About the Z-Score Calculator
Z-Score Calculator has four modes. Find a z-score from a value, the mean and the standard deviation. Find the value that belongs to a z-score. Find the z-score for a percentile, such as the z-score at the 90th percentile. Or find the area under the normal curve between two z-scores. In every mode it also shows the share of the group below and above the z-score, the two-tailed p-value and the area between minus z and plus z, which is the confidence level for that z. The normal curve areas are calculated with a high-precision method, accurate to many decimal places, so results match a printed z-table and go beyond it. The calculation runs in your browser and nothing is sent anywhere.
Updated September 2026
How to use the Z-Score Calculator
- 1Choose what you want to find: a z-score, a value from a z-score, a z-score from a percentile, or the area between two z-scores.
- 2Fill in the boxes. For a z-score, enter the value, the mean and the standard deviation.
- 3Read the answer in the big box, with the percentile shown below it.
- 4Use the smaller boxes for the left and right tail areas and the two-tailed p-value.
- 5Change any number to see the result update at once.
Why z-scores are useful
A raw number means little without context. A score of 82 might be excellent on one test and average on another. Turning it into a z-score puts it on a common scale that says how unusual the score is. Two people who took different exams can then be compared fairly.
Z-scores are used in statistics classes, in medical growth charts, in quality control, in finance for spotting unusual returns and in research for testing hypotheses. Values with a z-score beyond about 2 or 3 in either direction are often looked at as possible outliers.
Common z-scores to remember
- z = 0: the mean, the 50th percentile.
- z = 1: about the 84th percentile; 68.27 percent of values lie between −1 and +1.
- z = 1.645: the 95th percentile, a 90 percent two-sided confidence level.
- z = 1.96: the 97.5th percentile, a 95 percent two-sided confidence level.
- z = 2.576: the 99.5th percentile, a 99 percent two-sided confidence level.
- z = 3: about the 99.87th percentile; 99.73 percent of values lie between −3 and +3.
Using the four modes
Z-score answers how far a value is from its group. Value from z answers the reverse question, such as what score sits two standard deviations below the mean. Z from percentile is handy for cut-offs, such as the score a student needs to be in the top 10 percent. Area between finds the share of a group that lies between two z-scores, for example between −0.5 and 1.
If you do not have the mean and standard deviation yet, Standard Deviation Calculator finds both from a list of numbers, and Average Calculator gives the mean. For chances of separate events, use Probability Calculator.
Tips and limits
The standard deviation must be greater than zero. When you use a sample, use the sample standard deviation unless you know the population value. The z-scores here use the normal curve, and for small samples with an unknown population standard deviation a t-distribution is normally used, which this tool does not cover.
Extremely large z-scores give tiny probabilities that are shown in percentages with limited digits, so use the decimal probability shown with area results when you need more precision. For turning results into percentages of an amount, Percentage Calculator can help.
Features
- Z-score from a value, mean and standard deviation
- Value from a z-score
- Z-score from a percentile
- Area between any two z-scores
- Left tail, right tail and two-tailed p-value
- High-precision normal curve, including far tails
- Runs in your browser
Frequently asked questions
What is a z-score?
A z-score tells you how many standard deviations a value is above or below the mean. A z-score of 0 is exactly the mean, +1 is one standard deviation above it and −2 is two below. It lets you compare values from different scales, such as an exam score and a height.
How do you calculate a z-score?
Subtract the mean from your value and divide by the standard deviation: z = (x − μ) ÷ σ. For a score of 85 in a group with a mean of 70 and a standard deviation of 10, z = (85 − 70) ÷ 10 = 1.5, which means it is one and a half standard deviations above the mean.
How do I turn a z-score into a percentile?
The percentile is the area under the normal curve to the left of the z-score. A z-score of 1.5 gives 93.32 percent, so the value is higher than about 93 percent of the group. This tool shows it under the z-score, and the left tail box shows the same area as a percentage.
How do I find the p-value from a z-score?
For a one-sided test, the p-value is the right tail area for a positive z or the left tail for a negative z. For a two-sided test, it is double the smaller tail, which is shown as the two-tailed p-value. A z of 1.96 gives a two-tailed p-value of about 0.05.
Does this assume a normal distribution?
The percentiles and areas do, because they come from the normal curve. The z-score itself does not: it is just a way to rescale a value. If your data is far from bell-shaped, read percentiles with care.
What z-score gives a 95 percent confidence level?
About 1.96. The area between −1.96 and +1.96 is 95 percent of the normal curve. For 90 percent it is 1.645 and for 99 percent it is 2.576. You can check these with the percentile mode.