Convert a raw value to a z-score and read off the normal-distribution probability, computed in your browser.
Z-score Calculator Online
Convert a raw value to a z-score and read off the normal-distribution probability, computed in your browser.
The Z-score Calculator runs entirely in your browser. The value, mean, standard deviation and z-scores you enter stay on your device and are never uploaded.
Z-score Calculator converts a raw value to a z-score — how many standard deviations it sits from the mean — and instantly reads off the matching probability from the standard normal distribution. Enter a value with its mean and standard deviation, or switch to Raw z-score mode and type a z-score directly. The tool returns the percentile P(X < z), the upper tail P(X > z), and the two-tailed p-value used for significance testing, using an accurate erf-based approximation of the normal curve. It is built for students checking a statistics homework answer, analysts screening for outliers, and anyone running a quick hypothesis test who needs a z-table lookup without leaving the page. Every calculation runs locally in your browser — no numbers are uploaded.
Features
Converts value, mean and standard deviation into a z-score instantly
Raw z-score mode for when you already have z and just need probabilities
Shows P(X < z), the percentile / left-tail probability
Shows P(X > z), the upper-tail probability
Computes the two-tailed p-value used for significance testing
Accurate erf-based approximation of the standard normal CDF
Copy a plain-text summary of the z-score and all three probabilities
Guards against a zero or negative standard deviation
How to use the Z-score Calculator
Choose From value or Raw z-score mode
Enter the value, mean and standard deviation (or the z-score directly)
Read the z-score and the percentile, upper-tail and two-tailed probabilities
Copy the summary for your report or homework
Example
Input
x=85, μ=70, σ=10
Output
z = 1.5 · P(<z) 0.933
A value 1.5 standard deviations above the mean sits at the 93.3rd percentile.
Common errors & troubleshooting
The z-score result shows nothing or an error banner. — The standard deviation must be greater than 0 — a zero or negative σ makes the z-score undefined, so enter a positive value.
P(X < z) and P(X > z) don't add up to what you expected. — They always sum to 1 by definition; check whether your question actually needs the two-tailed p-value instead of a single tail.
Percentile looks reversed for a negative z-score. — A negative z means the value is below the mean, so P(X < z) will correctly be under 50% — that is expected, not a bug.
Typed a percentage or standard error instead of the standard deviation. — The Z-score Calculator expects the raw standard deviation of the distribution, not a percentage, variance, or standard error of the mean.
Frequently asked questions
What does the Z-score Calculator actually compute?
It computes z = (x − μ) / σ from your value, mean and standard deviation, then looks up the matching probability on the standard normal distribution using an erf-based approximation of the z-table.
What is a z-score in plain terms?
A z-score is how many standard deviations a value sits from the mean of its distribution. A z-score of 1.5 means the value is 1.5 standard deviations above the mean.
What is the difference between P(X < z) and the two-tailed p-value?
P(X < z) is the percentile — the probability of landing below that z-score. The two-tailed p-value doubles the smaller tail and is what you compare against a significance threshold like 0.05 in a two-sided hypothesis test.
Can I enter a z-score directly instead of a raw value?
Yes. Switch the Z-score Calculator to Raw z-score mode and type the z-score to get its percentile, upper-tail and two-tailed probability without entering a mean or standard deviation.
How accurate is the normal distribution probability?
The calculator uses the Abramowitz and Stegun erf approximation of the standard normal CDF, which is accurate to within about 0.00015%, close enough for coursework, QA checks and real analysis.
Does the Z-score Calculator upload my numbers?
No. Every calculation happens locally in your browser. The values you type never leave your device and are not sent to ArrayKit.
Related tools
Standard Deviation Calculator — Calculate population and sample standard deviation, variance and mean of a data set.