# Tire Rolling Circumference Calculation Example

The rolling circumference (RC), in turns, is further considered as input in various vehicle dynamics calculation like traction force calculation and grade ability calculation.

The formula used here is quite simple,

RC = 2 x ∏ x SLR……………….eq.1

Where,

Now, when the wheel is not fitted with the vehicle then it remains at its circular shape and

SLR = R

Where,

But, as soon as the tire is fitted with the vehicle (and loaded) it makes a flat contact with ground and thus its outer radius got reduced. In this condition, roughly,

SLR = 0.96 x R

So, the eq.1 turns to

RC = 2 x ∏ x 0.96 x R ………….eq.2

Pretty simple, right?

But how to know the outer radius (R) of a tire? For that you should note down your tire spec code and you must know how to decode it. The below example will clarify it further.

How to Read a Tire Specification Code?

Take the example of the below tire. And refer the below picture before proceeding further.  It has the spec code starting with P215/65R15.

Image source: wiki

As you can understand from the above picture that, the width of the tire is 215 mm.

And, the depth (height) of the tire is 65% of 215 that is 215 x 0.65 = 139.75 mm

The rim outer diameter for the wheel can be obtained from the “Rim diameter code”, which is 15 inch or 381 mm.

So, the rim outer radius  = 0.5 x 381 = 190.5 mm.

Hence, the outer radius of the wheel,

R = Depth of the tire + Rim outer radius = 139.75 + 190.5 = 330.25 mm

Further by using the eq.2, the rolling circumference for this example is

RC = 2 x ∏ x 0.96 x R = 2 x 3.14 x 0.96 x 330.25 = 1991.01 mm

## 7 thoughts on “Tire Rolling Circumference Calculation Example”

SLR = 0.96 x R, How do you generate 0.96

2. MechGuru says:

This is an approximation, to be more precise
SLR = R – (thread depth)

3. SAJEESH says:

how to calculate tread from tire cure lay out

4. engrsmile says: