Z-Score Calculator
Choose whether you know a value with its mean and standard deviation, or you already have a z-score. You get the z-score and the share of a normal distribution below it and above it.
Your numbers
How we calculate it
The z-score says how many standard deviations a value is from the mean: z = (value − mean) ÷ standard deviation. A value above the mean has a positive z-score and a value below it has a negative one.
The percentile is the area under the standard normal curve to the left of z. It is worked out with the error function to about 15 digits of accuracy, and you can check it against a z-table. A value of 85 with a mean of 70 and a standard deviation of 10 has z = 1.5, which is the 93.32nd percentile. A z-score of 1.96 gives 0.9750 below it.
Assumptions and limits
- The percentile assumes the data follow a normal (bell curve) distribution. For other shapes it is only a rough guide.
- The standard deviation must be above zero.
- Probabilities are shown to 4 decimal places and the percentile as a percent.
Frequently asked questions
What does a z-score tell me?
It tells you how unusual a value is compared with the rest of the group. A z-score of 0 is exactly average, and about 95% of values in a normal distribution fall between −1.96 and 1.96.
What is a percentile?
The percentile is the share of the group below a value. A value at the 93rd percentile is higher than about 93 out of 100 of the group.
Why does z = 1.96 give 0.975?
Because 97.5% of a normal distribution lies below 1.96, which leaves 2.5% above it. With the matching 2.5% below −1.96, the middle 95% lies between the two values.
Related calculators
- Standard Deviation CalculatorPaste or type a list of numbers and choose whether it is a whole population or a sample.
- Confidence Interval CalculatorEnter the sample mean, the sample standard deviation, the sample size and the confidence level.
- Mean, Median and Mode CalculatorType or paste a list of numbers.
- Probability CalculatorEnter the chance of event A and event B as percentages, and the number of times you try A.
Worked example (a fixed example using the starting numbers, it does not change as you type)
Inputs: I know = A value, the mean and the standard deviation; Value = 85; Mean = 70; Standard deviation = 10.
- Z-score 1.5000
- Probability below 0.9332
- Probability above 0.0668
- Percentile 93.32%
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