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.

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.

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.