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# Rim and Tire sizes (long)

```Hello Q-List:

someone posted off list to me and so I thought I would share this
information on upgrading to bigger rims and tires. Sorry if it's long,
but it is a detailed mathematical formula and explanation on how to
calculate the rolling circumference of any tire and rim combination.

I think there is a formula somewhere on the web, but you can calculate
rolling circumference pretty easily...

Firstly, it is not the size of the rim only that makes a difference, but
rather the rolling cicrumference (RC from now on) of the rim PLUS the
tire size. For example, a 175/65HR15 tire has a RC of 61.2". A
205/45SR17 tire has a RC of 64.8", so these are almost the same RC, but
your speedo will read too low by about 6%. A larger RC means your car
will accelarate slower, but have higher top end speed and lower highway
rpms. Your speedo will read too low if the RC of your new tire/rim combo
is bigger than the RC of the stock tires. Now for the math:

The formula for the circumference of a circle is: 2TTr, where
TT=pi=3.14169 and r=radius of the circle (rim + tire).

So, to calculate the RC (how long the tire would be if you cut it and
laid it on flat on the ground), you have to add the diameter (which is
2x the radius) of the rim PLUS add the diameter of the tire. Since the
175/65 are in millimeters, you first have to convert the 175/65 to
inches. BUT before you do that, the 175/65 number has to first be
converted to the actual tire height. 175/65 means that the tire (or
tread?) width is 175mm and the height of the tire is 65% of the tread
width. BTW, this ratio of 65% to the tread width is called the aspect
ratio. So, the height of the tire would be 175x65/100=113mm. Now take
this figure and divide by 25.4 to get the height of the tire in inches.
113.75/25.4=4.47". So the diameter of the rim + tire (called the RC) is:
TTx (15" [rim] + 4.47" [tire]) = 61.2".

If you have a spreadsheet program, enter values for rim size in A1
(15"), the tread width in A2 (175) and the aspect ratio in A3 (65) and
then enter this formula in A4 to get the RC: =
(3.14169*(A1+(A2*A3/100)/25.4))

Think of rolling circumference this way: for every ONE revolution of the
tire, the car will move forward exactly 61.2".

The letters, HR, SR, TR, VR are speed ratings (H being the lowest and Z
being the highest) and R simply means a radial tire (as opposed to say,
bias-ply tires). (BTW, are these still made?)

If you plan on upgrading your rims to a larger diameter, you need to get
a tire with a smaller aspect ratio or else your speedo will be off. A 5%
difference is the most you can change without worrying about your
speedo, since there are variations between tire companies of about 5%.

HTH.

Rob
Germany

```