Altman Z-Score Calculator

Introduction to Altman Z-Score distress prediction

In 1968 Edward I. Altman published a multiple discriminant analysis that compressed twenty-two candidate accounting ratios into a five-variable linear function able to separate manufacturers that went bankrupt from manufacturers that did not. The paper, Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy, matched thirty-three bankrupt manufacturers filing under the old Chapter X between 1946 and 1965 against thirty-three surviving manufacturers of similar asset size, and reported 95 per cent classification accuracy one financial statement before failure. That single number — the Z-Score — became the most widely reproduced credit screen in corporate finance, and it is still the reference point against which newer default models are benchmarked.

The insight that made the model work is that no single ratio predicts failure well. Current ratio, debt-to-assets and return on assets each look plausible on their own, yet each one is easy to defeat: a firm can hoard inventory to flatter liquidity, or defer maintenance to flatter earnings. Discriminant analysis instead finds the weighted combination of ratios whose group means are furthest apart relative to within-group spread, so the ratios discipline each other. Altman noted that the sales-to-assets ratio was, on its own, statistically insignificant between the two groups, yet it ranked second in contribution once combined with the other four — a result that is impossible to reach with single-ratio analysis.

Altman later published two re-estimated variants, and this calculator implements all three because using the wrong one is the single most common error in practice. The Z-Score applies to publicly traded manufacturers and uses market capitalisation. The Z′-Score applies to privately held manufacturers and substitutes book value of equity, with every coefficient re-fitted. The Z″-Score applies to non-manufacturing industrials and to developed and emerging-market credits; it drops the asset-turnover ratio entirely and re-fits the four survivors. The three models have different coefficients and different cut-off zones, so a score of 2.7 is a comfortable pass in one model and a warning in another.

How to use this calculator with a real set of filings

Start by choosing the model that matches the company, because the choice changes both which inputs are required and how the answer is read. The selector at the top of the form relabels the equity field and hides the sales field when it is not part of the model, so you cannot accidentally feed a book value into a market-value coefficient.

1. Pick the model. Public manufacturer, private manufacturer, or non-manufacturer / emerging market. If you are unsure, the comparison table further down maps company types onto models.
2. Take every figure from one reporting period. Use the latest annual report, or trailing twelve months for the income statement items paired with the matching period-end balance sheet. Mixing a quarterly sales figure with annual assets silently changes the meaning of the turnover ratio by a factor of four.
3. Enter working capital as current assets minus current liabilities. Negative values are legitimate and are entered as negative numbers.
4. Enter retained earnings from the equity section. An accumulated deficit is entered as a negative number; young firms often score badly here purely because they have not existed long enough to accumulate earnings.
5. Enter EBIT — operating profit before interest and tax. Use the same definition every period so the trend means something.
6. Enter the equity value the selected model asks for: market capitalisation (share price times shares outstanding) for the original model, book value of shareholders equity for Z′ and Z″.
7. Enter total liabilities — current plus non-current, which is the book value of total debt in Altman terminology.
8. Enter sales for the two manufacturing models. The Z″ model does not use it and the field is hidden.
9. Enter total assets. This is the denominator of four of the five ratios and must be greater than zero.

Units cancel out of every ratio, so you may enter thousands, millions or whole currency units — provided you use the same scale for all seven inputs. After calculating, the contribution table shows each ratio, its coefficient and the product of the two, and the scale graphic places the score against the zone boundaries of the model you selected. The Copy shareable link button writes the whole input set into the page URL, which is the fastest way to send a colleague the exact scenario you are looking at.

The discriminant formula behind each Z-Score model

All three models are linear discriminant functions of the same shape: a weighted sum of dimensionless accounting ratios. Because every ratio is a pure number, the score itself carries no units, and the coefficients are only meaningful together with the exact ratio definitions listed underneath each equation.

Original Z-Score (publicly traded manufacturers, 1968)

Formula: Z = 1.2 X_1 + 1.4 X_2 + 3.3 X_3 + 0.6 X_4 + 1.0 X_5

The 1968 paper printed the function as Z = .012X1 + .014X2 + .033X3 + .006X4 + .999X5 because the first four ratios were entered as percentages rather than decimals. Altman later restated it in decimal form, which is the version above and the version every data provider uses; the two are algebraically identical apart from the rounding of 0.999 to 1.0 on the turnover term.

