What This Calculator Does

A z-score, also called a standard score, answers a focused question: how many standard deviations is an observed value from a reference mean? Enter an observed value X, mean μ, and standard deviation σ; the page calculates a z-score and uses an approximate standard normal cumulative distribution function to show a percentile and left-tail cumulative probability.

It is useful for quick position comparisons involving exam scores, measurements, and values on different scales. The z-score is a standardization result; the percentile and probability additionally depend on a normal-model assumption. For permutation, binomial, or Poisson probabilities, use the Probability Calculator. For P values, use the P Value Calculator. For arithmetic checks, use the Mathematical Expression Calculator.

When to Use It

• You know a reference mean and standard deviation and want to see whether a value is above or below the mean.
• You want a percentile under a normal model.
• You want a quick estimate of where an observation falls in the left-tail cumulative distribution.
• You need to compare measurements using standard-deviation units.
• You are learning the relationship between z-scores, the standard normal distribution, and percentile tables.

If the data are strongly skewed, truncated, ordinal rather than continuous, or you need a hypothesis test, cutoff reverse-solve, right-tail/two-tail area, or confidence interval, do not treat this page’s single left-tail number as a complete statistical conclusion.

Inputs Explained

Observed Value X

X is the raw value to standardize, such as an exam score, measurement, or experimental result. It may be above, below, or equal to the mean and may be negative or fractional, but it must be finite.

Mean μ