About Find X From a Z-Score
This calculator reverses the z-score formula. Given z, the mean and the standard deviation it returns the raw score x, and the percentile that score sits at. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
How to use Find X From a Z-Score
- Choose what you want to find: z from x, x from z, a probability, a percentile to z, or a z-table lookup.
- Enter the values. For a raw score you need the mean and the standard deviation of the distribution.
- For a probability, pick Below, Above, Between or Outside and enter one or two limits.
- Read the headline answer, the percentile and the other areas. The shaded bell curve shows which area is meant.
- Open the working to see the formula with your numbers filled in.
Features
- Z from x, x from z, and percentile to z-score in one page.
- Probabilities below, above, between and outside, with the shaded area on a bell curve.
- Percentile and both tail areas for every z-score.
- Step-by-step working in written-out formulas.
- Full standard normal z-tables, for negative and positive z, on the z-table page.
- Accurate to many decimals, not rounded to the four digits of a printed table.
- Copy the results as text. Works on a phone.
Raw score from a z-score
Multiply the z-score by the standard deviation and add the mean.
x = mean + z x sdWorked examples
IQ: mean 100, sd 15, z = 2 gives x = 130
100 + 2 x 15 = 130.
Test: mean 70, sd 10, z = -1.5 gives x = 55
70 + (-1.5) x 10 = 55.
Privacy: how it works
- Everything is calculated in your browser tab. The values you enter are not sent to Ulkaa or to any other server.
Tips
- Percentile and probability below are the same number, shown once as a percent and once as a decimal.
- A z-score beyond 3 in either direction is rare for normal data, about 0.27% in total.
- To find a critical value for a confidence level, use percentile to z with 100 minus half the tail: 97.5 for 95%.
- The standard deviation must be greater than 0.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your values are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your values are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I find x when I know z?
Compute mean + z x standard deviation. A negative z gives a value below the mean.
Can I find the score for a given percentile?
Yes. Use the percentile to z-score page, which also shows the raw score.
More Z-Score Calculator pages
- Z-Score CalculatorTurn a raw score into a z-score and a percentile, or find the probability under the normal curve.
- Z-Table (Standard Normal Table)Look up the area to the left of any z-score, in the calculator or in the full tables below.
- Z-Score to Percentile CalculatorEnter a score, the mean and the standard deviation to get the z-score and its percentile.
- Percentile to Z-Score CalculatorEnter a percentile to find the z-score with that share of the distribution below it.
- Z-Score Probability CalculatorChoose a region, enter a value and read the probability under the normal curve.
- Probability Between Two Z-ScoresEnter a lower and an upper value to get the area between them under the normal curve.