Standardising · The normal curve
Z-Score Calculator
Turn a raw value into a z-score (how many standard deviations it sits from the mean), convert a z-score to a percentile, or go the other way — all placed on a shaded normal curve so you can see exactly where the value falls.
Result
In plain English
A z-score answers one question: how unusual is this value? It re-expresses a number as “how many standard deviations from the average” it sits, so values measured on totally different scales become comparable — and you can read off the percentile straight from the normal curve.
- z-score
- How many standard deviations a value is from the mean. z = 0 is exactly average; z = +2 is two SDs above; negative is below.
- percentile
- The share of the distribution that falls below your value. The 90th percentile means you scored higher than 90% of the group.
- μ and σ
- The mean (average) and standard deviation of the group you're comparing against — the yardstick the z-score is measured in.
- area below / Φ(z)
- The shaded part of the curve to the left of your value — exactly the percentile, as a probability between 0 and 1.
- the assumption
- Reading a percentile off a z-score assumes the data are roughly bell-shaped (normal). For very skewed data, treat the percentile as a rough guide.
Frequently asked
Is a z-score of 2 high?
Fairly high — about the 98th percentile, i.e. larger than ~98% of a normal distribution. Roughly 95% of values fall within ±2 SD of the mean, so |z| ≥ 2 is the usual “unusual” threshold — though it isn't automatically important or “significant.”
Can a z-score be negative?
Yes. A negative z-score just means the value sits below the mean; the sign gives the direction and the magnitude gives how many standard deviations away it is.
What does converting a z-score to a percentile assume?
That the data are roughly normal (bell-shaped). The z-score itself is always defined, but for very skewed data the percentile reading becomes only a rough guide.
How do I calculate a z-score?
Subtract the mean from your value and divide by the standard deviation: z = (x − μ) ÷ σ. The result is how many standard deviations the value sits above (positive) or below (negative) the mean. Because it strips out the original units, z-scores let you compare values measured on completely different scales — a test mark against a height, say — on one common ruler.