Z-Score Calculator

Enter a raw score, the mean and the standard deviation to get the z-score and the share of a normal distribution below and above it. The reverse tab turns a z-score back into a raw score. The working is shown with your numbers.

Free, no signupNo daily limitRuns in your browser - nothing you enter is uploadedUpdated 7 October 2026

Raw score (x)

Mean (μ)

Standard deviation (σ)

z-score

-Below (percentile)

-Above

Standard normal curve; the shaded area is the share below your value.

Worked example: one test score

A student scores 85 on a test where the class mean is 70 and the standard deviation is 10.

z = (x − μ) ÷ σ = (85 − 70) ÷ 10 = 1.5 area below z = 1.5 ≈ 0.9332 → about the 93rd percentile reverse: x = μ + z × σ = 70 + 1.5 × 10 = 85

If the scores are roughly bell-shaped, this student did better than about 93% of the class. A z of 0 is exactly average; −1 is one standard deviation below.

Reading z-scores

z	Share below	Meaning
−2	2.3%	Unusually low
−1	15.9%	Below average
0	50%	Exactly average
1	84.1%	Above average
1.96	97.5%	Edge of the middle 95%
2	97.7%	Unusually high

About 68% of a normal distribution lies within one standard deviation of the mean, 95% within two and 99.7% within three. Z-scores let you compare results on different scales - a z of 1.2 in maths and 0.8 in English means the maths result was further above that class's average.

What this calculator does not do

Percentiles assume a normal distribution.
The normal-curve area uses an approximation accurate to about seven decimal places, more than printed z-tables give.
It does not compute t-scores or p-values for hypothesis tests.

Frequently asked questions

What is a z-score?

A z-score says how many standard deviations a value is above or below the mean. z = (x − mean) ÷ standard deviation. A score of 85 in a test with mean 70 and standard deviation 10 has z = 1.5.

How do I turn a z-score into a percentile?

Find the area under the standard normal curve to the left of z. For z = 1.5 that area is about 0.9332, so the value is higher than about 93.3% of a normally distributed group. This calculator works out the area for you.

Can a z-score be negative?

Yes. A negative z-score means the value is below the mean; z = −1 is one standard deviation below.

How do I get the raw score from a z-score?

x = mean + z × standard deviation. With mean 70, standard deviation 10 and z = 1.5, x = 70 + 15 = 85.

Is the percentile accurate for my data?

Only if your data is roughly normally distributed. For skewed data the z-score is still correct, but the percentile from the normal curve will not match the real share of your data.

Related free tools

Standard Deviation CalculatorSample and population SD and variance, with a step table of every deviation.

Mean, Median & Mode CalculatorMean, median, mode(s) and range with the sorted data and working.

Percentage CalculatorX% of Y, percent of a total, increase/decrease, add or remove a percent, and marks.

Grade CalculatorCurrent class grade from scores and weights, with a letter grade and weight check.

Step-by-step guide: How to calculate a z-score →

Built and checked by Taimur Hassan Siddiqui, who has more than ten years in computer-science education. The formulas on this page are covered by an automated test suite, and the worked example on this page is one of its cases. Last updated 7 October 2026.