Thinking about a more efficient keyboard layout other than qwerty

Likely you are using a keyboard with the letters ‘q’ , ‘w’, ‘e’, ‘r’ on the top left, which is also commonly being referred to as the qwerty layout. This layout was created in 1870s. You may have asked the same question as everyone first started learning typing “why A is not next to B, why the layout looks like total random”. The answer to it was the inventor back then claims this randomness actually helps improve the typing speed by distributing the tasks equally to different fingers, and also due to some mechanical designs limitation that jamming too many frequently typed keys together is not a good idea.

Nowadays, many of those premises no longer holds true and constraint also being removed. Now you can literally make the keys as small as you want, or concentrate certain keys as close as you want without worrying about physical limitations. At the same time, the content that end users entered has also shifted so much that certain keystrokes got typed more frequently than 150 years ago. For example, in the modern digital world, the symbols got typed much more often and sometimes dramatically exceeded even certain letters. For a programmer, they use symbols like semicolon as frequently as how writers use period because semicolon actually means end of a statement in several programming languages. In a typical tweet, people have to use characters like “@” and “#” maybe without using any traditional punctuations.

There has been some efforts to adjust the keyboard layouts by adding certain keys like multimedia keys but the qwerty has certainly never been challenged to a degree that the society cares enough to make a change. Maybe because it is not a problem at all. I agree that for those who work extra hours they certainly not think because they cannot type fast enough. And maybe it is just such a prevalent layout that the cost of change and inconvenience that it will cause outweigh the benefit (many softwares like video games, editors actually choose certain shortcuts because they were convenient under qwerty).

The question now becomes, can you quantify the efficiency or even prove that for a different layout, there will be a significant efficiency gain, or if we take it one step further, out of all the different layouts, is there a way that we can find the most optimal layout that worth the effort to ditch what everyone has been using for the past 150 years.

Key Performance Indicator

There is a saying “if you cannot measure, you cannot manage”, so let’s first start by coming up with a way of measuring efficiency. There are common metrics like (word per minute – WPM) that people use to brag to their friends how fast a typer they are. If we introduce a different layout to two groups of people who are not biased (maybe students or kids who are just learning typing). That will be a great experiment. However, just like covid vaccine test, in order to be scientific, we will need to conduct experiments and the cost of that is just too prohibitive at the early selection stage. But sometime down the road, it certainly will be required.

Now let’s think about the typing process, it boils down to a sequence of actions about moving fingers fast and accurately to push down certain button. There has already been tremendous amount of conversations around what kind of keys are the easier to type, then there comes along inventions like mechanical keyboard, what kind of cherry switch is the most suitable, clicky versus linear etc. However, it is quite obvious that time spent is not only about pushing the button, but also moving the fingers to the right position. Think about how easy it is to type “asdf” because it is literally all next to each other. Now try to type “?\=`”, you will need to lift your pinkie finger to the corner of the keyboard and move it around even with the assistance from your eyes too.

So maybe one angle when we are looking for the best key layout is actually to seek for one that that the user to not move their fingers that much.

For those of you who has an engineering background, this probably already sounds similar to an optimization problem and some of you might already start thinking about “shortest distance”, “traveling salesman”. Yeah, there are many mature algorithms which is designed specifically to solve similar problems and find the shortest distance.

The question is now “can we find a keyboard layout that yields shorter traveling distance than ‘qwerty’ or even better, can we find the best layout that guarantees the shortest travelling distance given modern typing task”.

There are many assumptions that we are going to make in this exploration process and those assumptions might be too naive which lead us to flawed conclusion, but they will dramatically help simplify the problem at the beginning and we can challenge them later and build more complexities as we want.

Key Positions and Size

In a typical keyboard, most keys are same size (square or round) key caps that are perfectly aligned horizontally and tiled vertically. Certain keys even come with a different size like space bar being the biggest, left and right shift, enter, etc. For now, let’s assume that all keys have the same size and are positioning perfectly on a meshgrid, like a chess board. In that way, it is much easier to calculate any distance for two given keys without worrying about the specifics. Another benefit is that the keys can be stored in certain data structure and being calculated in an efficient way like ndarrays when it comes to computing.


