The Casio fx-82MS-2 is the calculator I've been using for the last number of years. This is the cheapest and most basic scientific calculator Casio offered at the time I purchased mine. Like the Texas Instruments TI-30X IIB model that I used in high school, it has a two-line display and a familiar button lay-out that has been common to nearly all scientific calculators for over fifty years. This style of two-line display calculators has been the norm for entry-model scientific calculators for over two decades, so I was a little shocked when I encountered the Casio fx-82CW in a general store.

The Casio fx-82CW was introduced in 2023 as the successor to the Casio fx-82MS and fx-82EX models.

Casio fx-82MS (left) and Casio fx-82CW (right) |

What immediately caught my eye was that the new Casio fx-82CW has what Casio calls a 'natural' display and input method. Such a display and input method mimic the appearance of mathematical equations as one would write them by hand or see them printed in a book.

This change is extremely significant, as the correct formatting of mathematical formulas, even without the need to carry out the calculations, has traditionally been problematic on far more capable desktop computers. Such display has technically been possible since the 1980's through LaTeX and similar markup languages, but those languages are not easy to learn and use. Microsoft Office introduced a mathematical formatting option only as recently as 2007 and to this day Adobe InDesign still requires third-party solutions to include mathematical equations in documents. Having had first-hand experience with the problems one encounters when attempting to correctly display complex mathematical equations on a screen, to see this functionality on the most basic and cheapest of scientific calculators was a real eye-opener.

For those who are perhaps less familiar with the hardships of using a two-line calculator, in the above image the equation input is the same for both calculators, with the same values for the variables. On the right, in the fx-82CW, the entire equation is visible and the result is displayed as a fraction, in the style that one would write it on a piece of paper. Its presentation is clear and uncomplicated, assuming one is familiar with such equations.

On the left is the same input and result shown on an fx-82MS. The input there is (-B+√(B^{2}–4AC))÷2A, which doesn't fit in its entirety on the single input line. This is problematic because you have to provide the calculator with the correct order of operations through the use of nested brackets. This in and of itself is not a problem, but combined with the limited character space on the single input line, you always end up in the situation where your opening and closing brackets aren't on the screen at the same time. When coupled with the mental effort required to 'translate' the formula as seen in a book or your own writing, this creates a situation where input errors are very likely, while checking for such errors is tedious and unwieldy.

To have a calculator with a more 'natural' display is thus a great quality of life improvement over how calculators have been developed and used during the last 60-odd years.

Of course, there have been calculators in the past that possessed such natural display capabilities and this is thus not a new invention. The first Casio calculator that could display algebraic formulas was the CFX-9970G in 1998, but this was a top-of-the-line graphical calculator with a matching price tag. Even today it's offered on eBay for about $100. More recently, the aforementioned Casio fx-82EX model already had the same display technology that the new fx-82CW uses. This model was released in 2015, and while it was very similar in mathematical functionality to the two-line fx-82MS-2 that was simultaneously on the market, it was about twice as expensive at roughly 25 euros. So, while it's a great thing to see this kind of display technology in Casio's cheapest offering, similar functionality has been available from them and their competitors for a number of years.

Which brings us to the other aspect of the fx-82CW that struck me, which is the renewed button layout. As mentioned earlier, the button layout on scientific calculators hasn't changed significantly since they were first introduced over fifty years ago. Both the fx-82MS and fx-82EX models still largely adhere to this traditional layout.

Button layout of fx-82MS (left), fx-82EX (middle) and fx-82CW (right) |

The greater possibilities introduced by the new screen has provided the opportunity for a design where the information concerning inputs isn't restricted to the limited space available on and around the buttons themselves. I believe that the designers at Casio recognised this opportunity and designed their new calculator with a two-fold aim. The first is to provide a large degree of consistency between the calculators input and its core functionality, and the second is a greater degree of accessibility for novel users who are used to working with simpler calculators, who are writing equations by hand and who are introduced to new ideas through natural language by teachers or textbooks.

