Percentile To Z Score Calculator

Work out percentile to z score instantly with clear inputs, formula shown and shareable results.

About Percentile To Z Score Calculator

Converting a percentile to a z score inverts the normal cumulative distribution. The 90th percentile is z = 1.2816, which on a mean 100, SD 15 scale is a score of 119.2 and a T score of 62.8. The relationship is strongly non-linear at the extremes: the 99th percentile is z = 2.33 but the 99.9th is 3.09.

Formulas

Inverse normal

z = probit(percentile / 100)

Score on a scale

score = mean + sd x z

Worked example

With the default values below, Percentile To Z Score Calculator returns z Score of 1.2816. Change any input above and every figure here is recalculated in your browser.

Inputs used

Percentile rankaccepts 0.01–99.99 %: 90 %
Distribution mean: 100
Distribution standard deviationminimum 0: 15

Results

z Score: 1.2816
Equivalent Score On Your Scale: 119.22
Equivalent T Score: 62.82
Percentile Recovered From The z Score: 90.000%

Step by step

1Values used
2Inverse normal
3Score on a scale
4z Score= 1.2816
5Equivalent Score On Your Scale= 119.22
6Equivalent T Score= 62.82
7Percentile Recovered From The z Score= 90.000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is the top of the scale so compressed?

Because the normal distribution has thin tails. Moving from the 99th to the 99.9th percentile takes only 0.76 of a standard deviation but excludes nine tenths of the remainder.

Does this need normality?

Yes. For a skewed distribution use empirical percentiles from the data rather than a normal transformation.