How do I convert a z-score to percentile?

Look up your z-score in a z-table to find the cumulative probability, then multiply by 100. For example, z = 1.0 corresponds to the 84th percentile. This calculator does this conversion automatically.

What z-score is the 95th percentile?

The 95th percentile corresponds to z = 1.645 for one-tailed or z = 1.96 for two-tailed situations. The 99th percentile is z = 2.326 (one-tailed) or z = 2.576 (two-tailed).

Z-Score Calculator - Calculate Standard Scores & Percentiles

Value (x)

Mean (μ or x̄)

Standard Deviation (σ or s)

What is a Z-Score?

A z-score (also called a standard score) tells you how many standard deviations a value is from the mean. It allows you to compare values from different distributions on a standardized scale.

Z-Score Formula

z = (x - μ) / σ

Where:

z = z-score
x = the value being standardized
μ = the mean of the distribution
σ = the standard deviation

To find the original value from a z-score:

x = (z × σ) + μ

Interpreting Z-Scores

Z-Score	Meaning
z = 0	Value equals the mean
z > 0	Value is above the mean
z < 0	Value is below the mean
z = 1	Value is 1 SD above mean
z = -2	Value is 2 SD below mean

Common Z-Score Benchmarks

z = ±1.96 → 95% confidence interval bounds
z = ±2.58 → 99% confidence interval bounds
z = ±3 → Typical outlier threshold

Applications of Z-Scores

Comparing scores from different tests
Identifying outliers in datasets
Calculating percentiles in normal distributions
Quality control in manufacturing
Standardizing data for statistical analysis

Frequently Asked Questions

How do I calculate a z-score?

To calculate a z-score, use the formula: z = (x - μ) / σ, where x is your value, μ is the mean, and σ is the standard deviation. For example, if a test score is 85, mean is 75, and SD is 10: z = (85-75)/10 = 1.0.

What does a z-score tell you?

A z-score tells you how many standard deviations a value is from the mean. z = 0 means the value equals the mean. z = 1 means it’s 1 SD above the mean. z = -2 means it’s 2 SD below the mean.

What is a good z-score?

It depends on context. For percentiles: z > 0 is above average. For outlier detection: |z| > 3 often indicates an outlier. For hypothesis testing at α=0.05: |z| > 1.96 is significant.

How do I convert z-score to percentile?

Use the z-table to find the cumulative probability. For z = 1.0, the percentile is 84.13%. For z = -1.5, it’s 6.68%. This calculator shows percentiles automatically.

What is the z-score for 95th percentile?

The z-score for the 95th percentile is approximately 1.645. For the 97.5th percentile (used in 95% two-tailed tests), z = 1.96.

How do I convert percentile to z-score?

Find the probability in the z-table body and read the corresponding z-value. For example, 90th percentile (0.90 probability) corresponds to z ≈ 1.28.

Z-Table - Full standard normal table
Standard Deviation Calculator - Calculate σ for your data
T-Test Calculator - Compare means statistically
Probability Calculator - Calculate probabilities
Normal Distribution - Learn about the bell curve