Why I like RPN

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)


The best calculator?

Opinions vary, especially when it comes to calculators. Especially calculators. You can roughly divide humanity, in that respect, in three camps: the righteous HP fans, the TI heretics, and the “I don’t care” pagans. Really? What is there to argue about a calculator? Who cares?

There once was a time where numbers mattered. For most of us that time was high school, and for some of us it was even college. Once you’re working as a professional you quickly discover that real life math is a lot easier than what was taught in college, there’s just a lot more of it. Enter Excel, and we rarely ever need a calculator again. And when we do, well there’s a calculator app on our smartphone, after all.

But the smartphone is small, and there’s no substitute for feedback of real buttons. And then there’s the annoying fact that nearly all modern calculators (real or app-ones) use algebraic entry modes.

Enter the trusted, 1980s vintage Hewlett-Packard 15C. The pinnacle of pocket calculators? The HP 42S was perhaps more advanced and had, in my eyes, a better button layout, but it is very hard to beat the 15C in elegance, size, and attitude.

An American made Hewlett-Packard 15C (made in the first week of 1987)

An American made Hewlett-Packard 15C (made in the first week of 1987)

What is it that I like about this calculator? First of all, the display. Good ole’ LCD segments, instead of dots; much easier on the eyes. Second of all, this is a USA-made calculator in a time when it meant something. It feels about three times as heavy as a modern day, similar sized calculator. Third of all, the horizontal layout may look weird, but it is actually easier to hold than modern-day vertically laid out calculators. And finally, it uses RPN. If you’re unfamiliar with that… You’re forgiven. But once you’ve used an RPN calculator you will never want to go back. What is RPN? I’ll save that for a separate blog post.

A few nice touches on this calculator; first of all, the backside contains a “cheat sheet” with often used unit conversions, used conventions for complex numbers (yes, the HP15C can natively calculate with complex numbers) and a diagram on how to insert the batteries (three SR44 button cells that can power the calculator for years).

The electronics are wrapped inside a sheet with three layers. The middle layer is conductive to protect the electronic against electrostatic charges; the outsides are non-conductive to protect against short-circuiting. The result is a dust resistant solid calculator that is said to be able to survive the electro-magnetic pulse of a nuclear explosion.

Mine was a “mint condition” used calculator that I bought on eBay. The seller did not quite understand the meaning of the word “mint”—the 15C nameplate was missing, and the keys were sticky, but I got it for a very good price so I decided to live with it. The sticky keys were resolved by soaking the calculator in distilled water for a day, and then squeezing a paperclip underneath the keys to remove the gunk. Let it sit for a few days and remove the last moisture with a 15 minute stay in the oven. Yes, these are calculators that laugh at such treatments! It works as new now.