Donaldson R F Z-Score Calculator
See how many standard deviations a value sits from the mean — and what percentage of a normal distribution falls below it.
–Z-score
–Below (left tail)
–Above (right tail)
–Two-tailed
What a z-score tells you
A z-score is (x − μ) ÷ σ: the number of standard deviations a value lies above (positive) or below (negative) the mean. Assuming the data follow a normal distribution, the percentage below the value is the cumulative probability for that z-score; about 68% of values fall within ±1, 95% within ±2 and 99.7% within ±3. The two-tailed figure is the probability of a value at least this far from the mean in either direction. Enter the population standard deviation, or the sample standard deviation if that is all you have.