Z Score Calculator
Use a raw value with its mean and standard deviation to find a z-score, or start with z to explore percentiles and standard-normal probabilities.
See the z-score in context
Enter your values, or try an example.
Your results and calculation will appear here.
Show calculation
How to use this calculator
- Choose value to z-score or z-score to probability.
- Enter your value, mean and standard deviation, or enter z directly.
- Calculate to see distance from the mean and the shaded area below z.
Worked example: exam score
mode: value · x: 84 · mean: 70 · sd: 10
Z-score = 1.4
This value is 1.4 standard deviations above the mean.
Example calculation
- z = (84 − 70) / 10 = 1.4.
- Probability below = Φ(1.4) = 0.9192.
- Probability above = Φ(-1.4) = 0.0808.
- Two-tailed standard-normal p-value = 2Φ(−|z|) = 0.1615. This is not a full hypothesis test.
Formula & assumptions
z = (x − μ) / σ; below = Φ(z); above = Φ(−z); two-tailed = 2Φ(−|z|).
- Standard deviation must be positive.
- A z-score describes distance from a mean; normal probabilities and percentiles assume a normal model.
- The two-tailed standard-normal p-value is not a complete hypothesis test.
Z Score to Percentile and Percentage
A z-score can be converted to a percentile using the standard normal cumulative distribution Φ(z). For example, z = 1.40 corresponds to approximately the 91.92nd percentile, meaning that 91.92% of the standard normal distribution lies below that value.
A z-score, also called a standardized score or z value, indicates how many standard deviations an observation is above or below the mean. A positive z-score is above the mean, while a negative z-score is below it.
Percentile = Φ(z) × 100%
Φ(1.40) ≈ 0.9192 → 91.92nd percentile
Sources
Reviewed: October 2026
Common questions
What does a negative z-score mean?
The value is below the mean. For example, z = −1 is one standard deviation below the mean.
Is a percentile always valid for my data?
No. The percentile shown here comes from a normal model, not the empirical rank of a value in your dataset.
How do I convert a z-score to a percentage?
Find the cumulative standard normal probability for your z-score and multiply it by 100. For example, a z-score of 1.40 corresponds to approximately 91.92% below that value. If you need the percentage above the z-score instead, subtract the cumulative percentage from 100%.
Reference tables
Look up standard normal probabilities in the complete Z Table. Browse all statistical tables.
Use these tools for mathematical information, not as a substitute for checking assumptions. Read our methodology or disclaimer.