Advanced Rolling Radius Calculator
Example Data Table
| Tire size | Loaded factor | Unloaded radius | Rolling radius | Revs per km |
|---|---|---|---|---|
| 205/55R16 | 97% | 315.950 mm | 306.472 mm | 519.314 |
| 225/45R17 | 96% | 317.150 mm | 304.464 mm | 522.738 |
| 265/70R17 | 95% | 401.400 mm | 381.330 mm | 417.368 |
Formula Used
The calculator starts with the tire size when that method is selected.
Sidewall height = section width × aspect ratio ÷ 100.
Overall diameter = rim diameter × 25.4 + 2 × sidewall height.
Unloaded radius = overall diameter ÷ 2.
Rolling radius = unloaded radius × loaded radius factor ÷ 100.
Rolling circumference = 2 × π × rolling radius.
Revolutions per distance = selected distance ÷ rolling circumference.
When the measured revolution method is used, circumference comes directly from distance divided by revolutions.
How to Use This Calculator
- Select the calculation method that matches your available data.
- Enter tire size, direct measurement, or measured revolution details.
- Set the loaded radius factor for real road behavior.
- Enter an indicated speed for wheel rpm and speed checks.
- Add an optional reference tire to compare speedometer effect.
- Press the calculate button to show results above the form.
- Use the CSV or PDF option to save the result.
Rolling Radius in Vehicle Physics
Rolling radius is the working radius of a tire while it carries load and moves on the road. It is usually smaller than the unloaded radius. The tire sidewall bends near the contact patch. That small change affects speed, gearing, traction studies, and wheel revolution estimates.
Why It Matters
A tire label gives section width, aspect ratio, and rim diameter. Those values describe geometric size. Real rolling behavior is different. Air pressure, vehicle weight, tread depth, construction, and road surface can all change the effective radius. A racing setup, an off road truck, and a daily commuter may use the same basic formula, yet need different load factors.
This calculator lets you start from a tire code, a direct diameter, a direct radius, or known revolutions over a distance. That makes it useful for design checks and field measurements. You can also compare a new tire with a reference tire. The comparison helps show speedometer error, wheel rpm change, and circumference difference.
Practical Interpretation
Use the unloaded size result for catalog comparison. Use rolling radius for motion analysis. The loaded percentage is a practical adjustment. A value near 96 to 98 percent often gives a reasonable starting point for many passenger tires. Heavy load, low pressure, or soft sidewalls can require a lower value.
The revolutions per mile and kilometer are important for drivetrain calculations. More revolutions mean a smaller rolling circumference. Fewer revolutions mean a larger tire. A small radius change may look minor, but it can alter indicated speed and engine rpm.
For best accuracy, measure tire revolutions on a straight path. Mark the tire and floor. Roll the vehicle several turns under normal load. Divide distance by turns. This direct method captures pressure, load, and tread condition.
Good Inputs Create Better Results
Enter sizes carefully. A 205/55R16 tire uses a 205 millimeter section width, a 55 percent aspect ratio, and a 16 inch rim. Enter the loaded percentage that matches your assumption. Then review the result table. Export the values when you need records for a report, shop note, or physics exercise. Keep units consistent. State whether radius is unloaded, or revolution based. This avoids mistakes during decisions and later shop discussions.
FAQs
What is tire rolling radius?
It is the effective radius of a tire while it rolls under load. It is usually smaller than the unloaded radius because the sidewall compresses at the contact patch.
Why is rolling radius different from tire radius?
The normal tire radius is often based on geometry. Rolling radius includes load, pressure, sidewall flex, and tread condition. That makes it better for motion and speed calculations.
What loaded radius factor should I use?
A starting value near 96 to 98 percent often works for many passenger tires. Use measured revolution data when accuracy matters more than a quick estimate.
Can this calculator compare tire sizes?
Yes. Enter the main tire and optional reference tire. The calculator shows circumference change and estimated actual speed at the entered indicated speed.
How do revolutions per mile help?
They show how many wheel turns occur over one mile. This value helps with gearing, odometer checks, engine rpm estimates, and drivetrain comparisons.
Is the direct measurement method accurate?
It can be useful if the measured diameter or radius is reliable. For real motion behavior, measured revolutions over distance usually gives a stronger practical result.
Does tire pressure affect rolling radius?
Yes. Lower pressure can increase sidewall deflection and reduce effective rolling radius. Higher pressure may reduce deflection, but load and tire design still matter.
Can I export the calculation?
Yes. After calculating, use the CSV or PDF buttons. They save the major radius, circumference, revolution, wheel rpm, and comparison values.