Zscore Calculator
Use this calculator to compute the zscore of a normal distribution.
Raw Score, x  
Population Mean, μ  
Standard Deviation, σ  
Zscore and Probability Converter
Please provide any one value to convert between zscore and probability. This is the equivalent of referencing a ztable.
Result
Given Z = 3.291,
P(x<Z) = 0.9995  
P(x>Z) = 0.00049916  
P(0<x<Z) = 0.4995  
P(Z<x<Z) = 0.999  
P(x<Z or x>Z) = 0.00099832 
Zscore, Z  
Probability, P(x<Z)  
Probability, P(x>Z)  
Probability, P(0 to Z or Z to 0)  
Probability, P(Z<x<Z)  
Probability, P(x<Z or x>Z)  
Probability between Two Zscores
Use this calculator to find the probability (area P in the diagram) between two zscores.
Left Bound, Z_{1}  
Right Bound, Z_{2}  
What is zscore?
The zscore, also referred to as standard score, zvalue, and normal score, among other things, is a dimensionless quantity that is used to indicate the signed, fractional, number of standard deviations by which an event is above the mean value being measured. Values above the mean have positive zscores, while values below the mean have negative zscores.
The zscore can be calculated by subtracting the population mean from the raw score, or data point in question (a test score, height, age, etc.), then dividing the difference by the population standard deviation:
z = 

where x is the raw score, μ is the population mean, and σ is the population standard deviation. For a sample, the formula is similar, except that the sample mean and population standard deviation are used instead of the population mean and population standard deviation.
The zscore has numerous applications and can be used to perform a ztest, calculate prediction intervals, process control applications, comparison of scores on different scales, and more.
Ztable
A ztable, also known as a standard normal table or unit normal table, is a table that consists of standardized values that are used to determine the probability that a given statistic is below, above, or between the standard normal distribution. A zscore of 0 indicates that the given point is identical to the mean. On the graph of the standard normal distribution, z = 0 is therefore the center of the curve. A positive zvalue indicates that the point lies to the right of the mean, and a negative zvalue indicates that the point lies left of the mean. There are a few different types of ztables.
The values in the table below represent the area between z = 0 and the given zscore.
z  0  0.01  0.02  0.03  0.04  0.05  0.06  0.07  0.08  0.09 
0  0  0.00399  0.00798  0.01197  0.01595  0.01994  0.02392  0.0279  0.03188  0.03586 
0.1  0.03983  0.0438  0.04776  0.05172  0.05567  0.05962  0.06356  0.06749  0.07142  0.07535 
0.2  0.07926  0.08317  0.08706  0.09095  0.09483  0.09871  0.10257  0.10642  0.11026  0.11409 
0.3  0.11791  0.12172  0.12552  0.1293  0.13307  0.13683  0.14058  0.14431  0.14803  0.15173 
0.4  0.15542  0.1591  0.16276  0.1664  0.17003  0.17364  0.17724  0.18082  0.18439  0.18793 
0.5  0.19146  0.19497  0.19847  0.20194  0.2054  0.20884  0.21226  0.21566  0.21904  0.2224 
0.6  0.22575  0.22907  0.23237  0.23565  0.23891  0.24215  0.24537  0.24857  0.25175  0.2549 
0.7  0.25804  0.26115  0.26424  0.2673  0.27035  0.27337  0.27637  0.27935  0.2823  0.28524 
0.8  0.28814  0.29103  0.29389  0.29673  0.29955  0.30234  0.30511  0.30785  0.31057  0.31327 
0.9  0.31594  0.31859  0.32121  0.32381  0.32639  0.32894  0.33147  0.33398  0.33646  0.33891 
1  0.34134  0.34375  0.34614  0.34849  0.35083  0.35314  0.35543  0.35769  0.35993  0.36214 
