The Altman Z-score calculator combines five accounting ratios into a single number using coefficients derived by multiple discriminant analysis. It was built to separate firms that later failed from firms that did not, and it remains the most widely reproduced credit screening statistic in finance — quoted in lending reviews, supplier credit checks and academic work more than half a century after it was first published.
Arb Digital publishes this in the free tool library at arbsbuy.com with all three published coefficient sets, because a Z-score quoted without naming the variant is close to meaningless. This page is unrelated to the live z-score calculator, which computes the statistical standard score of an observation against a mean and standard deviation. The two share a name and nothing else. Where the business valuation calculator asks what a company is worth, this one asks how far its balance sheet sits from the profile of firms that ran into trouble.
Which Variant This Calculator Implements
Three coefficient sets exist, and this tool implements all three explicitly. The default is the original 1968 model for publicly traded manufacturers: Z = 1.2·X1 + 1.4·X2 + 3.3·X3 + 0.6·X4 + 0.999·X5, with X4 using the market value of equity over total liabilities. Its zones are above 2.99 safe, 1.81 to 2.99 grey, below 1.81 distress.
The Z-prime model re-estimated the coefficients for private manufacturers, where no market capitalisation exists: Z' = 0.717·X1 + 0.847·X2 + 3.107·X3 + 0.420·X4 + 0.998·X5, with X4 using the book value of equity. Its zones are above 2.90 safe, 1.23 to 2.90 grey, below 1.23 distress.
The Z-double-prime model drops X5 entirely, because asset turnover varies so much between industries that including it made the score a proxy for sector rather than for distress: Z'' = 6.56·X1 + 3.26·X2 + 6.72·X3 + 1.05·X4, again on book equity. Its zones are above 2.60 safe, 1.10 to 2.60 grey, below 1.10 distress. A widely used emerging-market adaptation adds a constant of 3.25 to this score so that zero corresponds to a defaulted bond rating; because that constant shifts every zone boundary with it, this calculator reports the unshifted Z'' and leaves the adjustment to be applied deliberately rather than silently. The models are the work of Edward I. Altman, described on his NYU Stern faculty profile as the creator of the Z-score model for bankruptcy classification.
How to Use It
- Choose the variant that matches the company. A private services business scored on the original public-manufacturer coefficients will produce a number that looks precise and means nothing.
- Take every input from one balance sheet date and the matching income statement period. Mixing dates is the second most common error after mixing models.
- Use cumulative retained earnings, not the year's profit. X2 is a measure of accumulated self-funding and firm age, so the reserve balance is the right figure.
- Enter market capitalisation for the original model. Shares outstanding multiplied by the current price, not the book equity figure sitting below it.
- Read the bars, not only the total. Two firms can score identically with completely different weaknesses, and the contribution breakdown is where that shows.
The Formula / How It's Calculated
The five ratios are: X1 = working capital ÷ total assets, X2 = retained earnings ÷ total assets, X3 = EBIT ÷ total assets, X4 = equity ÷ total liabilities, and X5 = sales ÷ total assets. Each is multiplied by its coefficient and the products are added.
Run the defaults through the original model. Working capital is 2,200,000 − 1,300,000 = 900,000, so X1 = 900,000 ÷ 5,000,000 = 0.180. X2 = 1,400,000 ÷ 5,000,000 = 0.280. X3 = 620,000 ÷ 5,000,000 = 0.124. X4 = 3,600,000 ÷ 2,900,000 = 1.2414. X5 = 6,500,000 ÷ 5,000,000 = 1.300.
The weighted terms are 1.2 × 0.180 = 0.216, 1.4 × 0.280 = 0.392, 3.3 × 0.124 = 0.4092, 0.6 × 1.2414 = 0.7448 and 0.999 × 1.300 = 1.2987. The total is 3.06, which sits above the 2.99 threshold and lands in the safe zone. Switch to the private-firm model with the same figures and, because X4 falls to 2,100,000 ÷ 2,900,000 = 0.724 and every coefficient shrinks, the score drops to 2.35 — squarely in the grey zone. Switch to Z-double-prime and it rises to 3.69. Identical accounts, three defensible answers, three different verdicts. That is the strongest argument there is for naming the variant whenever the number is quoted.
What a Z-Score Is and Is Not
This point matters more than any arithmetic on the page. A Z-score is a classification statistic. Discriminant analysis was used to find the weighted combination of ratios that best separated two known groups of historical firms — those that had failed and those that had not — in a specific sample, over a specific period, in a specific economy. The score places a new firm relative to that historical separation.
It is not a probability of bankruptcy, and it does not predict that any company will or will not fail. A firm in the distress zone may trade for decades; a firm in the safe zone may collapse from a fraud, a lost contract or a liquidity event that no balance sheet ratio anticipated. The score has nothing to say about litigation, customer concentration, covenant terms, refinancing windows or management quality, and those are frequently the actual cause of failure.
The honest use is as a screen and a trend. A score that has fallen from 3.4 to 2.1 over three years is telling you something worth investigating, whichever zone it currently sits in. A single score in isolation, treated as a verdict on a named company, is a misuse of the statistic — and stating that plainly is more useful than any refinement of the coefficients.
Where the Score Breaks Down
Certain business types produce Z-scores that are structurally misleading rather than merely uncertain, and knowing which they are is most of the skill in using it.
Financial institutions are the clearest case. A bank's balance sheet is mostly financial assets and deposits, X1 has no meaningful interpretation, and leverage that would be alarming in a manufacturer is the normal operating model. Altman's models were never estimated on financials and should not be applied to them. Property companies have a related problem: assets are revalued rather than depreciated, so X2 and X3 move for reasons unconnected to trading.
