About Z-Score to Percentile Calculator
This calculator converts a raw score to a z-score and then to a percentile, the percentage of a normal distribution that falls below it. The calculator opens with the score 85 on a test with mean 70 and standard deviation 10. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The percentile is the area to the left of z under the standard normal curve, times 100. A z-score of 0 is the 50th percentile, 1 is about the 84th and 2 is about the 98th.
How to use Z-Score to Percentile Calculator
- 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.
Worked examples
x = 85, mean 70, sd 10 gives z = 1.5, 93.32th percentile
A z-score of 1.5 beats about 93% of values.
Common z-scores and their percentiles
| z | Area to the left | Percentile |
|---|---|---|
| -3 | 0.00135 | 0.13% |
| -2.576 | 0.004998 | 0.5% |
| -2 | 0.02275 | 2.28% |
| -1.96 | 0.024998 | 2.5% |
| -1.645 | 0.049985 | 5% |
| -1 | 0.158655 | 15.87% |
| 0 | 0.5 | 50% |
| 1 | 0.841345 | 84.13% |
| 1.645 | 0.950015 | 95% |
| 1.96 | 0.975002 | 97.5% |
| 2 | 0.97725 | 97.72% |
| 2.576 | 0.995002 | 99.5% |
| 3 | 0.99865 | 99.87% |
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.
What percentile is a z-score of 1?
About the 84th percentile, because 84.13% of a normal distribution is below one standard deviation above the mean.
Is a percentile the same as a percent?
No. A percentile is the percentage of values below yours. A score in the 90th percentile is higher than 90% of scores.
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.
- 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.
- Find X From a Z-ScoreEnter a z-score, the mean and the standard deviation to get the raw score.
- Probability Between Two Z-ScoresEnter a lower and an upper value to get the area between them under the normal curve.