Rolling Circumference Calculator:
Installing the wrong tire size on the vehicle will lead to an odometer deviation. The exact deviation can be calculated using the calculator below. When using a phone, it is best to switch to “landscape mode” to view the entire table.
The table provides two tire sizes: 205/55R16 and 225/40R18. These sizes can be changed to the sizes you wish to compare.
At the bottom, the speeds of both tire sizes are compared: if tire 1 rotates at speed x, then tire 2 rotates at speed y.
Since we are initially comparing the tire sizes statically, the deflection can remain at the preselected 0% and 0 mm. The outcome will then be n.a.
The explanation of static and dynamic height and circumference (under a load >0) is provided in the following paragraphs.
Explanation of Tire Height and Rolling Circumference:
Using the calculator, tire height and rolling circumference can be calculated. This is ideal when looking for a different tire size (for example, from 16 to 18 inches) that fits under the car without affecting the accuracy of the speedometer.
The tire in the example is labeled: 205/55 R16:
- 205 = tread width in mm
- 55 = tire height from road surface to wheel edge = 55% of 205 (0.55 x 205 = 112.75 mm)
- 16 = rim diameter in inches (1 inch = 25.4 mm, so 16 inches x 25.4 mm = 406.4 mm)
Enter these three values into the calculator to calculate the tire height and static rolling circumference in an unloaded state. The tire height is twice the height in millimeters plus the rim diameter in mm. In the example above, this means: 112.75 + 112.75 + 406.4 = 631.9 mm (or 63.19 cm). This calculator makes it easy to calculate the tire heights of different sizes and the difference in circumference and speed.
The two tire sizes standard in the table, 205/55 R16 and 225/40 R18, have a very small difference in height and circumference. Therefore, the speed difference on the speedometer is also minimal. This means that when the size 205/55 R16 is prescribed by the manufacturer, wheels with the tire size 225/40 R18 can also be mounted. The only question is whether the wider tires will rub against the wheel arches. If this occurs while steering, it can cause significant tire wear and be a reason for rejection during the inspection. In that case, wheel spacers provide a solution.
More information about the tires can be found on the wheels and tires page.
Static Rolling Circumference:
The static rolling circumference is the distance a wheel travels in one complete rotation when rolled over the ground without being loaded by the weight of the vehicle. There is no deformation due to deflection or any other form of loading.
For example, if the manufacturer originally fitted a 205/55 R16 tire size and someone wants to mount larger rims and tires, several factors must be considered. The offset value must be correct, the tires must not rub against the shock absorber, wheelhouse, or control arms, and the static rolling circumference should not differ too much from the other tire size. The static rolling circumference can be calculated using this calculator. As described above, we assume a deflection of 0% and 0 mm for the static rolling circumference. The following are the calculations to determine the static rolling circumference of a wheel.
- Tire Size: 205/55 R16
- Calculation of the Sidewall Height: 205 d7 (55/100) = 112.75a0mm
- Calculation of Total Tire Diameter: The total diameter of the tire is the sum of the rim diameter and twice the sidewall height:
– Totala0Diameter = (Rim Diametera0ina0Inches d7 25.4) + 2 d7 Sidewall Height
– The rim diameter in millimeters is: 16 d7 25.4 = 406.4a0mm
– Therefore, the total diameter is: 406.4 + 2 d7 112.75 = 631.9a0mm - Calculation of the Static Rolling Circumference: The circumference of the tire is calculateda0using the formula for the circumference of a circle:
Rolling Circumference = c0 d7 Totala0Diameter
Rolling Circumference = c0 d7 631.9
Rolling Circumference = 1984.76a0mm 248 1.98a0meters
The tire size 205/55 R16 has a static rolling circumference of approximately 1.98 m. When you mark a chalk line on the sidewall of the tire and the road surface, rotate the wheel one full turn, and then mark a line on the road surface at the point where the line on the sidewall returns, the distance between these marks will be 1.98 meters. This distance determines the speed displayed on the vehicle’s speedometer.