I think the designers did an excellent job at really looking at all the technical functionality these scientific calculators have amassed in the last decades and finding a logically consistent grouping of the major functionalities, even if this meant doing away with some of the ingrained staples of calculator design. Of course, a written text like this one is no substitute for the experience of actually using a device like this, but I nevertheless wish to highlight some of the choices they made and hopefully show how these differ from any other calculator I know.

The first thing that's noteworthy is that there is no equals sign to be found. Instead there is a [EXE] button which is positioned where the [=] button usually goes. 'EXE' is short for execute and simply executes the command you've input. This is perhaps a subtle change, but it's nevertheless important if one wishes to have a more consistent input. To press the [EXE] button after entering an equation makes perfect sense, and so does pressing [EXE] after defining a variable as 'A=1'. This is not the first calculator to move away from the equals sign, but the choice of execute has been particularly suitable for the purpose. Texas Instruments have chosen for [ENTER] on their TI-30XB models, but this has a strong connotation with the keyboards of desktop computers and doesn't imply that any activity will occur after the input.

Right above the [EXE] button is the minus sign, in the place where it is commonly found on a calculator. This minus sign performs subtraction, but interestingly the secondary function of this minus sign is the input for negative numbers. The operators for negative numbers and subtraction have always had two separate buttons on any calculator I've used, which are respectively labelled as [(-)] and [–]. But as both use the same signifier, the minus sign, to express their function in handwriting, it makes sense to have them in the same place.

Another button that is found in its usual place for Casio calculators is the button for input in scientific notation: [×10^{■}]. In the manual of the fx-82CW it's written that '*Pressing the* [×10^{■}] *key is the same as* *pressing* [×], [1], [0], [◼︎^{□}]'. This is how I always mentally approached this button, but this wasn't how it functioned on the fx-82MS and many other calculators. On the fx-82MS pressing the [×10^{x}] inputs '×10' as a single character and the exponent will be whatever number follows this character until a different operator is entered. This system thus gives the following results:

[1], [×10* ^{x}*], [3] = 1000

[1], [×10

^{x}], [1], [+], [2] = 12

[1], [×10

^{x}], [√], [9] = Syntax error

Even though mathematically all these equations should be equal to the number 1000, the results vary wildly on the fx-82MS. On the fx-82CW however, the input of the button is simply treated as a shortcut for writing the relevant expression and each of these inputs thus give 1000 as the answer. This is again a great step towards further consistency between the user's input and what is shown on the screen.

Buttons used for formatting on the fx-82MS (left), fx-82EX (middle) and fx-82CW (right) |

Another new addition I haven't encountered on any other calculator is the [FORMAT] button. The fx-82CW supports a number of different notational formats for displaying the result of a calculation, namely Standard, Decimal, Prime Factorization, Improper Fractions, Mixed Fractions, Engineering Notation and Sexagesimal. Once you performed a calculation, simply press the [FORMAT] button and you can choose any of these options from a menu.

This functionality isn't new, engineering notation was introduced on calculators in the 1970's, but any other calculator I've used had separate buttons for these options and most of the time these buttons aren't physically grouped together because they are also used for other kinds of input. This is confusing to anybody who didn't memorise the manual and it probably meant entire generations of students used a calculator for years without ever finding out what the 'FACT' function was on the [º ' "] button.

A criticism that has been levied against the removal of the [ENG] and similar buttons is that it's less efficient to display a result in engineering notation. After all, you now must go through a menu to do what before simply required a single button press. I do agree with this criticism for heavy users of a single kind of notation that can't be pre-set, and so I am curious to see how Casio will approach this problem in its more advanced or specialised calculators in the future. As it stands, the choice for this approach in this base level calculator is more than justified in my opinion. Core functionality is no longer hidden behind separate buttons with acronyms or other functions, but organised under a single button with a clear label and position. To any new or light user of a scientific calculator the [FORMAT] button will provide access to functionality they previously might have never known even existed.

Buttons used for variables on the fx-82MS (left), fx-82EX (middle) and fx-82CW (right) |

An important feature of this kind of non-graphical scientific calculators is the ability to store and recall variables. Equally important is the inclusion of two mathematical constants, namely π, or pi, and *e*, or Euler's number. While any basic scientific calculator I've ever used provided this functionality, how these variables were entered has been anything but consistent, or intuitive. On the fx-82MS for example, *e* is the tertiary function of the [ln] button. This makes some conceptual sense, as *e* is the base of the natural logarithm, but then on the fx-82EX *e* is the tertiary function of [×10^{x}], where π is also found as the secondary function on both the fx-82MS and the EX.

