How to Use Reverse Polish Notation on a Calculator

Most calculators are designed to recognize basic operations the same way they are written. Reverse Polish Notation (RPN) is a faster method of inputting equations. It can also help with performing complex operations on a calculator.

Anyone who can use a calculator can learn to use RPN calculators. Learning the basic principles can be done within 20 minutes, but mastering it will only come with practice. Hewlett Packard has manufactured RPN calculators in the past, and the one I use is a HP 48G. There are RPN calculators available online as well, such as on alcula.com.

It is important to know that the most common method of inputting data into calculators would be in the same order as it is written or spoken, RPN calculators do not do it in the same order. For example, to do the operation 3+4, on an RPN calculator we would press 3, ENTER, 4, +. A more common calculator would use 3, +, 4, ENTER (or the equal sign).

Step 1: The Stack

First, we must learn about the stack. RPN calculators have rows. The HP 48G calculator shows four rows. The stack is the collection of those rows. As numbers are placed in the first row (the bottom row) of the stack, the numbers above it move to the next highest row. Although only a specific number of rows are seen, there will be rows made for each new set of data that are not on the display screen. To put numbers on the stack, we press the number, and then press ENTER. To copy an entire row, we can press ENTER and the first row will be copied to the second row. This is how data is entered in calculator.

Step 2: Deleting Data

There are a few ways to remove data from the stack. To clear the bottom row of the stack, the button shaped like an arrow pointing to the left will clear it. To clear the entire stack, press the button DEL (delete).

Step 3: Swapping

It is also possible to swap rows in the stack. First enter 5 and then 10, so that 10 is on the bottom row and 5 is right above it. From that point, press the swap button. On the HP 48G, the swap button has an arrow pointing to the right, and says “SWAP” right above. On the calculator at alcula.com, the button says “SWAP.” With this button, even if we input data incorrectly, it is possible to fix it without deleting the data or entering it again.

Step 4: Addition

We will do basic arithmetic operations. To do addition, the order of numbers will not matter because we will end up with the same sum. To add 10+5, we will press 10, ENTER, 5, +. The 10 and the 5 will disappear from the stack and 15 will be left on the bottom row.

Step 5: Subtraction

To do subtraction, the order in which we input the numbers does matter. So, to subtract 10-5, we will press 10, ENTER, 5, -. That will give us 5. If we did 5-10, we would have -5.

Step 6: Multiplication

To do multiplication, just like with addition, the order does not matter because it does not affect the product. So, to input 10*5, we would press 10, ENTER, 5, *. 50 will appear on the bottom stack.

Step 7: Division

To do division, we must do it in order as well. Dividing 10/5 is done by inputting 10, ENTER, 5, ÷. That will give us 2 on the bottom stack. If we did the opposite, 5/10, the calculator will show 0.5.

Step 8: Exponential Functions

To do exponential functions, put the base first into the calculator, and then the power to which the base is raised. The base will be in the second row right above the power. Then press the exponent key. On the HP 48G, this looks like a y raised to the x power. On the calculator from alcula.com, that button says “POW.” If we want to compute 2 to the fifth power, first press 2, ENTER, 5, and then the exponent key (POW or y^x). The bottom row will show 32. Computing the number e to a specific power is also done the same way. First the power is placed on the stack, and then a button that says “e^x” or “EXP” is pressed.

Step 9: Logarithmic Functions

Logarithmic functions follow the same pattern as exponential functions. As an example, if we wanted to find the natural log of 10, we would first input 10 so it appears on the stack. Then we would press “LN.” Doing this yields an answer of approximately 2.3 (as with most scientific calculators, RPN calculators may approximate many more decimal places; 2.3 does not exactly equal the natural log of 10).

Step 10: More Complex Equations

One great advantage of RPN calculators is the ability to put in complex equations, although it requires practice to be able to do it correctly. Let us use the following equation as an example.

(11+5)/(6+2)

We can first add 11 and 5 in the numerator. This is done by inputting 11, ENTER, 5, +. 16 will appear on our stack. Then we do the addition in the denominator by pressing 6, ENTER, 2, +. The number 8 will appear on the bottom row, with 16 right above it. Now, just press ÷. The calculator will do 16/8 and give us the answer of 2. Inputting this same equation into a regular calculator requires more time to be done. With the RPN calculator, this equation is done by breaking it up into three simple arithmetic equations.

This has covered the most rudimentary steps of using an RPN calculator. Although it may first seem awkward at first, with practice it becomes easier. Spending more time on trying more complex calculations will lead to more discoveries and help you with the mathematics you have in your academic or professional pursuits.