We now compare the tire size 225/40 R18 and see that the rolling circumference is now 2.00 m. This difference is minimal, making this tire size suitable for the vehicle (provided it doesn’t rub against anything). However, when the size 225/45 R18 is calculated, a static rolling circumference of 2.07 m is observed. Compared to the 205/55 R16, this is too much of a difference, resulting in a lower indicated speed on the speedometer (the wheel takes longer to make a complete revolution). Therefore, this tire size is not recommended for installation.
In the instruction manual or on websites like Autoweek.nl, you can find the prescribed tire sizes for the vehicle. This calculator allows for the comparison of various tire sizes.
Dynamic Rolling Circumference:
The dynamic rolling circumference of a tire is the distance the tire travels in one complete revolution while operating under normal conditions. This occurs under the load of the vehicle and in interaction with the road surface. There is a difference between the dynamic and static rolling circumference due to factors such as tire deformation, load, speed, and tire pressure. The dynamic rolling circumference is usually lower due to the deflection of the tire.
In practice, we see that if one tire on the same axle has lower tire pressure than the other, this can lead to the vehicle pulling to one side and a crooked steering wheel when driving. This is because the two tires on the same axle have different tire heights and rolling circumferences. When the tire pressure of all tires is low and there are no differences on one axle, there is no immediate pulling to one side. However, an abnormal rolling circumference can develop, leading to a difference in speed display.
In the calculator, we calculate the dynamic rolling circumference when the deflection is greater than 0, in percentage or millimeters. For an accurate approximation, only enter one of the two, not both. If both are entered, the millimeter deflection is added to the percentage, which is unrealistic.
To determine the dynamic rolling circumference, we assume in this example that the underside of the tire is deflected by 15 mm due to the weight of the vehicle. This deflection of the tire reduces the total diameter of the wheel, as shown in green in the illustration.
- Static condition without deflection: 631.9 mm (see previous paragraph);
- Deflection: (112.75 – 15.0) = 97.75 mm;
- Dynamic condition: 616.9 mm.
We now calculate the rolling circumference using the dynamic data.
Rolling Circumference = c0 d7 total diameter
Rolling Circumference = c0 d7 616.9a0
Rolling Circumference = 1938.05 mm 248 1.94 meters
Since the static rolling circumference was 1.98 meters and the dynamic rolling circumference is now 1.94 meters, we can conclude that the load and tire pressure affect the distance traveled by the wheel, and thus also the speed indicated on the speedometer. The results in the calculator show that at 100 km/h, there is a speed difference of 2.37 km/h due to the 15 mm deflection.a0
When we approach the deflection as a percentage instead of a measured value in millimeters, it becomes much more theoretical. It cannot be assumed that at 10% deflection the total sidewall height (112.75 mm) decreases by 10%. The sidewall height is measured from the heel to the tread. At the heel to rim transition, there is no deflection. Also, the sidewall will be stiffer where it transitions into the shoulder. On average, we can establish that the non-deflecting portion of the sidewall is about 25 mm of the total length of the sidewall. At 10% deflection, the dynamic height can be calculated with the following formula:
Dynamic height = static wheel height – ((static sidewall height – 25) * (deflection percentage / 100)) – deflection in mm
Dynamic height = 631.9 – ((112.75 – 25) * (10 / 100)) – 0
Dynamic height = 623 mm.
With the dynamic height of 623 mm, the rolling circumference can be calculated again.
In the calculator, you can choose to enter the deflection in millimeters instead of percentage. In that case, the formula is filled in as follows:
Dynamic height = 631.9 – ((112.75 – 25) * (0 / 100)) – 30
Dynamic height = 592 mm.
Conclusion:
When comparing different tire sizes in the rolling circumference calculator, we do not base our understanding on the dynamic data. Although a wider rim changes the weight distribution between the tire and the road surface—spreading the weight over a larger area and consequently decreasing the pressure on a specific area, affecting the level of deflection of the tire—these differences are negligible.
By entering the dynamic data, such as the percentage or the number of millimeters of deflection, a more realistic result that is closer to reality is provided.
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