π― Z-Score Calculator
A z-score answers βis this value unusual?β by measuring distance from the average in standard-deviation units: z = (value β mean) / standard deviation. A score of 85 on a test averaging 70 with a spread of 10 gives z = 1.5.
Roughly 68% of values land within z = Β±1 and 95% within z = Β±2, so anything past Β±2 deserves a second look and anything past Β±3 is genuinely rare.
How to use this calculator
Enter the value, the mean and the standard deviation, then press Calculate for the z-score and a plain-English reading of it.
- Type the value you want to judge, for example a test score of 85.
- Type the mean of the group, for example 70.
- Type the standard deviation, for example 10.
- Press Calculate and read the z-score plus the interpretation line.
Frequently asked questions
What does this z-score calculator compute?
It computes z = (value minus mean) divided by the standard deviation, which measures how many standard deviations the value sits from the average. It then translates the score into plain language, from typical to very unusual.
Can you show a worked example?
A score of 85 with a mean of 70 and a standard deviation of 10 gives z = 1.5, meaning the score sits 1.5 standard deviations above the mean: between one and two deviations, somewhat unusual.
What counts as an unusual z-score?
About 68 percent of values fall within plus or minus 1 and about 95 percent within plus or minus 2, so scores beyond 2 deserve attention and scores beyond 3 are genuinely rare in bell-shaped data.
Can z-scores be negative?
Yes. A negative z-score simply means the value sits below the mean; the sign shows direction and the size shows distance. A z of -1.5 is exactly as unusual as a z of +1.5.