✓ Effortless Math · Free Tool

Z-Score & Normal Distribution Calculator

Enter a mean μ, a standard deviation σ, and a value x — get the z-score, the percentile P(X < x), the tail probabilities, a shaded bell-curve graph, and full step-by-step working.

Z-score:  z = (x − μ) / σ
z = ( value x − mean μ ) / std dev σ

The standard deviation σ must be positive. The mean μ and value x may be any real numbers. Decimals and negatives are fine.

Results

Z-score
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P(X < x) — percentile (left)
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P(X > x) — right tail
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68-95-99.7 rule context
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Graph — standard normal curve

Bell curveArea P(X<x)Value x

Step-by-step (z-score & percentile)