# 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

### Shibashis Ghosh

Hi, I am Shibashis, a blogger by passion and engineer by profession. I have written most of the articles for mechGuru.com. For more than a decades i am closely associated with the engineering design/manufacturing simulation technologies.
Disclaimer: I work for Altair. mechGuru.com is my personal blog. Although i have tried to put my neutral opinion while writing about different competitor's technologies, still i would like you to read the articles by keeping my background in mind.

## 7 Replies to “Tire Rolling Circumference Calculation Example”

SLR = 0.96 x R, How do you generate 0.96

1. MechGuru says:

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

1. engrsmile says:

2. SAJEESH says:

how to calculate tread from tire cure lay out

3. nilesh says:

hey tell us roll center position

4. Peter says:

I claim to know how to calculate the rolling-circumference , with use of loaded radius and surface-length on the ground.

This will give a higher factor then your 0,96 for low h/w tires( aspect ratio AR) and the other way around for fi 80%AR lower pressure gives more deflection so shorter loaded radius, and longer surface on ground , so in the end shorter rolling circumference.
Would like to brainstorm futher by mail with you.