Let’s start with speedometer pulse math. It’s very straightforward:
 
All K final drives emit 6 pulses per rear wheel rotation.
 
For this example I’ll use a K1/K100RS4V/K1100RS rear wheel – 160/60/18.
 
It has a circumference of 2040 mm so it turns 1,000,000/2,040=490.2 times per kilometer.
 
At 100 kph it rotates 49,020 times per hour. It generates 49,020*6=294,112 pulses in one hour. That’s 294,112/3,600=81.7 pulses per second or 81.7 Hz.
 
Both Karamba and K_Diag only emit 80Hz at the 100 kph setting which means that if you calibrate right on with either software you speedometer will still be running a little over 2% faster than your actual speed.
 
Also of note is that every single bike model puts out 80 Hz at the 100 kph setting so despite the change in tire circumference the software does not take that into account.
 
And it gets worse. If you enter 160/16-18 as an alternate tire size for any other model (K75S for example) then the K Diag software emits a 78 Hz signal at 100 kph which is even more erroneous – about 4.5%!
 
BUT there is hope!
 
Here’s my calculated table of correct frequencies for various rear tire sizes at various speeds:
JPG: https://www.kbikeparts.com/classickbikes.com/ckb.tech/0.ckb.tech.files/speedocal/K.Bike.Speedo.Cal.jpg
PDF: https://www.kbikeparts.com/classickbikes.com/ckb.tech/0.ckb.tech.files/speedocal/K.Bike.Speedo.Cal.pdf
 
You can use those values with a program like this tone generator freeware app to generate more accurate frequencies for speedometer calibration:
https://www.kbikeparts.com/classickbikes.com/ckb.tech/0.ckb.tech.files/speedocal/tone.exe
 
(You can type whatever you want into the initial popup.)

Hi Duck this is very interesting stuff and I think has answered a question I had around speedometers. 

On K1 (and also k1100RS) speedometers a value is written as per the pictures. (these are my spares)

MPH K= 4784,  KPH K=2973

These values are very close to the Pulses per Mile / Km from your calculations so must be the values used by the factory to calibrate the speedometers.

I have been using a signal generator to calibrate my speedometers and have been using 75Hz for 90kmh.

Using your calculation but entering 2973 for the km speedo I get 82.5 hz for 100km which is very close to your 81.7

I have checked  a collection of  speedometers and noticed all the 16v ones have either 4784 for MPH or 2973 for KMH. I would have thought K1100LT's might be different but checking eBay the all seem to be the same. 8v speedometers do not seem to have this number.

Interesting. I never noticed the "K=" on the 4V clusters but in looking at pics I have of US K1 and K1100 MPH clusters they all have the 4784. If that's the pulses per mile that BMW used for factory calibration then that would explain why they all show 10%-ish higher than actual speed.

My THEORY as to why BMW has speedos be off in that direction is that they would have less legal liability if speedos run too high vs. too low. Many of the cars I've owned also have speedos that run too high. The one car I've owned that had an accurate speedometer from the factory had a digital speedo.

K1100 RS vs LT speedos: It costs less to use the same calibrated speedo for both models.

BTW: Those aren't "my calculations." They are basic math based on tire circumference. Anybody else should come up with the exact same results.

duck wrote:
My THEORY as to why BMW has speedos be off in that direction is that they would have less legal liability if speedos run too high vs. too low. Many of the cars I've owned also have speedos that run too high.

duck,
dead on.
Where I do live, it is required by the authorities - a speedo is allowed to run up to 5% too fast, but never ever too slow. It is being checked at every MOT.

I recall having my various Airheads' speedometres calibrated by an elderly gent called Erv Simon from Simon's Speedo Hospital back in the 1980s and early '90s. He was from somewhere near the Chesapeake Bay area of Maryland, and is long gone now, but in the day offered up some interesting tidbits concerning his time working on BMW instruments. One was that nearly all /6, /7 and 1980s Airheads would have an up to 8 mph optimistic speedo reading, but that the odometres would be very nearly dead nut on target. He had a way of turning that small adjustment screw that rides in a groove whilst spinning the rubbery plastic cogs - similar to a K bike's - of the speedo in a calibration stand on his workbench. These are fully analogue so it was his patient hand and years of doing it that got a result. He was never able to close that 8 mph gap fully but he'd get it very close to accurate. 

Some people like a clock set ahead to fool themselves into rising on time. Some people prefer to know exactly at what speed the world is passing beneath them.

Duck, this is very useful information you're offering up to us. Thanks!