Math

Z-Score Calculator - Standard Score Percentile Online

Calculate the Z-score (standard score) for a data point. Find the probability and percentile from a standard normal distribution.

How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

🍬 Say you have 100 candies. If you eat 20 of them, you ate 20% (20 out of 100). This tool helps you quickly find out ‘what part of a number is something?’ — super easy!

📌 Direct Answer & Summary

A Z-score (also called a standard score) measures how many standard deviations a data point is from the mean of a distribution. A positive Z-score means the value is above the mean; a negative Z-score means it is below. Z-scores are used in statistics to compare values from different distributions and to find probabilities using the standard normal distribution.

What is Z-Score Calculator - Standard Score Percentile Online?

A Z-score (also called a standard score) measures how many standard deviations a data point is from the mean of a distribution. A positive Z-score means the value is above the mean; a negative Z-score means it is below. Z-scores are used in statistics to compare values from different distributions and to find probabilities using the standard normal distribution.

How to use it

  1. 1️⃣ Enter the data point value (x) you want to standardize.
  2. 2️⃣ Enter the mean (mu) of the population or distribution.
  3. 3️⃣ Enter the standard deviation (sigma) — it must be greater than zero.
  4. 4️⃣ The result shows the Z-score along with the formula used.
  5. 5️⃣ The percentile and probability cards show where this value falls in the standard normal distribution.

Formula

Z = (x - mu) / sigma

💡 See it in action — a real example

A student scores 85 on a test with a class mean of 70 and a standard deviation of 10. Z = (85 - 70) / 10 = 1.50. This score is 1.5 standard deviations above the mean, placing the student at approximately the 93rd percentile.

❓ Common questions

What is a good Z-score?
That depends on context. In quality control, values with |Z| greater than 3 are often treated as outliers. In academic testing, a Z-score of 1.0 means you scored better than about 84% of the population.
What does a negative Z-score mean?
A negative Z-score means the data point is below the mean. For example, Z = -1.5 means the value is 1.5 standard deviations below the mean, placing it at approximately the 7th percentile.
What is the difference between Z-score and percentile?
The Z-score is a raw measure of distance from the mean in standard deviation units. The percentile converts that Z-score into the proportion of values that fall below it, assuming a normal distribution.
Can Z-scores be used for non-normal distributions?
You can always calculate a Z-score, but interpreting it as a percentile only works reliably for normally distributed data. For skewed or non-normal data, the percentile conversion will be inaccurate.
What is the Z-score for the 95th percentile?
A Z-score of approximately 1.645 corresponds to the 95th percentile in a standard normal distribution. This value is widely used in hypothesis testing as the threshold for a one-tailed test at the 5% significance level.
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