Free Z-Score Calculator Online – Calculate Z-Score
Find the z-score and the probability under the normal curve.
About the Z Score Calculator
What is the Z Score Calculator?
A z score calculator standardizes a raw value against its distribution and gives its normal-curve probabilities.
Why use this calculator?
Test scores, height data and any bell-shaped measure need comparisons in "standard deviations above the mean" — the definition of a z-score.
How to use it
- Enter a raw score, the mean and the standard deviation.
- Read the z-score and the percentile (probability below).
- Also see the probability of being above the score.
Formula
z = (x − μ) ÷ σ; the standard normal CDF gives probabilities.
Assumes normality. For small samples, use a t-distribution instead.
Frequently Asked Questions
What does a z-score of -2 mean?
Two standard deviations below the mean — roughly the 2.3rd percentile in a normal distribution.
Is z-score same as a t-statistic?
Related but not identical: z uses a known σ, while t uses an estimated σ from a small sample.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
What is the difference between population and sample?
A population includes every member of a group; a sample is a subset. Sample statistics use n−1 in the denominator to correct for bias.
When should I use median instead of mean?
Use the median when data contains outliers or is skewed, because it is less affected by extreme values than the mean.
What does standard deviation tell me?
It measures how spread out the values are around the mean. A small standard deviation means the data clusters tightly; a large one means it is more scattered.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.