RPN Calculators -- the Short Version

RPN stands for "Reverse Polish Notation," a parenthesis-free method for performing calculations. In the United States this method has been popularized by the Hewlett-Packard Corporation¹, which sells a line of RPN calculators. The method depends on a stack of values as its organizing principle. When a number is entered, the previous entry is "raised" in the stack, so that several values can be stored. When a mathematical operation is performed, it is performed on the most recent value (or values, if more than one is required).

For example, to divide 80 by 81, you make these entries:

80
[Enter]
81
/

At first, this method may seem cumbersome, but in time one begins to see its great value -- one need never worry about algebraic order of precedence, because the order in which operations are performed is entirely controlled by the order in which the values are entered and the operations performed.

On some problems, the algebraic order of precedence can be depended on to provide the correct result. But many problems are difficult to state using the default precedence. In this next example, you want to multiply the result of two additions ((a + b ) * (c + d)). If you simply enter this problem into an algebraic calculator, you will get a + (b * c) + d, not (a + b) * (c + d), as you expected, because multiplications are performed before additions.

In order to solve this problem on an algebraic calculator, you must carefully place parentheses between the operations (assuming your calculator has parentheses). But in RPN notation, the problem is simple to solve:

a (vaue)
[Enter]
b (value)
+
c (value)
[Enter]
d (value)
+
*

Once you begin to get a feel for RPN, you will realize it is the easiest way to solve all but the simplest problems. You never have to press more keys than on an algebraic calculator, and you often press far fewer.