Young companies are penalised twice. X2 is small by construction because there has been no time to accumulate reserves, and a loss-making growth firm has a negative X3 as well. A well-funded three-year-old business with substantial cash in the bank can score in the distress zone while facing no short-term risk whatsoever — the score is describing its age, not its solvency. Asset-light businesses are distorted in the opposite direction: with a small total assets denominator, X3 and X5 inflate, and a software firm can post a striking Z-score on a modest balance sheet. That is one reason the Z-double-prime variant drops X5, and one reason the interest coverage ratio calculator and the current ratio calculator are worth running alongside it.
Reading the Contribution Bars
The bars break the total into its five weighted terms, which turns a single number back into a diagnosis. In the default original-model run, X5 alone contributes 1.30 of the 3.06 total — roughly 42 percent — and X4 contributes another 0.74. Between them, asset turnover and market-based solvency account for two thirds of the score.
That is worth knowing, because both are volatile. X4 moves with the share price and can halve in a quarter without a single accounting entry changing. X5 falls immediately if revenue drops or if the company makes an acquisition that adds assets faster than sales. A score resting on those two terms is much less stable than one built on X2 and X3, which reflect accumulated and current earning power.
The general rule is that scores dominated by X2 and X3 are the most durable, because those terms move slowly and reflect the operating business. A score propped up by X4 in a rising market is the most fragile, and it is exactly the configuration that produced apparently safe scores shortly before several well-known failures. Comparing the split across several years is far more informative than comparing the totals.
Getting the Inputs Right
Small definitional choices move the score more than most users expect, and three recur.
The first is EBIT. X3 wants operating earnings before interest and tax, and it should exclude one-off gains such as an asset disposal that inflates a single year. Where an income statement blends operating and non-operating items, deriving EBIT cleanly first with the EBITDA calculator is safer than reading a headline figure. The second is total liabilities, which must include everything — deferred tax, pension obligations, lease liabilities and provisions — not just interest-bearing debt. Understating it inflates X4, which carries a large coefficient in the Z-double-prime model. The debt-to-equity ratio calculator works from the same liability total, so the two should agree.
The third is negative equity. A company with accumulated losses can show negative retained earnings and negative book equity, which makes X2 and X4 negative and drives the score sharply down. That behaviour is intended rather than a defect, but it means the score can fall below the distress threshold on the strength of history rather than current trading, which is why the retained earnings calculator and the working capital calculator are useful for separating what accumulated in the past from what is happening now. Cross-sector ratio and leverage data such as the NYU Stern current-year dataset is useful mainly for showing how far normal ranges diverge between industries.
Arb Digital builds long-term online growth programmes for established businesses, so the earning power terms in this score have something to work with.
Web Growth Services Talk to Arb DigitalCommon Mistakes to Avoid
- Using the wrong variant — the same accounts scored 3.06, 2.35 and 3.69 under the three models above, and only one of those is the right answer for a given company.
- Putting book equity into the original model — X4 there is market capitalisation over total liabilities, and substituting book value understates the score.
- Entering the year's profit as retained earnings — X2 is the cumulative reserve, and using one year's figure collapses the term.
- Scoring banks, insurers or property funds — the models were not estimated on those balance sheets and the ratios do not carry the same meaning.
- Treating the score as a probability — it is a classification statistic relative to a historical sample, not a forecast about any particular company.
Related Free Tools From Arb Digital
Pair this with the current ratio calculator for the liquidity picture behind X1, the debt-to-equity ratio calculator for the leverage behind X4, the interest coverage ratio calculator for whether earnings service the debt, the working capital calculator for the X1 numerator, the retained earnings calculator for X2, the asset turnover calculator for X5, and the business valuation calculator when the question is worth rather than risk. The full free online tools hub lists everything else.
Frequently Asked Questions
The original 1968 model is Z = 1.2·X1 + 1.4·X2 + 3.3·X3 + 0.6·X4 + 0.999·X5, where the five ratios are working capital, retained earnings, EBIT, market equity over total liabilities, and sales, each over total assets except X4.
The original for publicly traded manufacturers, Z-prime for private manufacturers where no market capitalisation exists, and Z-double-prime for non-manufacturers, which drops the asset turnover term because it varies too much between industries.
The threshold depends on the variant. The original model treats above 2.99 as safe and below 1.81 as distress, Z-prime uses 2.90 and 1.23, and Z-double-prime uses 2.60 and 1.10. Quoting a score without naming the model leaves the zones ambiguous.
No. The score is a classification statistic that places a firm relative to a historical sample of failed and surviving companies. It is not a probability and not a prediction about any particular business, and many low-scoring firms trade normally for years.
It should not be. The models were never estimated on financial institutions, whose balance sheets consist largely of financial assets and deposits, so working capital and leverage ratios do not carry the meaning the coefficients assume.
Because X2 measures cumulative retained earnings, which a young company has had no time to build, and a loss-making growth firm also has a negative X3. The score is partly measuring firm age rather than solvency.
It applies the Z-double-prime coefficients and adds a constant of 3.25 so that a score of zero corresponds to a defaulted bond rating. Because that constant shifts every zone boundary, it should be applied deliberately rather than mixed with unshifted scores.
No. X2 uses the cumulative retained earnings reserve on the balance sheet, which reflects how much of the business has been funded from its own accumulated profits over its whole life.
This calculator performs arithmetic on figures you supply and is provided for general information only. It is not credit, investment or financial advice and it is not an assessment of any company. The Altman Z-score is a screening statistic derived from historical samples, not a prediction of bankruptcy — confirm any figure used in lending, investment or a transaction with a qualified professional.
