RPN Notation in calculators is unique to HP these days, and even then only limited to very few calculators. Personally, I *love* RPN entry and think it’s way better than DAL (Direct Algebraic Logic) that is used by all other calculators.

## Wrong reason

First let me explain what is *not* the reason I prefer RPN. Somehow the “lesser keystrokes” argument always comes up, but I don’t think it is that convincing. Consider this calculation that HP uses as an example to tout how much more efficient RPN is:

In algebraic notation you would enter it like either like this:

( 3 + 5 ) ÷ ( 7 + 6 ) =

Which is a whopping 12 keystrokes. Or, if you have a primitive desk calculator that doesn’t offer parenthesis, you would enter it like this:

7 + 6 [M+] 3 + 5 ÷ [MRC] =

Which is an impressive 10 keystrokes! No, then RPN:

3 [ENTER] 5 + 7 [ENTER] 6 + ÷

Which is 9 keystrokes. Wow! The difference! “But with complex calculations the difference will add up.” Well yes, with complex calculations your numbers tend to get longer too, so the *relative* difference will only get less. Will it really matter if a calculation takes 35 keystrokes or 40?

## So what is the advantage then?

The example is actually good, but for the wrong reason. What I truly like about RPN is that it makes entering the calculation so much easier. Let’s review the same example and see what happens when you enter it:

First you calculate the numerator:

3 [Enter] (“start a new calculation with this entry”)

5 [+] (“take 5, and add it to the running total” — Calculator shows 8)

Then you calculate the denominator:

6 [Enter] (“start a new calculation”)

7 [+] (“take 7, and add it to the running total” — Calculator shows 13)

Now, take the original total and divide that by what I have right now:

[÷] (Calculator shows 0.6154)

Because previous calculations are automatically stored in memory (“the stack”) complex calculations become far more logical to enter. Consider this calculation:

In algebraic notation you’d enter this as:

(( 1 × 3 × 5 ) + ( 2 × 4 × 6 )) ÷ ( 1 + 3 + 4 + 7 ) =

Or maybe as:

1 × 3 × 5 = + ( 2 × 4 × 6) = ÷ ( 1 + 3 + 4 + 7 ) =

But you’ll have to pay attention to the parenthesis. How much easier in RPN!

“Let’s do 1×3×5 first” 1 [Enter] 3 [×] 5 [×]

“Then do the other half of the numerator” 2 [Enter] 4 [×] 6 [×]

“Add those two together” [+]

“Now let’s do the denominator…” 1 [Enter] 3 [×] 5 [×] 7 [×]

“…and divide by it” [÷]

Entering your calculation, despite the “reverse entry” goes in a much more natural fashion than the acrobatics with memory and parenthesis that algebraic input demands.

(Equations provided by the online latex equation editor)