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Z-Score Calculator: Z-Score and Percentile

This free z-score calculator shows how many standard deviations a value lies from the mean. It also gives the percentile and the area under the normal curve to the left and right of the value.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

A z-score puts any value on a common scale. A mark of 85 means little until you know the class average and spread. Converting it to a z-score tells you how unusual it is, and lets you compare marks from different tests.

Enter the value, the mean and the standard deviation to get the z-score, its percentile and the tail probabilities.

How to Use This Tool

  1. Enter your value x.
  2. Enter the mean and the standard deviation of the group.
  3. Press Calculate.
  4. Read the z-score and the percentile.

How the Calculation Works

The z-score is (x − μ) ÷ σ. The percentile comes from the normal cumulative distribution, calculated with a precise approximation of the error function (accurate to about seven decimal places).

Worked Example

A score of 85 in a test with mean 70 and standard deviation 10 has z = 1.5. About 93.32% of students scored lower, so that is the 93rd percentile, and about 6.68% scored higher.

Common Uses

  • Comparing scores from different tests.
  • Spotting outliers, often beyond ±3.
  • Hypothesis tests and quality control.
  • Standardising data before analysis.

Tips and Common Mistakes

  • The standard deviation must be above zero.
  • About 95% of values lie between z = −2 and z = +2 for normal data.
  • Use the standard deviation tool to find σ from raw data first.

Next, you may need the standard deviation calculator, average calculator, percentage calculator, percent error calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

It is the number of standard deviations a value is above or below the mean. A z-score of 0 is exactly average, +1 is one standard deviation above, and −2 is two below.
z = (x − mean) ÷ standard deviation.
It is the share of a normal population that falls below your value. A z-score of 1 is about the 84th percentile.
The z-score always works. The percentile assumes the data follows a bell-shaped normal distribution, so treat it as an estimate for other shapes.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.