Carl I am not using anything to calculate the conversion. Attempting to do a conversion will not work as the 1/3" designation is only an archaic vestige of a measurement. It only corresponds to the actual imager size in that it is roughly 1.5 times bigger than the actual size, though even this varies quite a bit. It is best to think of it more like a label like ExtraSmall than a measurement. Links above show its vacuum tube origins.
Ever wonder why lens calculators don't let you type in an arbitrary size sensor? Because they have to be 'hard coded' with the real value because there is no straight conversion.
Though for the record I believe, like John and Brian, that it is not important to know what the actual size of a 1/3" imager is, though I would add, as long as one knows its not 1/3"!
Why does that even matter?
Take your own example from a ways back where you stated:
On a similar note, I need to find a new lens calculator. It is simple to calculate lens requirements based on a 1/3" or 1/4" imager when you measure the HFOV and distance to the camera. Not so when you consider the greater variety of modern camera imager sizes (1/1.8", 1/2.5", 1/3.6", 1/5" and 1/6" and the more standard 1/4", 1/3" and 1/2").
And then due to a lack of image size options in your calculator, you just looked up the formula like Tahir did in the same discussion:
But as per their paper http://www.theiatech.com/papers/Resolution_calculation.pdf.
HFOV = Camera Dist * Chip Width / Focal Length
which John then acknowledged as being correct. But if you were to use the listed format size of say 1/3" with the formula you would find you were way off. Just like Chris is in this well meaning but misguided IPVMU verification post:
H Sensor Size: 9.398 mm (1/2.7")
HFOV = Distance / (Focal Length / H Sesnsor Size)
16.75m (55 ft) = 3000m / (1680mm / 9.398mm)
PPF = H Resolution / HFOV
35 PPF = 1920px / 55ft
where the sensor size is really 6.5mm not 9.398.