On the fx-82CW, π and *e* are the secondary functions of the numbers 7 and 8, respectively. There they are positioned next to each other and together with other numerical input because that is how they are approached in the context of a calculator, as numerical input.

It thus makes sense that the programmable variables 'A' to 'F' are also found there, as well as the variables *x*, *y* and *z*. *z* replaces the 'M', or memory, function of previous models. This memory button was an early addition to scientific calculators to temporarily store numbers before more variables became available. To replace 'M' with *z* thus once again achieves greater consistency for users who aren't already familiar with the history of calculator design.

All input that is equivalent to a number is now done through the lower left segment of the keypad on the fx-82CW and this is a laudable approach.

Setting these variables has also changed to be more approachable in the fx-82CW and this is once again done by consolidating this function to a single button labelled [VARIABLE]. Compare this with the fx-82MS where [1], [SHIFT]+[RCL], [(-)], [=] are the required commands to store the number 1 as variable 'A'. This somewhat cryptic sequence makes a bit more sense when you're physically using the calculator, but it's nowhere near as instinctive as [VARIABLE], 'A', 'Edit', [1], [EXE].

Pressing the variable button on the fx-82CW also provides the user with an overview of the values of the available variables, something that is understandably absent from the two-line fx-82MS. While the fx-82EX provides the same overview as the fx-82CW, it nevertheless relies on a similar method as the fx-82MS for its input.

Buttons used for arithmetic on the fx-82MS (left), fx-82EX (middle) and fx-82CW (right) |

The most important function of a simple scientific calculator will undoubtably be arithmetic and the inclusion of exponentiation, roots and logarithms is essentially what differentiates a scientific calculator from a basic calculator. The styling conventions for these functions have been established long ago, with [*x*^{2}] for the square of a number, and [*x*^{3}] for its cube, and then [^] is used for adding any other number as the exponent. Needless to say, these stylistic conventions adhered largely to how the operators were displayed on the screen of the calculator, but still could appear somewhat inconsistent to the user. With the first implementation of their Natural-V.P.A.M. display method, on the fx-82ES from 2004, Casio simultaneously added some changes to the button styling for some of these arithmetic functions. What was previously represented by a letter like *x* or *a*, now became a little black square, presumably to indicate where the operator would be placed on the new and more complex screen. This purely visual system does away with letters in favour of shapes to convey vital information about its function. From 2004 until 2023 Casio didn't use this symbolic language consistently, however. On the fx-82EX most symbols were replaced with open or closed squares, yet for all exponent operators an *x* variable was still used. It seems like old habits were hard to shake. For the fx-82CW Casio once again went with consistency and used only squares where one is expected to find a number in the symbols for the operators. They also removed the unnecessary [*x*^{3}] button and removed all instances of Euler's number in the operators, instead opting to make the natural logarithm a secondary function of the general logarithm, while *e* can be found in the numerical section as previously mentioned.

This made this group of five buttons sleek, visually simple, easy to understand and consistent.

Finally, I must note the inclusion of one last button that I've never encountered before, and this is the [CATALOG] button. Once more this button does exactly what it says, as it opens a menu where all the calculator's functions are grouped in a handful of categories. This includes some probability functions that no longer have a separate button on the keypad. I doubt many people will use this menu to regularly input common functions, but as an overview of the calculator's capabilities this level of redundancy is a nice addition.

Overall, I'm impressed by the fx-82CW for its willingness to challenge and change several conventions that have been in place for decades. These
conventions by and large grew out of specific needs for specific users
in combination with the limitations of the available technology. Now
that the technology has gotten sufficiently affordable to provide these
complex and more advanced functions on the most basic of models, Casio has dared to see the impact this could have on users and rethink its core interface. In doing so it has created a great improvement for a first introduction to the more complex
calculators found in high school education, as well as a wonderfully clear
and workable calculator for unsophisticated daily use.