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Z-Score Calculator
See where a raw score sits in a normal distribution, as a z-score, a percentile, and a probability.
HOW TO USE
- 1Enter the raw score you want to place, the population mean and the population standard deviation.
- 2The z-score shows how many standard deviations the raw score sits above (positive) or below (negative) the mean.
- 3The percentile rank is the percentage of the population expected to score at or below the raw score.
- 4The probabilities give the chance that a random value from the population falls at or below, or above, the raw score.
EXAMPLE
INPUT
Raw score 85, mean 75, standard deviation 10
OUTPUT
z = 1 · 84.13th percentile · P(X ≤ 85) = 0.8413
FAQ
What is a z-score?
A z-score is the number of standard deviations a raw score is from the mean: z = (x − μ) / σ. A score of 85 with mean 75 and standard deviation 10 gives z = 1, one standard deviation above the mean.
How is the percentile rank calculated?
The percentile rank is the standard normal cumulative distribution function (CDF) at the z-score, expressed as a percentage, the area under the bell curve to the left of the score. A z-score of 1 sits at the 84.13th percentile.
What does a negative z-score mean?
The raw score is below the mean. Its percentile is below 50 — for example z = −2 sits at roughly the 2.28th percentile.
What is the difference between the two probabilities?
P(X ≤ x) is the probability a random value is at or below the raw score — identical to the percentile rank as a fraction. P(X > x) is the complementary probability that a value exceeds it. The two always add up to 1.
Is my data sent anywhere?
No. All calculations run entirely in your browser, your numbers never leave your device.