justyourcalculatorZ-Score Calculator
Standardize a value and read its probabilities from the normal curve.
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Z-Score Calculator
Z-scores and normal probabilities
Z-score
1.5
1.5 standard deviations above the mean
- P(Z < 1.5)left tail (percentile)
- 0.933193
- P(Z > 1.5)right tail
- 0.066807
- P(0 < Z < 1.5)
- 0.433193
- P(-1.5 < Z < 1.5)central area
- 0.866386
- P(Z < -1.5 or Z > 1.5)two tails
- 0.133614
How it was calculated
- z = (x - μ) / σ
- z = (85 - 70) / 10 = 15 / 10 = 1.5
- Percentile: Φ(1.5) = 0.933193, so about 93.32% of values are lower
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How the z-score calculator works
A z-score says how many standard deviations a value is from the mean: z = (x - μ) / σ. A z of 0 is exactly average, +2 is two standard deviations above, and -1.5 is one and a half below.
For normally distributed data, the z-score maps to a probability through the standard normal cumulative distribution Φ(z). Φ(z) is the share of values below z (the percentile); 1 - Φ(z) is the share above.
Probabilities here are computed with a double-precision normal CDF (accurate to about 15 digits), and the inverse uses Acklam's method refined against it, so they match printed z-tables and statistics software.
Using and checking your result
Published by JustYourCalculator. Check the units and assumptions above, and compare a known example before relying on the output. Calculations use browser arithmetic and may round displayed values.
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