How long is a dit at 12wpm?

Why even convert wpm?

I started to write a “little” project for the MicroBit in Python. To future proof the project I want to make sure to implement the speed in words per minute (wpm). This immediately begged the question of how long should I play the tone of a dit when I want to practice at 12wpm?

Basics

Morse Code is not just dits and dahs, there are also spaces. But how long is a dit, how long a dah and how long do I wait between two letters?

 .  = 1 u
 –  = 3 u
[s] = 1 u
[l] = 3 u
[w] = 7 u

u...unit of time
[s]... space between symbol (dits and dahs)
[l]... space between letters
[w]... space between words

Words, letters, symbols and units

What is actually a word? When you calculate words per minutes it makes a difference which word you take:

hi (2 letters)
Supercalifragilisticexpialidocious (34 letters)

And even if the words have the same amount of letters, it still makes a difference. Let’s compare, for example, “cook” and “need”.

cook = -.-.  --- --- -.- (13 symbols)
need = -. . . -..        (7 symbols)

Same amount of letters, but almost the double amount of symbols. But we’re not finished. Lets go deeper. Even if the letters have an equal amount of symbols, the letters still consume a different amount of time.

o: --- (11 u)
s: ... (5 u)

This difference in units is due to the fact that the letters were assigned to their symbols to account for their likelihood1 to show up in a (german)2 text.

PARIS

To standardize things a certain word was used to measure the words per minutes. This word is “PARIS”3.

So on our quest to find out the amount of time consumed by one dit, lets calculate the units in “PARIS”.

wpm to baud

First let’s translate the letters to morse:

P = .--.
A = .-
R = .-.
I = ..
S = ...

Now let’s count the dits and dahs… and don’t forget the spaces.

10x  .  -> 10x 1 u = 10 u
 4x  -  ->  4x 3 u = 12 u
 9x [s] ->  9x 1 u =  9 u
 4x [l] ->  4x 3 u = 12 u
                     ----
                     43 u

After checking with the wpm article on Wikipedia I found, that a word includes the wordspace [w] of seven units after the word. In this case “*PARIS *” equals to 50 units.

Maths

Note: For the sake of simplicity, I will write to the unit words per minute w/min4. Further down you’ll see why.

To be able know how long my Dit should last at 12w/min I need to answer three questions.

  1. How many units are in a minute at 12w/min?
12 w/min = 12 * PARIS[w] = 12 * 50 u
 x w/min =  x * 50 u/min
  1. How can I convert words per minute to words per second?
 1 min = 60 s

60 w/min = 1 w/s (word per second)
 1 w/min = 1/60 w/s
 x w/min = x/60 w/s
  1. How can i convert words per minute to minutes per word?
 2 w/min = 1/2  min/w
10 w/min = 1/10 min/w
 x w/min = 1/x  min/w

Now we need to combine these three informations to be able to convert words per minute to seconds per unit. Since a Dit usually takes less than a second I will convert to Milliseconds (a thousandth of a Second).

x w/min = x * 50 u/min 
        = x*50/60 u/s 
        = 60/(50x) s/u 
        = 6000/(5x) ms/u
	= 1200/x ms/u

Congratulations! We can now calculate how long a Dit takes at 12 words per minute. Now we’ll switch back to old notations.

12 wpm = 1200/12 ms/u 
       = 100 ms/u

The table for 12wpm looks as follows:

 .  = 100 ms
 –  = 300 ms
[s] = 100 ms
[l] = 300 ms
[w] = 700 ms

For any other wpm you just have to use the equation x wpm = 1200/x ms/u.

I hope this post was easy to understand. If you have any further questions, drop me a line.

Footnotes:

  1. See Letter frequency (Wiki) ↩

  2. The Morse Code as we now know it was revised by German writer Friedrich Clemens Gerke (1801-1888). ↩

  3. To make things more complicated: Sometimes the standard word CODEX is used. But we won’t talk about this here. ↩

  4. the word per signals a fraction/division. m is usually used for Meter, min for Minutes ↩