Z′-Score (privately held manufacturers)

Formula: Z^′ = 0.717 X_1 + 0.847 X_2 + 3.107 X_3 + 0.420 X_4 + 0.998 X_5

Here is book value of equity divided by total liabilities. Notice that the weight on the equity cushion falls from 0.6 to 0.420 and the weight on liquidity falls from 1.2 to 0.717: book equity is a slower-moving, less informative signal than a live market price, and the fitted model discounts it accordingly.

Z″-Score (non-manufacturers, developed and emerging markets)

Formula: Z^″ = 3.25 + 6.56 X_1 + 3.26 X_2 + 6.72 X_3 + 1.05 X_4

The constant 3.25 is a deliberate standardisation, not a fitted intercept: Altman added it so that a score of zero corresponds to a defaulted, D-rated credit, which lets the score be mapped directly onto bond-rating equivalents. Some references publish the same model without the constant; in that convention the safe and distress boundaries become 2.60 and 1.10 instead of 5.85 and 4.35. This calculator uses Altman own presentation of the model, constant included, and states the thresholds it applies alongside every result.

The five ratios

The ratio definitions are shared across the models, with the single exception of the equity measure in the fourth ratio.

Formula: X_1 = (Working capital) / (Total assets)

Formula: X_2 = (Retained earnings) / (Total assets)

Formula: X_3 = EBIT / (Total assets)

Formula: X_4 = (Market value of equity) / (Book value of total liabilities)

Formula: X_4^′ = (Book value of equity) / (Total liabilities)

Formula: X_5 = Sales / (Total assets)

• X₁ measures net liquid assets relative to total capitalisation. Altman tested the current ratio and the quick ratio too; working capital over assets discriminated better on both a univariate and a multivariate basis.
• X₂ is cumulative profitability, and doubles as an age proxy — a firm cannot have large retained earnings without having earned them over time. It is why young firms score low even when currently profitable.
• X₃ is operating earning power before financing and tax distortions. It carries the largest weight in the original model because insolvency ultimately occurs when asset earning power falls below the liabilities they support.
• X₄ asks how far asset values can fall before liabilities exceed them. In the original model the numerator is market capitalisation of all equity, preferred plus common, and the denominator is the book value of total debt.
• X₅ is asset turnover, a measure of management ability to generate sales from the asset base. It is the ratio that behaves worst across industries, which is exactly why the Z″ model omits it.

Note that total assets and total liabilities are denominators, so the calculator requires both to be strictly positive and refuses to produce a score otherwise rather than returning an infinite or misleading value. Working capital, retained earnings and EBIT may be negative, and book value of equity may be negative for a company with an accumulated deficit; market value of equity may not be negative because a share price cannot be.

Zones of discrimination and how to read the score

Altman derived the boundaries empirically rather than from a probability model. In the original sample every firm scoring above 2.99 was a survivor and every firm scoring below 1.81 was bankrupt; the interval between them contained all of the misclassifications, and Altman named it the zone of ignorance or grey area. For analysts who wanted a single cut-off he also reported an optimal value of 2.675, the midpoint of the 2.67 to 2.68 interval that minimised total misclassifications.

A score inside the safe zone is a statement about the historical sample, not a guarantee: Altman own follow-up work shows that median Z-Scores for a given bond rating have drifted over three decades as leverage norms changed, and that the model exhibits rising Type II error (healthy firms flagged as risky) when applied to modern, more leveraged balance sheets. The direction and speed of travel matter more than the level. A manufacturer sliding from 3.6 to 2.5 over two years deserves attention even though 2.5 is not a distress reading, whereas a firm that has sat stably at 2.2 for a decade is telling you something different.

Worked example: scoring the same company under all three models

Take a manufacturer with the following simplified annual figures, all in millions of the same currency: working capital 50, retained earnings 120, EBIT 40, market value of equity 200, book value of equity 90, total liabilities 150, sales 300, total assets 250. Press Load worked example in the calculator to populate these numbers for whichever model is selected.

Step 1 — form the ratios.

• X₁ = 50 / 250 = 0.20
• X₂ = 120 / 250 = 0.48
• X₃ = 40 / 250 = 0.16
• X₄ = 200 / 150 = 1.3333 using market value, or 90 / 150 = 0.60 using book value
• X₅ = 300 / 250 = 1.20

Step 2 — apply the original public-manufacturer coefficients.

Formula: Z = 1.2(0.20) + 1.4(0.48) + 3.3(0.16) + 0.6(1.3333) + 1.0(1.20) = 3.44

The five contributions are 0.240, 0.672, 0.528, 0.800 and 1.200. The total of 3.44 sits above 2.99, so the firm is in the safe zone, and the contribution table makes clear that asset turnover alone supplies more than a third of the score.

