Online calculators

In my teaching I move around my university, giving classes in different locations, often to the same group of students. And often in a class I need to do a quick and dirty calculation – to demonstrate a computational point, or to work through an example or exercise. For this purpose I like to use a calculator, as the calculator paradigm is one with which all students are familiar. This is not the case with a computer algebra system.

My university has standardized on Microsoft Everything as its desktop of choice, so in all classes I have access to its Windows Calculator. In its current (XP) form, this has two modes: standard, and scientific:

In my classes, I always use scientific mode, so I have access to the trigonometric and exponential functions. However, bizarrely enough, there’s no square root key in scientific mode. To obtain square roots, you either have to raise your number to the power of 0.5, or use the key combination INV, x^2. Given that the x^2 key is redundant, as squaring can be done using x,= , the omission of a square root key seems unpardonable. The same omission seems to have continued into the new, “beefed up” calculator which will be bundled with Windows 7, as you can see here.

Given this, I thought it may be interesting to see if there are any good online calculators out there. Well, of course there are – lots in fact. Most however, don’t suit my purposes very well. Here is my wishlist for the perfect calculator:

1. It must look like a hand-held calculator.
2. Keyboard entry should be possible – I should be able to type in “sin(sqrt(pi/3+1))” and receive an answer.
3. All the standard transcendental functions: trigonometric, hyperbolic and their inverses, exponential and logarithmic.
4. Complex number arithmetic, and conversion between Cartesian and polar forms.
5. Basic combinatorial functions: factorials, combinations and permutations.
6. Basic number theory: modular arithmetic (including inverses), gcd.
7. Some sort of “memory”, or method of defining variables.

Web2.0Calc

This fine calculator is available at http://web2.0calc.com/, and a screenshot of it is:

This is very near the perfect calculator. It fulfils my wishlist, and provides much more besides: matrices, some statistical functions, and even some plotting and equation solving. However, there are a few glitches:

• You can’t change the precision, even though this is supposed to be possible.
• Even though you can enter “i^3” and receive -i, you don’t seem to be able to raise other complex numbers to integer powers. For example: “(2+5i)^2” returns nothing.
• There doesn’t seem to be a way of calculating modular inverses. Even though the extended Euclidean algorithm is supposed to be implemented, it doesn’t seem to work

As you can see from the screenshot, your input and result is returned in LaTeX form above the calculator. This is nice, but not always useful. It seems that the LaTeX code is turned into an image, which is then resized if necessary to fit that space. This can result in an unreadably squashed or stretched image.

ecalc

This is a sort of “generic calculator”, whose website describes it as “The Best Online Calculator”:

As you see, it does a good line in unit conversion. It does not have the breadth of web2.0calc, but what it does, it does well. For example, it can compute the quotient of two complex numbers, which web2.0calc doesn’t seem to be able to manage. It also can solve equations, and perform conversions between bases (binary, octal, decimal and hexadecimal). However, it provides no way of defining variables.

Encalc

This is a calculator which drops the key-mode entry completely for text entry only:

You can find it at http://www.encalc.com/. Its website claims that its strength “lies in its ability handle units and dimensional analysis, to define variables and its large database of constants.” It is in fact a powerful scientific calculator, with a clean simple interface. However, there does not seem to be documentation available (there is a FAQ) so it is not easy to find out exactly what Encalc can and can’t do. It doesn’t seem to support hyperbolic functions, factorials, complex numbers, or number theory. I’d like this calculator greatly if these operations were supported, and if there was better documentation.

Instacalc

This is another calculator which has eschewed keys for text entry:

It’s available at http://instacalc.com/. It has been claimed to be one the “Top 10 Online Applications” at theresourced.com. Instacalc can be embedded in a web page, and its results shared with other users. It has borrowed some of its functionality from spreadsheets, and its ability to update calculations in real time is impressive. For example, suppose you have

a=30

in one cell, and

sin(a)

cos(a)+cos(a/3)+cos(a/5)

in two other cells. If you change the first cell to, for example

a=45

then the results of the other two cells will change automatically.

Documentation is available at http://instacalc.com/blog/.

Conclusions…

I think the perfect online calculator is yet to be produced, although web2.0calc and Instacalc are both in the right direction. Web2.0calc has the most impressive functionality – but not all of it works as it should – and Instacalc has one of the best interfaces.

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