Z-Score Calculator · Practical guide
What Percentile Is a Z Score of 1.5?
A z-score of 1.5 puts you at the 93.3rd percentile — higher than roughly 93% of a normally distributed population.
At a glance
Z = 1.5 Is the 93.3rd Percentile
Assuming a normal distribution, a z-score of 1.5 means the value is 1.5 standard deviations above the mean, and the area under the curve to its left is 93.32%. So roughly 93.3% of values fall below it and only 6.7% fall above. This calculator estimates the percentile from the standard normal cumulative distribution function, which is exactly the table lookup you'd do by hand.
Interactive tool
Z-Score Calculator
Enter your own values, then compare the result with the examples below.
Results
Percentiles for Common Z Scores
| Z score | Percentile | Share above it |
|---|---|---|
| −2.0 | 2.3% | 97.7% |
| −1.0 | 15.9% | 84.1% |
| 0.0 | 50.0% | 50.0% |
| 1.0 | 84.1% | 15.9% |
| 1.5 | 93.3% | 6.7% |
| 2.0 | 97.7% | 2.3% |
| 3.0 | 99.9% | 0.1% |
What 1.5 Looks Like in Real Terms
Two quick examples. On a test with mean 75 and standard deviation 8, z = 1.5 corresponds to a score of 75 + 1.5 × 8 = 87. For men's height in the US (mean ≈ 69 in, σ ≈ 3 in), z = 1.5 is about 73.5 inches — 6 ft 1.5 in. In both cases the person or score stands taller than about 93% of the group.
A Caveat About Normality
The percentile conversion assumes your data is approximately normal. For skewed data — incomes, reaction times, city populations — the same z-score can correspond to a very different real-world rank. The z-score itself is always valid; the percentile interpretation depends on the distribution's shape.
Frequently Asked Questions
Is a z score of 1.5 good?
It depends on context, but statistically it is strong: better than about 93% of a normal population, and inside the ±2 range considered typical rather than an outlier.
What percentile is a z score of −1.5?
The mirror image: the 6.7th percentile. About 6.7% of values fall below it and 93.3% above. Percentiles for ±z always sum to 100%.
How do I convert a percentile back to a z score?
Use the normal table in reverse. The 93.3rd percentile maps back to z = 1.5; the 50th percentile is z = 0; the 97.7th is z = 2.
Does z = 1.5 always mean the 93rd percentile?
Only when the underlying data follows a normal distribution. The calculator's percentile uses that standard assumption; skewed data will not match the table.