Z-Score Calculator
See how many standard deviations a value sits from the mean — then flip it around to recover the raw value from any z-score.
Go the other way — value from a z-score
How it works
A z-score answers one question: how far is this value from the average, measured in standard deviations? The formula is z = (x − μ) / σ, so it subtracts the mean and divides by the spread.
A positive z means the value is above the mean, negative means below, and zero means it's right on the average. A z of 2 says the value is two standard deviations up — unusual, since roughly 95% of a normal dataset falls within two either side.
Going the other way, x = μ + z·σ rebuilds the raw value. If a class averages 70 with a standard deviation of 10, a z of 1.5 corresponds to a score of 70 + 1.5×10 = 85.
Frequently asked questions
What counts as a high or low z-score?
Roughly speaking, z-scores between −2 and 2 are ordinary — that band holds about 95% of a normal distribution. Past ±2 the value starts looking unusual, and beyond ±3 it's genuinely rare, the kind of outlier worth a second look.
Can a z-score be negative?
Absolutely. A negative z-score just means the value falls below the mean. A score of −1.2 sits 1.2 standard deviations under the average, while +1.2 sits the same distance above it.
Why does the calculator show a dash?
If the standard deviation is zero, every value equals the mean and dividing by zero has no answer, so you'll see a dash. Give it a real, non-zero spread and the z-score appears.
Do I need the population or sample standard deviation?
Either works — just be consistent. Use whichever matches your data: population σ when your numbers cover the whole group, sample s when they're a subset. The z-score formula treats the input the same way regardless.