Z-Score & Normal Distribution Calculator (Free)

Use this free z-score calculator to standardize a value and read its probability under the normal distribution. Enter the mean, the standard deviation and a value x, and you’ll get the z-score, the percentile P(X < x), the tail P(X > x), and a shaded bell curve.

How to use the calculator

1. Enter the mean μ and standard deviation σ of the distribution.
2. Enter the value x you want to standardize.
3. Read the z-score, the probabilities, and the bell-curve graph.

What a z-score means

A z-score tells you how many standard deviations a value is from the mean: z = (x − μ)/σ. The calculator then converts that z-score into a probability using the standard normal distribution.

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Frequently asked questions

How do you calculate a z-score?

Subtract the mean from the value and divide by the standard deviation: z = (x − μ)/σ. A value of 130 with μ=100, σ=15 gives z = 2.

What does P(X < x) tell me?

It’s the percentile — the probability that a randomly chosen value is below x. For z = 2 it’s about 0.9772, or the 97.7th percentile.

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What is the 68-95-99.7 rule?

About 68% of data lies within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3.

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