Each key on your keyboard usually carries two meanings like you can change the case for letters and entering a different symbol by holding the shift key. This is certainly an important topic as it is those symbols that previously got assigned to the corners or even share the same physical switch that grows its usage lately. If there is a need to separate out certain characters, or even promote certain character to be at a prominent positions are certainly changes that worth exploring. In that case, we will treat all printable characters on a keyboard as its own entity with several exceptions.

Maybe for numeric characters, it worth the effort to exclude them for now as regardless of which frequency to use, they gains its benefit of staying in the numerical order regardless of its usage. At the same time, the case for letters might keep sharing the same key as I can totally imagine what kind of criticism that we will receive if a share the same key as upper case Z. What the hell? There might certainly relationship in symbols like pairs of brackets, smaller than or greater than. In reality, there are even autocomplete features that very few developers have to type the closing parenthesis or brackets because they come autocompleted by IDE. In that case, maybe temporarily removing those closing symbols also makes sense.

So now this is what we ended up with 58 characters:

26 letters
32 symbols: ~!@#$%^&*()_+`-=[]\;’,./{}|:”<>?

Distance Definition

This is probably the most important part of this analysis as it directly determines how our final score will get calculated.

Simple Travel Distance

A naive scenario will be treating all different keys as physical locations. Calculating the total traveling distance for typing a sentence will be equivalent to calculating the total distance of a taxi trip which we just need to sum up the distance between subsequent characters in this physical space.

In order to type the word “hello”, it includes 5 keystrokes and 4 inter button movements. The totally traveling distance will be the sum of moving D(h, e), D(e, l), D(l, l) and D(l, o). One might say that D(l,l) requires no travel at all as it is just pushing the same button twice.

In our case, we can easily calculate the Euclidean distance between e and h as their horizontal difference is 3 and vertical difference being 1. So based on the Pythagorean theorem that the direct distance will be calculated as sqrt(3^2 + 1^2) = 3.16 = D(e,h). In this way, we can calculate the distances being

D(h,e) = sqrt(3^2 + 1^2) = 3.16
D(e,l) = sqrt(6^2 + 1^2) = 6.08
D(l,l) = 0
D(l,0) = sqrt(1) = 1
=> D(hello) = 3.16 + 6.08 + 1 = 10.24

Well, pretty straightforward right? so let’s see if we can write a small Python script so it can be calculated easily.

After we populated the keyboard layout for qwerty and extract the coordinates, now we can write a function that takes in any given layout, any given text, and then we will calculate the total traveling distance. (note: the np.linalg.norm is a pretty handy and high performing function to calculate the Euclidean distance between coordinates)

It matches our calculation!

Different Layouts in Action

Now we have some basic functions to help us evaluate performance. Why don’t we feed it some real life layouts and content and see how it works in action.

So far, other than qwerty, there are indeed some alternatives like coleman or dvorak. Let’s create those two layouts and compare it with qwerty.

In order to work with some real life content, there are some small adjustments that I made to the code which I previously mentioned to skip through travels which involves the characters that we have not entered yet. And also created a counter so the returned travel distance is normalized so we can compare it across even different content or text length.

Here we grabbed the Shakespeare’s sonnets from the Gutenberg project and it is interesting to see that our popular qwerty outperforms other mainstream layouts by quite a bit.

However, now this prompts a few other questions:

  1. is there any other layout that we can generate that proves to outperform qwerty. In theory, we can generate all the possible permutations of layouts and calculate the travel distance for each and find the best one, is it computational feasible, is there a good algorithm that we can use, if not, will there be any approximation technique that we can deploy?
  2. here we are assuming that we actually have only 1 finger. In reality, there are regions and the distance should be calculated in a different way that letter “f” and “j” are really fast traveling wise as both of your index fingers are resting there.
  3. we should also try to work with some different content just to play with as there might be some adjustments depending on your profession that certain keys might need to be adjusted

Hopefully this helps you understand the keyboard is actually a fascinating topic and I will try to cover some of the pending questions in more depth in future writings.

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