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Free z-score to percentile calculator for the standard normal distribution. Get cumulative probability P(Z ≤ z), approximate percentile rank, and the right tail P(Z > z)—ideal for intro statistics, standardized tests, and normal-model checks.
Last updated: April 13, 2026
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Assumes a standard normal curve (mean 0, standard deviation 1). For raw scores use z = (x − μ) / σ first.
Approximate percentile
97.5002
About 97.5002% of the standard normal distribution lies below z = 1.96
P(Z ≤ z)
0.975002
Left / cumulative area
P(Z > z)
0.024998
Right-tail area
Standard normal CDF
Φ(1.96) = 0.975002
Quick reference (empirical rule)
Interprets your z-score as “what fraction of a standard normal population lies below this value,” expressed as a percentage.
The cumulative area from −∞ to z. This is the number you would read from a standard normal table for that row/column.
One minus the CDF. Useful for upper-tail rejection regions and “greater than” statements in hypothesis tests.
This tool expects z for N(0,1). If you only have a raw score, divide its distance from the mean by the standard deviation, then paste z here.
Use alongside z-tables to verify hand calculations for AP Stats, research methods, and business analytics modules.
After finding a percentile from z here, you can cross-check with an inverse normal calculator by feeding the same cumulative probability.
z = 1.96 (two-tailed 95% reference)
Φ(1.96) ≈ 0.9750 → percentile ≈ 97.5002
So about 97.50% of the standard normal lies below 1.96; the upper tail is about 2.50%.
Your input is parsed as a real number z. We evaluate the standard normal cumulative distribution Φ(z) using the error function relationship Φ(z) = ½(1 + erf(z/√2)). The reported percentile is 100Φ(z). The right tail is 1 − Φ(z). All of this assumes the bell-curve model on our Math & Science calculators hub.
Φ(z) = P(Z ≤ z) for Z ~ N(0, 1)percentile = 100 × Φ(z)P(Z > z) = 1 − Φ(z)Explore normal CDF and inverse normal for the full forward-and-inverse workflow.
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