Something that I’ve noticed is that Reverse Polish Notation (RPN) isn’t used much these days. Why is that? It’s much more effective for students to know how to use because of how much time is saved on exams. Some graphing calculators use it, but if you’re not allowed to use that, there are financial calculators that work just as well for statistics. Whatever your math class, there’s most likely an RPN calculator that will come in very handy.
How it Works
The calculator input method that is most commonly used today is known as “algebraic.” It’s where you input it the way you see it written out on paper. If you use the keys, “1 + 2 =,” you will get “3” as the answer. The reason why RPN is more efficient is because you’re doing fewer keystrokes and you don’t use an equals key to get your answer. You use an execution such as division, addition, multiplication, or subtraction. Instead, there is an enter key that allows you to store numbers.
The storing of numbers that I’m talking about is best thought of as slots. On the HP 12C, the financial calculator I recommend, you have three slots of number storage. This allows for amazing calculations. You could actually do (3 x 4) + (5÷3) x ((5×2)÷4) without having to stop or write anything down. This comes in very handy when you’re taking algebra and have to deal with matrices or when you have longer, more complex calculations.
How it Works: Storage Slots
I’m sure that this concept of slots will be confusing. So here’s a little bit on how they work. Think of each slot as a set of parentheses. In slot one, you can do one calculation, then you can start another slot or two (depending on the calculator). Then, the executions you do (+ – x ÷) go from right to left. Here’s an example of how it would be written on paper when you’re using a calculator with three slots:
(1+1) x (2+2) ÷ (3+3)
RPN calculators would store it like this: 2, 4, 6. If you think of it as right to left with executions, you would do “÷ x” to get the answer: 1.33. Of course, you could also do the math in your head and just input “2 ENTER 4 x” 8. “6 ÷” and your answer would be 1.33. Just remember that the order is always going to be right to left when you execute. To avoid confusion, remember these two things:
- Input in RPN calculators is always left to right
- Performing an execution (+ – x ÷), the order is always right to left
When all three slots are full, you can use one “fourth slot” that doesn’t store anything. This way, you can enter numbers into three slots and then start by performing an execution with the third number.
How it Works: Basic Arithmetic
Let’s get down to business: Keystrokes. I will use quotation marks to signify keystrokes. When there’s a number after the keystrokes (quotation marks), the number will be what shows up on the calculator display. I will always write a period at the end of what shows up on a display so that it doesn’t get too confusing. I mentioned that it’s very different when you’re inputting numbers into an RPN calculator. For comparison, here are the keystrokes you use on a regular calculator: “1 + 2 =” 3. On an RPN calculator: “1 ENTER 2 +” 3.
Using the mentality of slots, this would be: 1, 2, __. So you just have to use the addition key to add 2 to 1. Subtraction shows the reverse nature best: 1, 2, __. If you subtract 2 from 1, you will get -1. If you don’t put in your numbers right, you will get 1 instead of -1. This is why it’s very important to remember that the slots will input numbers left to right and then you execute right to left.
This will seem extremely unnatural at first. Trust me, if you’ve never seen or heard of this before, it’s going to be weird. As you practice, you will better understand how it works. I do not recommend doing what I did: In order to get used to the calculator, I used it in class instead of my usual calculator. I’ll include methods of practicing how to use this thing so that you get a feel for it.
How it Works: Basic Calculations with Parentheses
In algebraic input calculators you get for $10 to $20, you can’t do (3×4) + (5-3) without stopping or writing it down. With an RPN calculator, here are the keystrokes to do this: “3 ENTER 4 x” 12. “5 ENTER 3 -” 2. “+” 14. This is done with nine keystrokes. In an algebraic input calculator, you do “3 x 4 =” 12. “5 – 3 =” 2. “2 + 1 2 =” 14. That’s 13 keystrokes! Remember, the reason why this works in RPN input calculators is because of the slots.
How it Works: Complex Calculations with Parentheses
Let’s say you have this equation: (4+(3÷2)x5) – (5+(34-23)÷3) x (4x(2÷3)-6). Notice how I used only three sets so we can stick to our mentality of three slots. You and I both know that there are a lot of keystrokes that will happen, so there’s no need to count how to do this with an algebraic input calculator. Before we get started, it’s important to know that the three large parentheses are all one number in each of the three slots. The parentheses inside should be done first. Here are the keystrokes to do the equation:
“4 ENTER 3 ENTER 2 ÷ +” 5.50. “5 x” 27.50. “5 ENTER 3 4 ENTER 2 3 – +” 16. “3 ÷” 5.33. “-” 22.17. “4 ENTER 2 ENTER 3 ÷ x” 2.67. “6 -” -3.33. “x” -73.89.
Before you start to worry, it’s important to remember from earlier: When all three slots are full, there is a free fourth slot that doesn’t store anything.
Which Calculators Use RPN?
Before I get into it, I’d like to let you know that it’s hard to find calculators that still use RPN that aren’t made by HP these days. I don’t really have a brand loyalty to HP because I can’t find very many other brands that actually have RPN as an input method. If you find other brands that have an RPN input method that’s still in production today, please let me know in the comments below.
HP 12C / HP 12C Platinum – Financial Calculator
Earlier, I said that this was a calculator that I recommended the most to people. Whether you think it has any value or not, this financial calculator works very well in most settings in which a graphing calculator isn’t allowed. Some of the main functions include time value of money (TVM) functions. This is a very handy calculator for anybody in economics, real estate, banking, or accounting.
The HP 12C Platinum has an algebraic input mode on it, but I don’t think it’s worth it because you’re doing all of those unnecessary keystrokes again. The HP 12C has a lot of features on it and it even does a lot of statistical calculations such as averages, linear regression, and standard deviation. If you want to practice using an emulator, they make one for HP 12C and the HP 12C Platinum.
HP 35s Scientific Calculator
If you’re not studying anything that requires time value of money functions, but still has math involved, then I highly recommend the HP 35s. It’s recommended by HP for use in engineering, science, and medicine. It has both RPN and algebraic input modes. If you don’t see yourself needing the functions or power of the HP 12C, then this is a great second.
Here’s a short list of other calculators that use RPN.
HP 17bii+ Financial Calculator
HP 50g Graphing Calculator
HP Prime Graphing Calculator