Focal length calculator vs. real life results - where's the error?

[Heiko Saele]

I need to figure out what focal length do I need on a 1/3" chip camera (JVC GY-HD 251 in 4:3 mode!) to cover an object width of 4.50 meters when the camera is at a distance of 6 meters.

I found this nice focal length calculator at the Fujinon site Lens calculatorFUJINON (EUROPE)
and it tells me I need 6mm, which is definitely not the case, because the Fujinon lens on the camera in question already has 5.5mm, and it is nowhere near covering that area.

My first question is: the GY-HD 251's chip is a 16:9 chip. Does that mean when I use it in 4:3 the chip size isn't 1/3" anymore, but smaller? I think so, but I'm not really sure here.

Now for the next confusing real life experience vs. theoretical calculator: I got another camera, a 1/2", 4:3 (I believe it's a real 4:3) with a 6.7mm lens, so I thought I'd check out how the coverage of this combination of chip size and focal length would be.

The result was that I could cover the 4.5m width tightly inside the 90% safety area of the camera's viewfinder.
HOWEVER, the Fujinon focal length calculator tells me that with that chip size, 4:3 and 6.7mm focal length I should be able to cover an object width of 5.73m.

I might be off with the measuring about 10cm here and 10cm there, but 4.50 meters real life coverage versus 5.73 meters from the calculator - how is that accounted for? Do I have to substract 20% from what the calculator tells me? I mean I'd understand a 10% difference because the safety margin of the camera is 10% (or is it, I'm not even sure about that...). But 20% or even more? I just don't get it. Or maybe the 1/2" camera is also a 16:9 chip and therefore I'm also losing width?

Can someone please help me out with this, I'm totally lost here... but I need to find out quick if it's just buying a 0.8x converter or a whole new lens - which will of course be substantially more expensive than the converter...