Jarque Bera Normality Calculator
Calculate the Jarque–Bera skewness/kurtosis statistic with its large-sample chi-square approximation.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use population central moments divided by n, without sample skewness or kurtosis bias corrections.
JB=n/6×(skewness²+(kurtosis−3)²/4); asymptotic p=exp(−JB/2)
Worked example
Values −2,−1,0,1,2 have skewness zero and moment kurtosis 1.7, giving JB=0.352083333.
Assumptions and input details
Requires nonzero variation. The chi-square df=2 reference is asymptotic and can be poor for small samples; no normality certification, adjusted small-sample JB or multiple-testing correction.
References: NIST: Jarque–Bera test
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Compare an empirical sample CDF with a fully specified normal CDF using the two-sided KS distance.
Enter a list of numbers to calculate mean, median, modes, quartiles, population and sample standard deviation, with a frequency histogram.
Calculate a normal probability below, above or between entered values. See standardized z scores, a probability breakdown and a bell curve with the selected region.
Reserved advertising space.