How do I calculate a z-score by hand?

Subtract the mean from the raw value, then divide that difference by the standard deviation. The formula is (x - μ) / σ, where x is the data point, μ is the mean, and σ is the standard deviation.

What does a z-score of 0 mean?

A z-score of 0 means the data point is exactly at the mean. It is neither above nor below average.

Can a z-score be negative?

Yes, a negative z-score indicates the data point is below the mean. The absolute value tells you how many standard deviations away it is.

How is percentile rank related to z-score?

Percentile rank shows the percentage of scores in a distribution that a particular z-score is higher than. A z-score of 1.5 roughly corresponds to the 93rd percentile.

When would I need to find the probability between two z-scores?

You use this when you want to know the proportion of data that falls within a specific range, such as between -1 and 1 standard deviations from the mean in a normal distribution.

Statistics3 options compared

Z-score Calculator

Calculates z-scores for normal distributions, converts between z-scores and probabilities, and computes probabilities between two z-scores. Students, researchers, and professionals in fields requiring statistical analysis frequently use this tool to understand how data points relate to a distribution's mean and standard deviation. It aids in hypothesis testing, confidence interval estimation, and...

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Editors’ Top PickBased on community votes

Omni Calculator

omnicalculator.com

The z-score calculator can help you determine the standard score for a data point.

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Other OptionsRanked by votes

02
02
Calculator.net
calculator.net
Calculator to find out the z-score of a normal distribution, convert between z-score and probability, and find the pr...
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03
03
SmartCalc
smartcalc.top
Free z-score calculator: enter a value, mean and standard deviation to get the z-score and percentile rank for test s...
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Side by side

Z-score Calculator options compared

Tool	Best for	Strengths	Limitations
Omni Calculator omnicalculator.com	Quick z-score calculations	Highest community votes Simple input fields for raw value, mean, and SD	No percentile rank or probability conversion shown on the main screen
Calculator.net calculator.net	Full probability conversions	Converts between z-score and probability in both directions Supports probability between two z-scores
SmartCalc smartcalc.top	Percentile rank and distance in one step	Shows z-score, percentile rank, and distance from mean together Explains formula with example (x=85, mean=70, SD=10)

Buyer's guide

How to choose a z-score calculator

When picking a z-score calculator, first decide what you need the result for. If you just want the standardized score quickly, choose a tool that asks for raw value, mean, and standard deviation and shows the z-score immediately. If you need to turn the z-score into a probability or percentile, look for a tool that includes probability conversion features, especially one that can find the area between two z-scores. If percentile rank or a visual reference to a reference table matters, pick a calculator that displays that alongside the score.

Questions

Z-score Calculator FAQ

How do I calculate a z-score by hand?: Subtract the mean from the raw value, then divide that difference by the standard deviation. The formula is (x - μ) / σ, where x is the data point, μ is the mean, and σ is the standard deviation.
What does a z-score of 0 mean?: A z-score of 0 means the data point is exactly at the mean. It is neither above nor below average.
Can a z-score be negative?: Yes, a negative z-score indicates the data point is below the mean. The absolute value tells you how many standard deviations away it is.
How is percentile rank related to z-score?: Percentile rank shows the percentage of scores in a distribution that a particular z-score is higher than. A z-score of 1.5 roughly corresponds to the 93rd percentile.
When would I need to find the probability between two z-scores?: You use this when you want to know the proportion of data that falls within a specific range, such as between -1 and 1 standard deviations from the mean in a normal distribution.

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