1.1  0.36433  0.3665  0.36864  0.37076  0.37286  0.37493  0.37698  0.379  0.381  0.38298 
1.2  0.38493  0.38686  0.38877  0.39065  0.39251  0.39435  0.39617  0.39796  0.39973  0.40147 
1.3  0.4032  0.4049  0.40658  0.40824  0.40988  0.41149  0.41308  0.41466  0.41621  0.41774 
1.4  0.41924  0.42073  0.4222  0.42364  0.42507  0.42647  0.42785  0.42922  0.43056  0.43189 
1.5  0.43319  0.43448  0.43574  0.43699  0.43822  0.43943  0.44062  0.44179  0.44295  0.44408 
1.6  0.4452  0.4463  0.44738  0.44845  0.4495  0.45053  0.45154  0.45254  0.45352  0.45449 
1.7  0.45543  0.45637  0.45728  0.45818  0.45907  0.45994  0.4608  0.46164  0.46246  0.46327 
1.8  0.46407  0.46485  0.46562  0.46638  0.46712  0.46784  0.46856  0.46926  0.46995  0.47062 
1.9  0.47128  0.47193  0.47257  0.4732  0.47381  0.47441  0.475  0.47558  0.47615  0.4767 
2  0.47725  0.47778  0.47831  0.47882  0.47932  0.47982  0.4803  0.48077  0.48124  0.48169 
2.1  0.48214  0.48257  0.483  0.48341  0.48382  0.48422  0.48461  0.485  0.48537  0.48574 
2.2  0.4861  0.48645  0.48679  0.48713  0.48745  0.48778  0.48809  0.4884  0.4887  0.48899 
2.3  0.48928  0.48956  0.48983  0.4901  0.49036  0.49061  0.49086  0.49111  0.49134  0.49158 
2.4  0.4918  0.49202  0.49224  0.49245  0.49266  0.49286  0.49305  0.49324  0.49343  0.49361 
2.5  0.49379  0.49396  0.49413  0.4943  0.49446  0.49461  0.49477  0.49492  0.49506  0.4952 
2.6  0.49534  0.49547  0.4956  0.49573  0.49585  0.49598  0.49609  0.49621  0.49632  0.49643 
2.7  0.49653  0.49664  0.49674  0.49683  0.49693  0.49702  0.49711  0.4972  0.49728  0.49736 
2.8  0.49744  0.49752  0.4976  0.49767  0.49774  0.49781  0.49788  0.49795  0.49801  0.49807 
2.9  0.49813  0.49819  0.49825  0.49831  0.49836  0.49841  0.49846  0.49851  0.49856  0.49861 
3  0.49865  0.49869  0.49874  0.49878  0.49882  0.49886  0.49889  0.49893  0.49896  0.499 
3.1  0.49903  0.49906  0.4991  0.49913  0.49916  0.49918  0.49921  0.49924  0.49926  0.49929 
3.2  0.49931  0.49934  0.49936  0.49938  0.4994  0.49942  0.49944  0.49946  0.49948  0.4995 
3.3  0.49952  0.49953  0.49955  0.49957  0.49958  0.4996  0.49961  0.49962  0.49964  0.49965 
3.4  0.49966  0.49968  0.49969  0.4997  0.49971  0.49972  0.49973  0.49974  0.49975  0.49976 
3.5  0.49977  0.49978  0.49978  0.49979  0.4998  0.49981  0.49981  0.49982  0.49983  0.49983 
3.6  0.49984  0.49985  0.49985  0.49986  0.49986  0.49987  0.49987  0.49988  0.49988  0.49989 
3.7  0.49989  0.4999  0.4999  0.4999  0.49991  0.49991  0.49992  0.49992  0.49992  0.49992 
3.8  0.49993  0.49993  0.49993  0.49994  0.49994  0.49994  0.49994  0.49995  0.49995  0.49995 
3.9  0.49995  0.49995  0.49996  0.49996  0.49996  0.49996  0.49996  0.49996  0.49997  0.49997 
4  0.49997  0.49997  0.49997  0.49997  0.49997  0.49997  0.49998  0.49998  0.49998  0.49998 
How to read the ztable
In the table above,
 the column headings define the zscore to the hundredth's place.
 the row headings define the zscore to the tenth's place.
 each value in the table is the area between z = 0 and the zscore of the given value, which represents the probability that a data point will lie within the referenced region in the standard normal distribution.
For example, referencing the righttail ztable above, a data point with a zscore of 1.12 corresponds to an area of 0.36864 (row 13, column 4). This means that for a normally distributed population, there is a 36.864% chance, a data point will have a zscore between 0 and 1.12.
Because there are various ztables, it is important to pay attention to the given ztable to know what area is being referenced.