Z-Score

Compute the standard score z = (x - mean) / standard deviation

About this calculator

The Z-Score Calculator standardizes a raw value with z = (x − mean) ÷ standard deviation, then converts it into standard-normal probabilities: the percentile P(Z ≤ z), the right tail P(Z > z), and the two-tailed probability P(|Z| > |z|). The normal CDF uses the Abramowitz–Stegun approximation, accurate well past the four displayed decimals. A non-positive standard deviation is rejected with a clear error. Useful for test scores, IQ scales, quality control, and any comparison across different normal distributions.

How to use the Z-Score calculator

  1. Enter the values for your problem into the input fields.
  2. Read the result — it updates instantly as you type.
  3. Check the formula and the visual explanation to follow how the answer was found.
  4. Copy the page URL to share the exact calculation.

Common examples

  • Score 85 with mean 70 and σ = 10 → z = 1.5, percentile 93.3193%
  • IQ 130 with mean 100 and σ = 15 → z = 2, right tail 2.2750%
  • x = 45 with mean 60 and σ = 12 → z = −1.25, percentile 10.5650%
  • x equal to the mean (70, σ = 5) → z = 0, exactly the 50th percentile

Frequently asked questions

How does the Z-Score calculator work?

Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.

When would I use the Z-Score calculator?

It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.

How accurate are the results?

Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.