Step 3 — rerun the same company as a private firm. Replacing market value with book value of equity gives X₄ = 0.60, and the Z′ coefficients give contributions of 0.1434, 0.4066, 0.4971, 0.2520 and 1.1976, for a total of 2.50. That is inside the Z′ grey zone of 1.23 to 2.90 — the same underlying business, but no market cushion to point at and a model that weights the remaining evidence differently.

Step 4 — rerun it as a non-manufacturer. The Z″ model ignores sales entirely: 3.25 + 6.56(0.20) + 3.26(0.48) + 6.72(0.16) + 1.05(0.60) = 3.25 + 1.312 + 1.5648 + 1.0752 + 0.630 = 7.83. Against the 5.85 safe boundary that is a comfortable pass, roughly a BBB bond-rating equivalent on Altman published mapping.

The three answers — 3.44, 2.50 and 7.83 — are not contradictory, and they are not comparable either. Each is a position on its own axis with its own boundaries, which is exactly why quoting a bare Z-Score without naming the model is meaningless.

Choosing between the three models

Some company types fall outside all three. Banks, insurers and other financial institutions have balance sheets in which working capital is not a meaningful concept and leverage is a regulated input rather than a risk signal; Altman models were never fitted on them and should not be used for them. Very young companies are penalised twice, through a low retained-earnings ratio and often a low turnover ratio, so a distress reading for a three-year-old firm frequently reflects age rather than fragility. Asset-light software and services firms carry intangible value that never enters total assets, which deflates X₁, X₂ and X₃ while inflating X₅.

Data quality checks before you trust the number

Most wrong Z-Scores are wrong because of the inputs, not the arithmetic. The checks below take a minute and catch the great majority of mistakes.

• Scale consistency. One field in thousands and the rest in millions produces a ratio that is off by a factor of a thousand. The calculator warns when any ratio is implausibly large.
• Period alignment. Trailing-twelve-month EBIT and sales belong with the period-end balance sheet that closes the same window.
• Equity measure. Confirm you have entered market capitalisation for the original model and book equity for Z′ and Z″. The form relabels the field when you switch models precisely because this is the easiest thing to get wrong.
• Total liabilities, not net debt. Altman denominator is the book value of all liabilities, including payables, provisions, deferred tax and lease liabilities — not just borrowings.
• EBIT definition. Decide once whether to use reported operating profit or an adjusted figure that strips unusual items, then keep it fixed across periods.
• Market value timing. Market capitalisation moves daily. Choose the balance sheet date for a historical score, or today for a current score, and label which one you used.
• Restatements and acquisitions. A large acquisition inflates total assets immediately while earnings and retained earnings catch up later, so the score dips for mechanical reasons.

Limitations, calibration drift and modelling assumptions

The model assumes that the historical relationship between these five ratios and failure still holds, that the firm resembles the estimation sample, and that the financial statements are a fair representation of economic reality. Each of those assumptions can fail.

• Population fit. The original coefficients were fitted on US manufacturers with assets between roughly one and twenty-five million dollars, in an era of far lower leverage. Applying them outside that population is extrapolation.
• Calibration drift. Median Z-Scores by bond rating have shifted materially since the 1990s, which means a fixed 2.99 boundary flags more healthy firms as risky today than it did in 1968.
• Accounting quality. Operating leases, pension deficits, securitised receivables, capitalised development costs and off-balance-sheet vehicles all move the ratios without changing the underlying economics.
• Snapshot nature. The score sees no refinancing wall, no covenant, no litigation and no committed facility. Two firms with identical Z-Scores can have completely different liquidity runways.
• Market reflexivity. In the original model X₄ imports market sentiment, so the score falls when the share price falls, whether or not fundamentals moved.
• Short horizon. Altman own accuracy tables show roughly 95 per cent accuracy one year before failure, about 72 per cent two years before, and little useful signal beyond that.
• Classification, not probability. The output is a discriminant score. Converting it to a default probability requires an additional mapping that this calculator deliberately does not invent.

Pair the Z-Score with measures it cannot see: operating and free cash flow, interest and fixed-charge coverage, net debt to EBITDA, the maturity profile of borrowings, and available undrawn facilities. The Z-Score earns its place because it is cheap, consistent and comparable across a portfolio — not because it is complete.

Common questions about Z-Score analysis

Sources

Important disclaimer

This Altman Z-Score calculator is provided for informational and educational purposes only and does not constitute financial, investment, legal, or accounting advice. Do not rely on this tool as the sole basis for decisions. For material lending, investment, or restructuring decisions, consult appropriately qualified professionals and review primary financial statements.