Z-Score Calculator
Convert a raw score to a z-score, convert between z-scores and probabilities, and find the probability between two z-scores.
Change the values and press Calculate to work out your own figures.
z-score from a raw score
Enter a raw score, the mean and the standard deviation.
Show the working
- z = (x − μ) ÷ σ = (5 − 3) ÷ 2 = 1
Probabilities for a z-score
Enter a z-score.
Show the working
- Φ(2) = 0.9772498681
z-score for a probability
Enter a probability and say which area it is.
Show the working
- Invert the standard normal CDF: z = 1.959963985
Probability between two z-scores
Enter a left and right z-score.
Show the working
- Φ(0) − Φ(-1) = 0.3413447461
How to use it
Enter a raw score, the mean and the standard deviation. Enter a z-score. Enter a probability and say which area it is. Enter a left and right z-score.
Probabilities can be typed as decimals, fractions or percentages. Show the working gives the formula with your numbers in it.
Key facts
z = (x − μ) ÷ σ
What a z-score says
A z-score says how many standard deviations a value is from the mean: z = 2 is two standard deviations above. For normal data about 95% of z-scores lie between −2 and 2.
Questions
What is the z-score of 5 if the mean is 3 and SD is 2?
1.
What z-score is the 97.5th percentile?
1.959963985.
Formulas
z = (x − μ) ÷ σ
Sources
Limitations
- Probabilities can be typed as decimals (0.25), fractions (1/4) or percentages (25%).