come from Altman’s later re-estimations of the same model.
Disclaimer: This calculator is foreducation and illustration only. The Z-score is a statistical screen estimated on mid-century US manufacturers; it does not know a company’s cash position, debt schedule, or industry, and scores for financial firms are meaningless. A zone label is not a prediction that any particular company will or will not fail, and nothing here is investment, credit, or trading advice.