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CW timing and bandwidth calculator

Where speed in words per minute comes from

The reference word is PARIS — it lasts exactly 50 time units including the gap after it. A speed of 20 WPM means that word fits into a minute twenty times, from which the time unit — which is also the length of a dot — comes to 1200 / 20 = 60 ms. The whole of the rest of the timing follows from it.

·−·between lettersdotdashbetween words
The letter «A» (·−) and the start of the next one. The gap between elements inside a letter equals one dot
Speed
Character speed (WPM)
Overall speed (WPM, Farnsworth method)
Bandwidth
Factor K (5 — fading channel, 3 — without)
Bandwidth for comparison (Hz)
Timing
Dot
Dash (3 dots)
Gap between elements
Gap between letters
Gap between words
Bandwidth and gain
Keying speed
Required bandwidth
Gain from noise bandwidth

When the overall speed equals the character speed, this is ordinary timing. Lower it, and the characters stay at full speed while the gaps stretch: that is how people learn to hear letters as whole shapes without having time to count them.

📐 Formulas​

Length of a dot (the PARIS standard):

t [ms] = 1200 / WPM

The rest of the timing, in dots:

dash              = 3 t
gap between elements = 1 t
gap between letters  = 3 t
gap between words    = 7 t

Farnsworth spacing. The characters stay at speed c and only the gaps are stretched so that the overall speed comes out at s. In the word PARIS 31 units belong to the characters themselves and 19 to the gaps, so what has to be shared out is:

Δ [ms] = 60000 / s − 31 × 1200 / c
gap between letters = 3 Δ / 19
gap between words   = 7 Δ / 19

Keying rate: one dot per second is one baud.

B [Bd] = 1000 / t = WPM / 1.2

The necessary bandwidth from ITU-R Recommendation SM.1138-3, the row «Continuous wave telegraphy, Morse code»:

Bn = B × K
K = 5 — a fading channel
K = 3 — a non-fading channel

The noise-bandwidth advantage over a wider receive chain:

G [dB] = 10 × lg(B_ref / Bn)
Limits of the calculator:
  • K is not a property of the signal but the allowance for distortion built into the recommendation. The real occupied bandwidth depends on the shape of the edges: soft keying is narrower than hard, which is exactly why transmitters shape their edges.
  • The ITU's own example for 25 WPM gives B = 20 baud and a bandwidth of 100 Hz. Here it is worked out exactly to PARIS — 20.83 baud and 104 Hz. The difference comes from rounding in the recommendation, not from an error.
  • The advantage is counted by noise bandwidth alone, at the same spectral density and with ideal filters. How much of it you actually get depends on the operator's ear or on the decoder — which is no longer about the filter.
  • With Farnsworth spacing the bandwidth is set by the character speed, not by the overall one: the width of the spectrum comes from the shortest element, and stretched gaps do not affect it.

🎯 Where it is used​

  • Setting up a key or a trainer: enter your speed and see how long a dot lasts in milliseconds.
  • Comparing modes honestly: 20 WPM against a 2400 Hz SSB filter gives about 14.6 dB of bandwidth advantage — what the same advantage would have cost in power.
  • Choosing a filter: a 250 or 500 Hz filter in a transceiver is already much wider than the signal itself, and the rest is margin for mistuning and drift.
  • Planning how to learn: picking the «character speed / overall speed» pair to start from.
Practical notes:
  1. 1200 / WPM is worth simply memorising: 20 WPM — 60 ms, 25 WPM — 48 ms, 12 WPM — 100 ms.
  2. Learn CW with Farnsworth spacing: the characters at 20–25 WPM from the start, with the overall speed brought down to 10–12. Slowing the character speed itself is the commonest mistake: it teaches the brain to count dots instead of hearing letters.
  3. The bandwidth advantage grows slowly: halving the speed buys only 3 dB. So sending too slowly does not rescue a contact, it only makes it longer.
  4. You can see the same timing in motion, and hear it, in the contact-structure trainer and on the code tree.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «CW timing and bandwidth calculator». CyberDev.Space. https://cyberdev.space/en/radio/cw/timing (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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