Z-Score Calculator
Enter a value, a mean and a standard deviation to get the z-score and its percentile.
What this tool does
A z-score says how many standard deviations a value is from the mean: z = (x − mean) ÷ standard deviation. A score of 85 where the mean is 70 and the standard deviation is 10 has z = 1.5, which is higher than about 93.32% of values in a normal distribution.
Computes z from your value, mean and standard deviation.
Gives the share of a normal distribution below and above that value.
How to use it
- Enter the value (x).
- Enter the mean and the standard deviation.
- Read the z-score and the percentages.
- Use the distance sentence to interpret it.
Why use this calculator
Turns a value, a mean and a standard deviation into a z-score and the share of a normal distribution below and above it. Raw scores on different scales cannot be compared directly. A z-score puts them on a common scale, so you can say how unusual a result is and compare a test score with another test.
Why we built it
We built the z-score calculator to give the standard score and the share of a normal distribution below and above it. Find the inputs with the standard deviation calculator and the mean, median and mode calculator.
For a neighbouring job there is also the Confidence Interval Calculator and the Percentile Calculator.
Who this tool is for
- Students comparing scores on different scales
- Teachers explaining the normal curve
- Analysts spotting outliers
When to use it
- Comparing scores from different tests.
- Spotting unusually high or low values.
- Converting a score to a percentile.
- Statistics homework.
How it works
z = (x − μ) ÷ σ. The percentage below is the cumulative probability of the standard normal distribution at z. About 68% of values lie within one standard deviation of the mean, 95% within two and 99.7% within three.
Example: x = 85, μ = 70, σ = 10 gives z = 1.5; the cumulative probability is 0.9332, so 93.32% of values are below 85.
The percentages assume a normal (bell-shaped) distribution. For skewed data they will not be accurate.
A worked example
These are the values the calculator opens with, so you can see exactly what it does with them. Change any value on the page and the result updates; the figures below come from the same calculation.
| Input | Value |
|---|---|
| Value | 85 |
| Mean | 70 |
| Standard deviation | 10 |
With those inputs, the calculator returns:
- Z-score: 1.5
- Share of values below x: 93.32%
- Share of values above x: 6.68%
- Within 1 standard deviation of the mean: No
- Distance from the mean: 1.5 standard deviations above
What you give it, and what you get back
| Item | Details |
|---|---|
| Value, mean, standard deviation | Numbers in the same units; the standard deviation must be above zero. |
| Output | Z-score, percent below, percent above, and the distance in standard deviations. |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| Standard deviation error | It must be greater than zero. | Enter a positive number. |
| Percentile seems off | The data are not normally distributed. | Use an empirical percentile of your data. |
| Sample vs population | The formula needs the right deviation. | Use the standard deviation calculator for your data. |
Assumptions and limitations
- Percentiles assume a normal distribution.
- Does not compute the mean or deviation from raw data.
Frequently asked questions
What is a z-score?
The number of standard deviations a value is above or below the mean.
How do I calculate a z-score?
Subtract the mean from the value and divide by the standard deviation.
What does a negative z-score mean?
The value is below the mean.
What is a good z-score?
It depends on context. A z-score above 2 or below −2 is unusual in a normal distribution.
How do I convert z to a percentile?
Use the cumulative normal probability, shown in the results.
Is my data sent anywhere?
No. The calculation runs in your browser and nothing leaves the page.
Sources and accuracy
The z-score is the value minus the mean divided by the standard deviation, and the associated percentile is read from the standard normal distribution.
Figures last checked against the source on . Standards and rates can change — if you are relying on this for something that matters, confirm against the source above. Think a figure is wrong or out of date? Send a correction.