Z-Score Calculator

Calculate z-score, percentile, and probability from a value, mean, and standard deviation.

By Konstantin Iakovlev · Updated April 2026 · Source: Khan Academy

Z-Score

-1.0000

Percentile

15.87%

Details

Z-Score-1.0000
Percentile Rank15.87%
P(X ≤ x)0.158655
P(X > x)0.841345

Use the Z-Score Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only and does not constitute tax, financial, or legal advice. Results are estimates based on the information you provide and current rates. Always consult a qualified tax professional or financial advisor for advice specific to your situation.

How It Works

A z-score locates a single data point within its dataset and returns its percentile rank along with the probability of seeing a value above or below it. That makes it a practical lens for judging performance, whether you are weighing a 2026 Q1 sales figure of $1.5 million against the industry average or sizing up one student's result on a standardized test. The payoff is data-driven judgment and a reliable way to flag outliers.

Also called the standard score, the z-score comes from subtracting the population mean (μ) from a raw score (x) and dividing by the population standard deviation (σ), written as Z = (x - μ) / σ. Standardizing in this way puts otherwise unlike distributions on a common footing. From there, the percentile and probability follow from the cumulative distribution function (CDF) of the standard normal distribution.

Reading the output, a positive z-score sits above the mean and a negative one sits below it, but a large z-score does not automatically mean 'good' performance; the surrounding context decides that. The result is only as trustworthy as its inputs, so make sure the mean and standard deviation genuinely describe the population you intend to analyze.

Example: Analyzing 2026 Employee Performance Bonuses

  1. 1 Imagine a company's 2026 Q4 bonus pool averages $5,000 per employee with a standard deviation of $1,200. An employee received a bonus of $7,400. We want to find their z-score, percentile, and probability.
  2. 2 Input: Value (x) = $7,400, Mean (μ) = $5,000, Standard Deviation (σ) = $1,200. Calculation: Z = ($7,400 - $5,000) / $1,200.
  3. 3 Intermediate Result: Z = $2,400 / $1,200 = 2.0. Using a standard normal distribution table or calculator, a z-score of 2.0 corresponds to a percentile of approximately 97.72%.
  4. 4 Final Result: The employee's bonus has a z-score of 2.0. This means their bonus is two standard deviations above the average. They are in the 97.72nd percentile, indicating that approximately 97.72% of employees received a bonus less than or equal to theirs. The probability of an employee receiving a bonus greater than $7,400 is 1 - 0.9772 = 0.0228 (2.28%).

Source: Khan Academy · Last updated: April 2026

Frequently Asked Questions

What does a z-score of 2 mean?
A z-score of 2 means the value is 2 standard deviations above the mean. Approximately 97.7% of data falls below this point in a normal distribution, making it relatively unusual.
How do you calculate a z-score?
Z = (X - mean) / standard deviation. For a test score of 85 with a class mean of 75 and standard deviation of 5: z = (85-75)/5 = 2.0. This means you scored 2 standard deviations above average.
What is a good z-score?
Context determines whether a z-score is "good." In testing, a z-score above 1.0 means above average. In quality control, values outside ±3 are flagged as outliers. In research, z-scores help determine if results are statistically significant.

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