Im running 180 55 Pirelli Angel GT width size is 9" (228mm) from tire edge to edge. Weird i have never measured them before.
The 180 you have does not have a "width" of 228 mm. I am surmising you measured the sector of the tire as well. Or you could call it the perimeter of the tire from edge to edge.
Tires need to be measured like you had a plus sizes caliper. Or put two yard sticks along the outside of the tires just below the swing arm and measure the distance in between. Making sure to keep the sticks parallel.
Someone will come on here and describe it better, but your 180 is not 228 across. Would look cool, but not accurate in the way this discussion is understood.
180 x 55 x 17 are the
nominal tire dimensions. It is what the factory would like the tires to be; tire manufactures may stray a bit from this specification. With the stock rim there is no need to calculate variation due to rim width changes, unlike many car owners that change rims. Tire manufacturers have a little leeway to play with width and aspect ratios and not be absolutely faithful to the factory tire dimensions as long as they don't exceed the width or overall diameter to avoid fitment interference.
180 = the tire sidewall at the widest point, excluding raised lettering (tire section).
55 = the aspect ratio between the tire width and sidewall height, this is used to calculate the sidewall height between the rim and the contact patch.
17 = the inner tire diameter
The second number (55) is actually a percentage which represents the ratio of sidewall height to the tire's width. The sidewall height can be calculated by multiplying the tire width (180mm) by the aspect ratio percentage (.55). The height of one sidewall is:
180mm x .55mm = 99mm sidewall height
To calculate the overall diameter of a tire, the sidewall height must be multiplied by 2 (the tire diameter is made up of 2 sidewalls, the one above the wheel and the one below the wheel touching the ground) and add the diameter of the wheel.
99mm + 99mm + 431.8mm (17") = 629.8mm (24.8") diameter
The contact patch will be less than the tire width (section). In fact, contact patch is one area where tire manufacturers can use tire curvature to affect the handling, feel and capability of the tire to complement the tire compound. Sit on your FJR and have someone run water on the pavement between the center of the bike and the rear tire, then roll the bike forward. The water track will show the actual contact patch width. In theory, if you were to hold your FJR at 160° to vertical and do this test again the contact patch width should still be similar in width to the 180° contact patch.
Typically, a shorter sidewall (smaller aspect ratio, such as 40 vs 55) will flex less than a taller sidewall, and would offer a stiffer ride, Good for track, bad for touring. The thing that sets apart the various manufacturers and tire models are the rubber compound(s), weave and material of the tire carcass and tire profile. The various 'formulas' can result in different tire shapes, each tuned for a particular goal that the tire manufacturer set as their design objective.
The fact that people observe different tire dimensions isn't surprising. It is in no way an indication that one tire is better or has an advantage over the other, there are many different ways to arrive at the same solution. In fact, each different tire model is intended to provide different solutions to the riding and handling experience. When you buy a tire and look at all the different available models of 180 x 55 x 17 tires you should pay attention to what you want out of the tire and what the tire can provide. "I want the longest tire wear" is a single goal, "I want the best dry track tire" is another single goal. Most of us are looking for a tire which offers good tread life, sticks well both dry and wet, can handle a touring load and isn't harsh. Fortunately, tire manufactures offer tire models which fill all these requirements, choose wisely
(and don't be beguiled by tire appearance).
I wouldn't be surprised if the above is true for 120 x 70 x 17 tires also.