Standard Score Calculator
Standard score calculator works out z score and Raw score from What to compute, Raw score (x) and Mean (μ). The default figures on this page give z score of 1.250000; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
2 steps
- z = (x - mu) / sigma = (85 - 70) / 12 = 1.25.
- Area to the left of z under the standard normal curve: Phi(1.25) = 0.89435023, i.e. the 89.435th percentile.
Its 7 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the standard score calculator calculates
Converts between a raw score and a standard score z = (x - μ) / σ, computes the mean and standard deviation from a data set when they are not known, gives the percentile and tail areas under the normal curve, and computes the one-sample z statistic with its p-value.
How to use this standard score calculator
Enter What to compute, Raw score (x), Mean (μ) and Standard deviation (σ). Z score updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind z score, Raw score and Percentile (area to the left).
The method follows NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.6.6.1 Normal Distribution, NIST/SEMATECH e-Handbook of Statistical Methods, 7.2.2 Two-sided and one-sided tests / 1.3.5.2 Confidence limits for the mean and Abramowitz M, Stegun IA. Handbook of Mathematical Functions, chapter 26.
x = 85 in a distribution with mean 70 and sd 12 example
With What to compute: z-from-raw, Raw score (x): 85, Mean (μ): 70, Standard deviation (σ): 12, the calculator returns z score: 1.25, T score (mean 50, sd 10): 62.5, Deviation score (mean 100, sd 15): 118.75. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects z score, Raw score and Percentile (area to the left). The inputs you can vary are What to compute, Raw score (x), Mean (μ), Standard deviation (σ), z score and Data set.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
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Frequently asked questions
How do you calculate a standard score?
Converts between a raw score and a standard score z = (x - μ) / σ, computes the mean and standard deviation from a data set when they are not known, gives the percentile and tail areas under the normal curve. Open “How this is worked out” beside the result to see each step for your own figures.
Is 95% 2 standard deviations?
Converts between a raw score and a standard score z = (x - μ) / σ, computes the mean and standard deviation from a data set when they are not known, gives the percentile and tail areas under the normal curve. On the figures this page opens with — raw score (x) 85, mean (μ) 70 and standard deviation (σ) 12 — the z score is 1.25. Put your own figures in their place and the working updates beside the result.
Is a standard score of 80 average?
On the figures this page opens with — raw score (x) 85, mean (μ) 70 and standard deviation (σ) 12 — the z score is 1.25. No single number fits everyone: change any figure above and the answer updates as you type, with each step of the arithmetic beside it.
How do you convert standard score to standard deviation?
It needs What to compute, Raw score (x), Mean (μ), Standard deviation (σ), z score and Data set. Nothing else is required, and the figures stay in your browser.
What information do I need for the standard score calculator?
You need What to compute, Raw score (x), Mean (μ), Standard deviation (σ), z score, Data set, Standard deviation basis and Sample mean (x̄). The page opens with default figures that give z score of 1.250000, so you can see the scale before entering your own.
What does this standard score calculator show?
It shows z score, Raw score, Percentile (area to the left), P(Z < z), P(Z > z), Two-tailed p-value, Mean used and Standard deviation used, with the working and any warnings for your entries.