Calculators in 2020

I’m old enough to have seen the beginning of calculators, which had just replaced slide rules. Now, cell phones and tablets are about to replace calculators for good. They may have done it already. Or maybe calculators are here to stay. This article attempts to shed some light on this not-so-hot issue, and I do this by comparing pretty much everything available at the beginning of 2020. No one is safe.

Some things about electronic calculators that you may have noticed if you’ve been around as long as I:

1. They replaced slide rules very quickly, in the late 1970’s.
2. They evolved just as quickly during the 1980’s.
3. They don’t seem to have changed for the last 30 years.

Students of the history of technology might explain this as the emergence of an optimized design which, once found, fits the function so perfectly that there’s no need to change. They might say that this “perfect calculator” is a TI-84 with more or less bells and whistles, given the prevalence of that model and its successors in the marketplace. No doubt, RPN devotees will shout just as loudly that this “perfect design” is the HP-48G and its successors. Both sides are right, and they have been so for 30 years. So we may ask ourselves, is there a hope for the future?

Let me start by asserting just as loudly that the majority of “best calculator” articles that are written today are complete garbage. They focus on how smoothly screens pop or slide (both for physical and software-based calculators), or how many unit or currency conversions they offer. Thus, you will see numerous articles ranking Pcalc as the “best calculator” based on those criteria. The developers seem to believe it, too, for that’s how they call it in their own advertising. That even impelled me to buy the rather expensive app for my iPhone when it was on sale, leading to significant disappointment, for there are plenty of competitors that are way better but are hardly ever reviewed. This may be because there are three types of calculator users:

1. Technical professionals, also known as “nerds”
2. High-school and college students
3. People who can’t add, even with their fingers

Since the last group combines the largest economic power, it’s little wonder that colorful apps with large buttons and limited capabilities, like Pcalc, are doing so well (read the reviews), but the real fight is in pleasing the other two groups. Their requirements are not all that different from each other, especially after the students enter their second year after having passed freshman calculus, at which point there’s no longer a problem taking a really powerful calculator to an exam.

So what is “real power”?

Here’s a partial list of things that might be asked of a “scientific” calculator, in the context of a technical job or a college class:

• Obtain numerical results for calculations involving simple operations, as well as standard analytic functions with real numbers (sin, cos, log, and so forth).
• There should be a way to store intermediate results, especially if calculations follow a rigid order. A number of calculators do this with a single “M” register, which seems to be enough for most uses. RPN calculators have the “stack,” containing up to four levels.
• If there’s some way to check for correctness, so much better. Thus, a later development is algebraic input, where the whole calculation is visible to the user before it is executed.
• If there’s a way to recall previous calculations, that’s also a bonus. Some calculators had a paper tape where results were printed, more modern ones store them in memory.
• Ditto for constants and common formulas that otherwise one might have to look up in a book. Unit conversions are particularly nasty, especially when doing engineering calculations. The formula thing got a number of calculators in trouble when used in exams.
• If a function is not already built in, there should be a way to input it, thus programmable calculators were born. Now, writing a serious program into a calculator gets tedious quickly, so this is for simple formulas only.

And then, there are a few things that are nice to have, but not absolutely necessary:

• Solve implicit equations, and systems of equations, involving those same operations and functions. It is desirable to obtain all real solutions, a plus to get complex solutions as well.
• Plot functions in order to see where roots and relative maxima/minima might exist. 2D is a must, 3D not so much.
• Do the algebra for a complicated derivative, integral, or transform.
• Do math with vectors and matrices.
• Give values for unusual functions that arise in some circumstances, such as Bessel functions; gamma, beta, zeta functions; prime numbers, arbitrary precision calculations, and so forth.

Scientific calculators have fulfilled the first list of requirements, and much of the second, quite well without having to change too much for the last 30 years, but now they have a challenger, and I believe they won’t be able to withstand it anymore. Enter the smartphone-based software calculator.

