Z-Score Calculator

1. Enter the value you want to score.
2. Enter the mean of the data set.
3. Enter the standard deviation, which must be above zero.
4. Read the z-score and the percentile it corresponds to.

Here is what each result means:

A z-score, or standard score, tells you how far a value sits from the mean, measured in standard deviations. A z-score of 0 is exactly average, a positive score is above the mean, and a negative score is below it. A z-score of 1.5 means the value is one and a half standard deviations above the mean.

Z-scores put values from different data sets on the same scale, so you can compare them fairly. A test score and a height, for example, become comparable once each is expressed as a z-score. On a bell-shaped curve, the z-score also maps to a percentile, the share of values below it.

It subtracts the mean from the value and divides by the standard deviation, then reads the percentile from the normal curve.

1. Subtract the mean from the value.
2. Divide by the standard deviation for the z-score.
3. Convert the z-score to a percentile using the normal curve.

To find the standard deviation from a data set first, use the standard deviation calculator, then bring it here.

A student scores 85 where the mean is 70 and the standard deviation is 10.

Calculation: z = (85 - 70) / 10 = 15 / 10 = 1.5. The score is 1.5 standard deviations above the mean. On a normal curve, that puts it near the 93rd percentile, so about 93 percent of students scored lower.

On a bell-shaped curve, common z-scores map to familiar percentiles.

About 68 percent of values fall within one standard deviation of the mean, and 95 percent within two, the empirical rule.

The two are closely linked but answer different questions.

You need the standard deviation of the set to compute a z-score, so the two work hand in hand.

The Distance from the Mean

A value far from the mean gives a larger z-score, positive if above and negative if below.

The Standard Deviation

A larger standard deviation shrinks the z-score, since the same gap is now a smaller share of the spread.

The Shape of the Data

The percentile assumes a roughly normal curve. Skewed data can make the percentile less reliable.

Comparing Scores

Put results from different tests or scales onto one comparable footing.

Finding a Percentile

Turn a value into the share of a normal population below it.

Spotting Outliers

Flag values more than two or three standard deviations from the mean.

1. Using the Wrong Standard Deviation

Use the standard deviation of the same data set the value comes from.

2. Dividing Before Subtracting

Subtract the mean first, then divide by the standard deviation.

3. Forgetting the Sign

A value below the mean gives a negative z-score. The sign shows direction.

4. Assuming a Normal Curve Always Fits

The percentile relies on a bell shape. Skewed data can make it misleading.

5. Confusing Z with a Percentage

A z-score is a count of standard deviations, not a percentage. The percentile is the percentage.

The z-score is exact; the percentile uses a close normal approximation.

A z-score tells you how many standard deviations a value is from the mean. A z-score of 1.5 means the value is one and a half standard deviations above average. A negative score means it is below the mean.

Subtract the mean from the value, then divide by the standard deviation. For a value of 85 with a mean of 70 and a standard deviation of 10, the z-score is (85 minus 70) over 10, which is 1.5.

A negative z-score means the value is below the mean. A z-score of -2, for example, is two standard deviations below average, which sits near the 2nd percentile on a normal curve.

A z-score maps to the share of a normal curve below it. A z of 0 is the 50th percentile, 1 is about the 84th, and 2 is about the 98th. This tool reports the percentile for you.

Most values fall within two standard deviations of the mean, so a z-score beyond plus or minus 2 is unusual, and beyond plus or minus 3 is rare. Whether that is good depends on the context.

For a normal curve, about 68 percent of values lie within one standard deviation of the mean, 95 percent within two, and 99.7 percent within three. It is a quick guide to how z-scores spread.

Because each z-score is measured in standard deviations, it removes the original units. A test score and a height both become z-scores, so you can compare how far each stands from its own average.

The z-score itself does not, but the percentile does. If the data is skewed, the z-score is still valid, but the percentile from the normal curve may be less accurate.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Standard score (Wikipedia).
• Z-scores explained (Maths Is Fun).
• The normal distribution (Wikipedia).