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Z-Score Calculator

Convert raw scores to z-scores and read off normal distribution probabilities, including left-tail, right-tail, and two-tailed p-values from z.

Mean (mu)

Standard deviation (sigma > 0)

Value (x)

This treats x as a value from a normal distribution N(mu, sigma^2) and computes its z-score and probabilities.

z score calculatorp-value from z (two-tailed)

z-score

1.96

P(X <= x) (left-tail)

0.975002

P(X >= x) (right-tail)

0.024998

Two-tailed p-value for |z|

0.049996

Use this for quick normal distribution look-ups like z = 1.96 or z = -2.5.

P(Z <= z)

0.975002

P(Z >= z)

0.024998

Two-tailed p-value

0.049996

Enter a mean, standard deviation, and raw score x to compute its z-score.
Read off left-tail, right-tail, and two-tailed probabilities from the normal distribution.
Alternatively, enter a z value directly to convert z scores to p-values.

The underlying variable is approximately normally distributed with mean mu and standard deviation sigma.
Probabilities are computed using a high-quality approximation to the standard normal CDF.
Results are rounded for readability but retain enough precision for most homework and exam questions.

Is this the same as using a z table?: Yes. This z score calculator automates the same standard normal lookup you would do with a printed z table, but gives you left, right, and two-tailed probabilities instantly.
Can I use this for p-values in hypothesis tests?: Yes. Enter your test statistic as a z-score or compute it via mu, sigma, and x, then use the two-tailed probability as the p-value for a two-sided z test.
Does it support t-distributions?: This tool focuses on the normal distribution and z-scores. For small samples or unknown variance, you would typically use a t-distribution instead.

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