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Z-Score Calculator

Enter a value, mean, and standard deviation to get its z-score, percentile, cumulative probability, and two-tailed p-value.

Direction

Everything is calculated in your browser. Nothing is uploaded.

Results
Z-scorez = (x - μ) / σ
1.5
for a value of 85
Where it falls
z = 1.5-3-2-10123
93.32%
Percentile ≤ 93rd
0.933193
Cumulative P(Z ≤ z)
0.066807
Right tail P(Z ≥ z)
0.133614
Two-tailed p P(|Z| ≥ |z|)
How it was found

z = (85 - 70) / 10 = 1.5

A value of 85 sits 1.5 standard deviations above the mean. About 93.32% of a normal distribution falls at or below it, and 6.68% falls above.

Percentiles and probabilities assume a normal, bell-shaped distribution.

How to calculate a z-score

  1. Enter the value and its distribution

    Type the raw value you are testing, then the mean and the standard deviation of the group it belongs to.

  2. Read the z-score

    The z-score appears at once, showing how many standard deviations the value sits above or below the mean.

  3. Check the percentile and probabilities

    See the percentile, the cumulative and right-tail probabilities, and the two-tailed p-value read from the normal curve.

  4. Switch to reverse mode when needed

    Flip to reverse mode to enter a target z-score instead and get the raw value that produces it.

Why use this tool

Z-score, percentile, and p-value together

One value, mean, and standard deviation give you the z-score, the percentile it maps to, the cumulative and right-tail probabilities, and the two-tailed p-value at the same time.

See where it falls on the curve

A small bell-curve diagram shades the area to the left of your score, so you can see the percentile rather than just read a number.

Reverse mode for raw scores

Enter a target z-score with the mean and standard deviation and the calculator returns the raw value behind it, useful for grading curves and cut-off marks.

A standard deviation of zero is caught

A spread of zero would divide to find a z-score with no defined answer, so it is flagged clearly instead of showing a broken result.

Runs entirely in your browser

Every figure is calculated on your device as you type. Nothing is uploaded, stored, or logged.

About this tool

A z-score, also called a standard score, tells you how many standard deviations a value sits above or below the mean. Enter a raw value, the mean, and the standard deviation, and this calculator returns the z-score along with the percentile it maps to, the cumulative probability of landing at or below it, and the two-tailed p-value. Positive scores land above the mean, negative scores fall below it, and a score of zero sits exactly on it.

The percentile and probabilities are read from the standard normal distribution, the familiar bell curve, so a z-score of 1.5 places a value near the ninety-third percentile with about 6.7 percent of the curve above it. A small diagram shades the area to the left of your score so you can see the result at a glance. Switch to reverse mode to work backwards: give a target z-score, the mean, and the standard deviation, and the calculator returns the raw value that produces it, which is handy for grading curves and cut-off scores.

Every figure updates as you type and nothing is uploaded. A standard deviation of zero is caught before it can divide, because a spread of zero leaves every value equal to the mean with no z-score defined. For the spread itself, the standard deviation calculator turns a list of numbers into a mean and standard deviation, the probability calculator covers single and combined events, and the percentage calculator handles quick percentage changes.

Frequently asked questions

What is a z-score?
A z-score is the number of standard deviations a value lies from the mean. It is found by subtracting the mean from the value and dividing by the standard deviation. A z-score of 2 means the value is two standard deviations above the mean, while a z-score of minus 1 means it is one standard deviation below.
How do you turn a z-score into a percentile?
The z-score is mapped onto the standard normal distribution, the bell curve, to find how much of the curve lies to its left. That fraction, expressed as a percentage, is the percentile. A z-score of 0 sits at the 50th percentile, and a z-score of about 1.28 sits near the 90th.
What is the two-tailed p-value?
The two-tailed p-value is the probability of seeing a value at least as far from the mean as yours in either direction. It is twice the tail beyond the absolute z-score. A z-score of 1.96 gives a two-tailed p-value of about 0.05, the common threshold for statistical significance.
Can I find the raw value from a z-score?
Yes. Switch to reverse mode and enter a target z-score along with the mean and standard deviation. The calculator multiplies the z-score by the standard deviation and adds the mean to return the raw value that would produce that score.
What happens if the standard deviation is zero?
A standard deviation of zero means every value equals the mean, so there is no spread to divide by and the z-score is undefined. The calculator detects this and shows a clear message instead of a broken result. Enter a standard deviation greater than zero to continue.
Is my data uploaded anywhere?
No. Every calculation runs in your browser as you type. Your numbers are never sent to a server, stored, or logged.

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