How do you calculate the statistical z-score?

Subtract the population mean from your raw score and divide by the population standard deviation: z = (x − μ) / σ.

What does a z-score tell you?

A z-score tells you how many standard deviations a value is from the mean. A z-score of 0 is exactly the mean, +1 is one standard deviation above, and −1 is one below.

What is a good Altman Z-score?

For the original Altman model, a score above 2.99 is considered 'safe', 1.81 to 2.99 is the 'grey' zone, and below 1.81 is 'distress'.

Z-Score Calculator

Q: What is the Altman Z-score?

The Altman Z-score is a financial model that combines five business ratios to estimate the probability of corporate bankruptcy.

This page combines the most common meanings of “z-score”: the statistical standard score used to standardize data and find probabilities under the normal distribution, and the Altman Z-score used in finance to diagnose business distress.

Raw value (x)

Mean (μ)

Std. deviation (σ)

z-score

—

z = (x − μ) / σ

Percentile

—

Area under standard normal

Prob. above x

—

= 1 − Φ(z)

The classic Altman Z-score (1968) for publicly traded manufacturing firms: Z = 1.2X₁ + 1.4X₂ + 3.3X₃ + 0.6X₄ + 1.0X₅
Enter the five ratios below (as decimals, not percentages).

X₁ = Working Capital / Total Assets

X₂ = Retained Earnings / Total Assets

X₃ = EBIT / Total Assets

X₄ = Market Value Equity / Total Liabilities

X₅ = Sales / Total Assets

Altman Z-score

—

Z = 1.2X₁ + 1.4X₂ + 3.3X₃ + 0.6X₄ + X₅

Risk zone

—

Distress < 1.81, Grey 1.81–2.99, Safe ≥ 2.99

What is a z-score (standard score)?

In statistics, a z-score tells you how far and in what direction a data point is from the mean, measured in standard deviations. This is essential in hypothesis testing, outlier detection and converting any normal distribution to the standard normal.

z = (x − μ) / σ
where x = raw value, μ = mean, σ = standard deviation.

Once you have z, you can look up the probability from the standard normal distribution Φ(z). This calculator approximates Φ(z) numerically and returns: percentile = Φ(z) × 100 and probability above x = 1 − Φ(z).

What is the Altman Z-score?

The Altman Z-score is an accounting-based model introduced by Edward Altman in 1968. It combines liquidity, profitability, leverage and activity ratios to predict the risk of corporate failure. It is widely cited in financial analysis and credit risk literature.

Original Altman (public manufacturing):

Z = 1.2X₁ + 1.4X₂ + 3.3X₃ + 0.6X₄ + 1.0X₅

Interpretation:

Z < 1.81 → Distress zone
1.81 ≤ Z ≤ 2.99 → Grey zone
Z > 2.99 → Safe zone

FAQs

Which z-score should I use?

Use standard z-score for statistical data, distributions, test scores. Use Altman Z-score for company financial health.

Do I need population or sample standard deviation?

For a strict z-score, use population σ. For sample data you may still standardize with sample s, but interpret with care.

Full original guide (expanded)

This unified tool exists because “z-score” is used by statisticians, data scientists, educators and also by financial analysts with very different meanings. Here you get both in one place, with explicit formulas, classifications and output labels suitable for professional documentation and audit trails.