Z-Score Calculator
Compute z-scores, convert between z-scores and probabilities, and find probabilities between two z-scores
Calculate Z-Score
Enter your values to compute the z-score for a data point in a normal distribution.
Calculation Result
The z-score represents how many standard deviations your data point is from the mean.
Interpretation:
A z-score of 0 means your data point is exactly at the mean.
Z-Score to Probability Converter
Convert between z-scores and probabilities (equivalent to using a z-table).
Conversion Result
This is the cumulative probability from the left tail to the z-score.
Probability Between Two Z-Scores
Calculate the probability (area under the curve) between two z-scores.
Probability Result
The area under the normal distribution curve between the two z-scores.
Understanding Z-Scores and Normal Distribution
What is a Z-Score?
A z-score measures how many standard deviations a data point is from the mean of a distribution.
Where x is the raw score, μ is the mean, and σ is the standard deviation.
Normal Distribution
The normal distribution is a symmetric, bell-shaped curve where:
- ≈68% of data falls within 1 standard deviation
- ≈95% within 2 standard deviations
- ≈99.7% within 3 standard deviations
Z-Table and Probability
A z-table shows the cumulative probability for different z-scores. It tells you the area under the curve to the left of a given z-score.
This calculator performs the same function as a z-table, converting between z-scores and probabilities.