A z-score (standard score) tells you how far a number sits from the average, measured in standard deviations.
About this calculator
A z-score (standard score) tells you how far a number sits from the average, measured in standard deviations. If your CBSE maths score is 85 when the class mean is 70 with SD 10, your z-score is 1.5 — you are one and a half SDs above average, roughly the 93rd percentile on a normal bell curve.
Teachers use z-scores to compare marks across sections with different difficulty. Quality teams use them to flag factory readings that fall outside expected variation. Medical labs report some blood values as z-scores when comparing you to a reference population.
Enter the raw value, the mean, and the standard deviation. The calculator returns the z-score and an approximate percentile using the standard normal CDF. Negative z means below average; positive z means above. Values beyond ±2 are uncommon; beyond ±3 are rare and worth a second look.
For related work use the [[mean-median-mode]] calculator to find mean and SD from raw data, the [[confidence-interval]] calculator to build a range around a sample mean, and the [[probability]] calculator for event odds.
Common uses
- Compare exam marks across batches with different averages and spreads
- Spot unusually high or low readings in lab or factory QC data
- Convert raw scores to percentiles for scholarship or cutoff lists
- Standardise heights, weights, or sales figures before ranking
- Check whether a data point is a likely outlier before removing it
Frequently asked questions
What is a z-score in simple terms?
A z-score is how many standard deviations a value is from the mean. z = 0 means exactly average. z = 2 means two SDs above the mean, which is higher than about 97.5% of values on a normal curve.
How do I calculate z-score for exam marks?
Subtract the class mean from your score, then divide by the standard deviation. Example: score 78, mean 65, SD 8 gives z = (78 − 65) / 8 = 1.625.
What z-score is considered an outlier?
Many textbooks treat |z| > 2 as unusual (outside the middle 95%) and |z| > 3 as a clear outlier (outside 99.7%). Context matters — small SDs make moderate z-scores more common.
Can z-score be negative?
Yes. A negative z-score means the value is below the mean. z = −1.5 is one and a half standard deviations below average, around the 7th percentile.
What is the difference between z-score and percentile?
The z-score is a standardised distance from the mean. The percentile is the percentage of values at or below that point. z = 0 is the 50th percentile; z = 1 is about the 84th percentile.