Z-Score Calculator — Value, Percentile
Convert a value to a z-score and a z-score to a percentile (standard normal). Client-side.
Value → z-score
% below · % above
z-score → percentile
percentile (area to the left) · % above
How to use
- 1 Value → z-score: enter a value, the mean and the standard deviation.
- 2 z-score → percentile: enter a z-score to get the area under the normal curve.
- 3 Percentiles come from the standard normal distribution.
Why use this tool
- Convert a raw score to a z-score, and a z-score to a percentile.
- See how far a value is from the mean in standard deviations.
- Runs entirely in your browser.
Frequently asked questions
What is a z-score?
The number of standard deviations a value is from the mean: z = (x − μ) / σ. A z of +1 means one standard deviation above the mean.
How is the percentile found?
From the standard normal cumulative distribution function — the area under the bell curve to the left of the z-score.
What is a “good” z-score?
It depends on context. About 68% of values fall within z = ±1, 95% within ±2, and 99.7% within ±3 (the empirical rule).
How accurate is the percentile?
It uses a standard erf approximation accurate to about ±0.0005 in probability — plenty for coursework.
What is Z-Score Calculator?
A z-score calculator converts a raw value to a standard score z = (x − μ) / σ — the number of standard deviations from the mean — and maps a z-score to a percentile using the standard normal distribution.
Features
Standard score
Computes z = (x − μ) / σ, the signed number of standard deviations from the mean.
Live result
z updates instantly as you change the value, mean, or standard deviation.
Free & private
Runs on your device — nothing is uploaded.
Example
Input
x = 85, μ = 70, σ = 10Output
z = 1.5Common use cases
-
1
Standardize a value
Express a raw score relative to its distribution for comparison.
-
2
Grade curving
See how far above or below average a test score falls.
-
3
Outlier checks
Flag values with a large |z| as potential outliers.
Zerethon's z-score calculator computes the standard score z = (x − μ) / σ in your browser — how many standard deviations a value sits from the mean. Enter the value, mean, and standard deviation to get z live. Everything runs client-side — nothing is uploaded.
- Category
- Math
- Pricing
- Free
- Privacy
- Browser-based
- Signup
- Not required
References
- z-Score — Wolfram MathWorld — Wolfram MathWorld
- Standard score — Wikipedia
Privacy
Your data never leaves your browser unless explicitly stated. Z-Score Calculator runs entirely client-side — no server upload, no logging, no tracking of your input.
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