Convert a value to a z-score from the mean and standard deviation, and get its percentile and the tail areas of the normal distribution.
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With value (x) 130, mean (μ) 100, standard deviation (σ) 15, the z-score is 2.
| Value (x) | 130 |
|---|---|
| Mean (μ) | 100 |
| Standard deviation (σ) | 15 |
| Z-score | 2 |
|---|---|
| Percentile (area below) | 97.72498681% |
| Area above | 2.275013195% |
| Two-tailed p-value | 4.55002639% |
| Area within ±|z| | 95.44997361% |
A z-score says how many standard deviations a value lies above or below the mean. If the data follow a normal (bell-shaped) distribution, the z-score also gives the share of values below it, its percentile. The calculator evaluates the normal distribution accurately in the far tails, so very unusual values still get meaningful probabilities.
z = (x − μ) ÷ σ. Percentile = Φ(z) × 100, where Φ is the standard normal cumulative distribution. A z-score says how many standard deviations a value lies above or below the mean. If the data follow a normal (bell-shaped) distribution, the z-score also gives the share of values below it, its percentile. The calculator evaluates the normal distribution accurately in the far tails, so very unusual values still get meaningful probabilities.
With value (x) 130, mean (μ) 100, standard deviation (σ) 15, the z-score is 2. Percentile (area below): 97.72498681%; Area above: 2.275013195%; Two-tailed p-value: 4.55002639%; Area within ±|z|: 95.44997361%.
This is an estimate based on the inputs and assumptions shown on this page, not professional advice. Check anything with financial, health or safety consequences independently.
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The value is two standard deviations above the mean. Under a normal distribution about 97.7% of values are lower, so it is near the 98th percentile.
About 1.645. A z-score of 1.96 marks the 97.5th percentile, which is why ±1.96 bounds the middle 95% of a normal distribution.
The z-score itself still measures distance from the mean in standard deviations, but its percentile from the normal curve can be misleading for skewed data. Check the data's shape first.