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RPN(Reverse Polish Notation) calculator

RPN (Reverse Polish Notation) Calculator: The Basics

In the world of mathematics, calculators play a vital role in simplifying complex calculations. One such type of calculator is the RPN (Reverse Polish Notation) calculator. RPN calculators use a different approach to calculate arithmetic operations compared to other calculators. In this article, we will explore the basics of the RPN calculator, how it works, and its advantages and disadvantages. Check Our More Online TOOL’s

RPN (Reverse Polish Notation) Calculator

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A calculator is a device that is used to perform mathematical operations. It has been an essential tool in the field of mathematics for decades. There are different types of calculators, such as algebraic calculators, scientific calculators, financial calculators, and RPN calculators. In this article, we will focus on RPN calculators.

Key Takeaways

  • Reverse Polish notation can be defined as the act of writing mathematical expressions in a way where the operators follow the operands.
  • Hence, the evaluation of this expression progresses from left to right, as it takes each term individually into the stack and performs the corresponding operation.
  • Postfix notation was crucial in developing computers and devices such as calculators.
  • Moreover, postfix conversion to and from prefixes and infixes notations involves stack-based algorithms and computers.

What is an RPN Calculator?

An RPN calculator is a type of calculator that uses postfix notation to perform calculations. Unlike algebraic calculators, RPN calculators do not use parentheses or equal signs to perform arithmetic operations. Instead, they use a stack-based system to perform calculations. This system is known as Reverse Polish Notation.

How Does an RPN Calculator Work?

The RPN calculator works by using a stack-based system. Each number or operator entered into the calculator is placed on a stack. When an operator is entered, the calculator performs the operation on the top two numbers in the stack and replaces them with the result. For example, if you enter the expression “5 3 +” into the calculator, the calculator will add 5 and 3 and replace them with 8 on the stack.

Advantages of RPN Calculators

There are several advantages of using an RPN calculator. One of the biggest advantages is that it is easier to use than algebraic calculators. With an RPN calculator, you do not need to worry about parentheses or order of operations. Another advantage is that RPN calculators are faster than algebraic calculators. RPN calculators require fewer keystrokes to perform calculations, making them faster to use.

Disadvantages of RPN Calculators

While there are advantages to using an RPN calculator, there are also some disadvantages. One of the biggest disadvantages is that RPN calculators can be difficult to learn. The stack-based system used by RPN calculators can be confusing for new users. Another disadvantage is that RPN calculators are not as widely used as algebraic calculators, making them harder to find.

RPN Calculator vs. Algebraic Calculator

The biggest difference between an RPN calculator and an algebraic calculator is the way they perform calculations. Algebraic calculators use infix notation, which means that operators are placed between operands. RPN calculators use postfix notation, which means that operators are placed after operands. Another difference is that RPN calculators require fewer keystrokes to perform calculations than algebraic calculators.

Popular RPN Calculator Models

There are several popular RPN calculator models available on the market. Some of the most popular models include the HP 12C, the HP 15C, and the HP 50g. These

Tips to Use an RPN Calculator Efficiently

Using an RPN calculator efficiently requires some practice and knowledge of the postfix notation system. Here are some tips to help you use an RPN calculator efficiently:

  • Start with simple calculations and work your way up to more complex ones.
  • Get familiar with the different operations and their symbols, such as + for addition, – for subtraction, * for multiplication, and / for division.
  • Keep track of the stack and the numbers and operators that are currently in it.
  • Learn how to swap, roll, and stack numbers in the stack.
  • Memorize common constants such as pi and e.

How to Convert from Infix Notation to RPN

Converting from infix notation to RPN can be done using the shunting-yard algorithm. The algorithm works by converting the infix notation expression to postfix notation. Here are the steps:

  1. Create an empty stack for operators.
  2. Create an empty output queue for operands and operators.
  3. Scan the infix notation expression from left to right.
  4. If the token is an operand, add it to the output queue.
  5. If the token is an operator, pop operators from the stack and add them to the output queue until an operator with lower precedence is at the top of the stack. Push the operator onto the stack.
  6. If the token is a left parenthesis, push it onto the stack.
  7. If the token is a right parenthesis, pop operators from the stack and add them to the output queue until a left parenthesis is encountered. Discard the left and right parentheses.
  8. When the input expression has been completely scanned, pop the remaining operators from the stack and add them to the output queue.

Applications of RPN Calculator

RPN calculators have various applications in different fields. Here are some examples:

RPN Calculator for Programming

RPN calculators can be used for programming applications, such as parsing expressions and evaluating them. They are also useful in stack-based programming languages like Forth and PostScript.

RPN Calculator in Scientific Calculations

RPN calculators are used in scientific calculations, such as physics and chemistry, where complex calculations are required. They are also used in engineering, where calculations involving trigonometry, logarithms, and exponentials are common.

RPN Calculator in Finance

RPN calculators are popular in finance, particularly in the field of accounting. They are used to calculate interest rates, compound interest, and present and future values.

Polish Notation vs Reverse Polish Notation

The Polish notation (PN) was introduced by Polish logician Jan Lukasiewicz in 1924. It is a format of writing mathematical expressions where the operand follows the operator. Here is a comparison between the PN and RPN.

Polish Notation Reverse Polish Notation
They are also known as prefix notation. Can also be referred to as postfix notation.
The operator comes first, then the operand. The operand comes first, followed by the operator.
It is applied from left to right, operating on the terms individually. It is also applied from left to right, operating on the terms individually.
  These Don’t use brackets. This method doesn’t use brackets.
Computers in the 1970s and 80s used RPN for faster and easier computation. Computers in 1970s and 80s used RPN for faster and easier computation.
Example: + 7 9 Example: 7 9 +



RPN calculators are a unique type of calculator that use postfix notation to perform calculations. They have several advantages, such as being easier and faster to use than algebraic calculators. However, they also have some disadvantages, such as being difficult to learn and less widely used. Despite this, RPN calculators have many applications in different fields, such as programming, scientific calculations, and finance.


Q1. Is reverse polish notation better?

Many consider RPN to be superior to the standard method of writing mathematical expressions. The reason is that the conventional method uses brackets that complicate the expression. Therefore, many terms take up time and effort. RPN takes each word one by one and operates. It is much faster and makes the process easier.

Q2. Is reverse polish notation still used?

Yes. Stack-based languages and calculators still utilize RPN. However, its share is insignificant and advanced algorithms have replaced it.

Q3. How to convert infix to reverse polish notation?

Infix notations are the conventional format for writing mathematical expressions. Infix to postfix notation conversion can be done using computers and stack-based algorithms. However, here there’s a straightforward method of transformation that can be done using a pen and paper. First, solve the infix notation and get the result. Then, using the value, write a reverse Polish expression. It is essential to note that many ways to write a single expression in RPN exist.

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