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.
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.
The table below is a righttail ztable. Although there are a number of types of ztables, the righttail ztable is commonly what is meant when a ztable is referenced. It is used to find the area between z = 0 and any positive value, and reference the area to the righthand side of the standard deviation curve.
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 