Z-Score Calculator
Calculate a z-score and its probability from a value, mean, and standard deviation.
Runs in your browser — nothing is sent or saved.
How to calculate a z-score
- Enter the raw value, the mean, and the standard deviation.
- Choose whether the standard deviation is the population value or a sample estimate.
- Read the z-score and the probability.
- Copy the link to save or share it.
The z-score formula
A z-score, or standard score, tells you how many standard deviations a value sits from the mean. The z-score formula is z equals the value minus the mean, divided by the standard deviation. A positive z-score is above the mean, a negative one is below, and a z of 0 is exactly at the mean. So a score of 85 in a group with a mean of 70 and a standard deviation of 10 has a z-score of 1.5, meaning it is one and a half standard deviations above average.
Population versus sample
The z formula is the same either way, but which standard deviation you use matters for interpretation. With the population standard deviation you get a true z-score, and the percentile comes straight from the standard normal curve. With a small sample estimate, a t-score is often more appropriate than z, so the tool lets you label which one you are using and reminds you of the caveat.
From z-score to probability
Because a z-score places a value on the standard normal distribution, it maps to a probability. The tool shows the percentile, which is the area to the left of your z-score, along with the area to the right and the two-tailed probability. A z-score of 1.5 sits at about the 93rd percentile, so roughly 93% of values fall below it.
FAQ
How to calculate z-score values?
If you want to know how to calculate z-score figures, subtract the mean from the value, then divide by the standard deviation. The tool applies z equals (x minus mean) divided by standard deviation and shows the working.
What does a z-score tell me?
How far a value is from the mean, measured in standard deviations. A z of 2 means two standard deviations above the mean; a z of minus 1 means one below.
How do I turn a z-score into a probability?
Look up the area under the standard normal curve. The tool does this for you, giving the percentile and the tail probabilities.
Should I use a z-score or a t-score?
Use a z-score when you know the population standard deviation. With a small sample where you have only an estimate, a t-score is usually the better choice.
Is my information private?
Yes. Everything is calculated in your browser and nothing you enter is uploaded or saved.