Examples — Computing with RPN45
1  Pearson correlation coefficient and regression line

2  Sample and true standard deviation 
3  Lottery 1 ENTER 39 ENTER Tap RAN# repeatedly to get your random numbers, skipping any duplicates.

4  Odd root of a negative integer Interestingly, most calculators can't handle this, producing an error message instead. Or a complex number. 
5  Cubic equation shows the real root x_{1} = 2.000. Verifying x_{2} (assuming the real part 1.000 is still in X, the imaginary part 1.732i in Y): 
6  Linear equation in two unknowns x + y = 62 Putting all unknowns to the left side of the equal signs, we get: 1*x + 1*y = 62 The coefficients map to the storage registers as follows:
Store the coefficients and execute the calculation: 1 STO 4 1 STO 5 62 STO 6 We get x = 46 (father) and y = 16 (son). 
7  Euler's identity 
8  Cube root of a complex number For natural numbers n, the nth root of a complex number has n solutions. The method shown above only produces the principal solution. 
9  Complex numbers in polar form 
10  Calculating with complex numbers

11  The "DATE" Function

12  Calendar Reform Input: 2.091752 DATE 1 DATE results in Thursday, 14 September 1752 In Russia the October Revolution was in fact a November Revolution: 
13  Extended Σ+ Functions Example: Find half of the sum of the vectors (6,7) and (8,11). 
14  Weighted Mean
What's the average gas price? Clear the statistics registers with CLEAR. Enter the values shown above (for each pair: y ENTER x, then Σ+). 
15  Remarkable Formulas Make sure the calculator is set to angular mode DEG and activate mode CMPLX. 4^{} ENTER 3^{} √x x 4 I 3 1/x y^{x} →∠ (read the imaginary part of the result as 10°) 2  Benjamin Peirce, an American mathematician (1809 bis 1880), called the following relation "a mysterious formula": Activate CMPLX mode, then compute Pi minus the right side of the equation: π 2 ENTER 1 Re↔Im ÷ LastX ln x – (the result is 0, as expected) 