Several reasons why it will dominate the market:

1. It’s always in your pocket. You can’t forget it, and you don’t need to carry extra weight.
2. The battery is always good. Because you do keep your phone charged, don’t you?
3. It has a beautiful, high resolution color screen. This is important for graphics.
4. You can use touch and do gestures such as pinch-zoom.
5. “Firmware” updates are seamless, so bugs can be squashed and features can be added without the user having to do anything.
6. Typically, it is much faster than a hardware one, because it runs on a faster processor.
7. You can have a lot more keys in the same space, because keys can change with a swipe.
8. It’s a lot cheaper. Prices range from free to 10 dollars at most.

There are some cons, however:

1. No hardware keys, so it’s harder to feel the keypresses. A number of software calculators make the phone beep or vibrate on keypresses, which helps some.
2. If your phone has a small screen (mine is an iPhone SE, which is small by today’s standards), it may be hard to see the key labels, and even push the keys accurately.
3. The phone also has Internet, which can be used for cheating in an exam.

Yes folks, this may be the only thing that’s keeping hardware calculators alive in the 2020’s: the fact that students could use software calculators to cheat in exams. But I think this will go away too.

So what are good software calculators in early 2020? I did quite a bit of research on current offerings in order to write this article, and I’d hate it to go to waste. I looked at calculator apps for iOS and Android. Many of them run on both platforms, although many others don’t. There are hundreds of calculator apps, so I’ll focus on those with scientific capability and good ratings. Many of these are emulators running the original software embedded in classic hardware calculators, or simply try their best to look and behave like those calculators, but as we’ve seen above, the flexibility afforded by the mobile platform can create a better user experience than simply copying a classic machine, so I’ll focus on those that don’t try to do that.

In order not to bore you with repetitious detail, I’m showing the result as a comparison table, plus some notes. I’ll be looking at whether or not the app supports algebraic input, so you can check the calculation is correct before you execute it, whether it can make graphs, has statistics, bases other than decimal, can store into more than one memory, has a record of recent calculations, built-in constants and conversion factors, can do symbolic algebra (also known as CAS in the market) and, finally, whether you can write your own functions and programs.

Notes:

Pcalc is advertised as “the best calculator.” You can see from the specs that this is pure hype.

Desmos has a very small keyboard, which makes it hard to use on small phones.

nCalc FX for iOS, pictured at right, does not yet support base calculations. Its Android version, which is named “Free Advanced calculator 991 es plus & 991 ex plus,” does support base calculations. It seems to be a calculator interface built on top of the Symja CAS system, so that many more functions are available through the “programming” interface.

Calculator Infinity, on the left, boasts a nicely polished interface, which takes good advantage of the phone/tablet screen. Its Android version does not yet support symbolic manipulation. Its list of functions is healthy, but not nearly as large as that in nCalc.

Calculator + has a complex iAP system to add featires incrementally. The 5 dollar option has most of what you need, or you can fork out 16 bucks for everything, which is more than all other apps, except Pcalc.

SC-323PU has a mode resembling the built-in calculator, but then it has a few more modes. No graphing, though. Its manual is always one click away.

ChampCalc, HiPER, and HiEDU, all for Android only, are very similar. They include an extensive reference of equations, which other apps also support, and are easy on the eye. HiPER and ChampCalc also support up to 100 decimal figures. HiPER and HiEDU can also do some simple graphing. But HiPER can do symbolic calculations, which the other two cannot. There’s also the slightly cheaper CalcTastic, which only has one memory.

In my week or so of heavy testing, I was in awe at the power of nCalc despite its numerous bugs and the tiny button labels on my iPhone SE. This app is currently receiving frequent updates, so I expect the bugs will be short-lived and we’ll have a clear winner. Meanwhile, Calculator Infinity supports just about all the math the average user is likely to need, and it already has a very smooth interface. For three bucks apiece (less in Android), you can afford to get both and decide which one you’re going to use.