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.
Open the Confidence Interval Calculator
About Z-score Calculator
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.
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