Advanced Tyre Rolling Radius Form
Formula Used
Sidewall height: width × aspect ratio ÷ 100
Rim diameter in millimetres: rim inches × 25.4
Unloaded radius: rim radius + sidewall height
Static loaded radius: unloaded radius × (1 − static deflection ÷ 100)
Dynamic radius: static loaded radius × (1 + dynamic growth ÷ 100)
Effective rolling radius: dynamic radius × (1 − slip ÷ 100)
Rolling circumference: 2 × π × effective rolling radius
Revolutions per kilometre: 1,000,000 ÷ rolling circumference
Speedometer error: (new rolling radius ÷ reference rolling radius − 1) × 100
Engine rpm: wheel rpm × gear ratio × final drive ratio
How To Use This Calculator
- Enter the tyre section width, such as 205 for a 205/55R16 tyre.
- Enter the aspect ratio printed on the tyre sidewall.
- Enter rim diameter in inches.
- Add static deflection to model load compression.
- Add dynamic growth for speed related expansion.
- Add slip percentage when modelling traction loss.
- Enter a reference rolling radius to calculate speedometer error.
- Press the calculate button and review the result above the form.
- Use the CSV or PDF button to save the calculation.
Example Data Table
| Tyre Size | Width | Aspect | Rim | Deflection | Estimated Rolling Radius | Revs Per Km |
|---|---|---|---|---|---|---|
| 195/65R15 | 195 mm | 65% | 15 in | 3% | 309.40 mm | 514.42 |
| 205/55R16 | 205 mm | 55% | 16 in | 3% | 303.55 mm | 524.34 |
| 225/45R17 | 225 mm | 45% | 17 in | 3% | 307.23 mm | 518.06 |
Tyre Rolling Radius Guide
Overview
A tyre rolling radius calculator helps convert printed tyre codes into practical motion values. A tyre does not travel by its advertised outside diameter alone. The sidewall flexes under load. The tread also squashes slightly where it meets the road. That contact patch changes the effective radius used in speed, distance, and gearing calculations.
Why Rolling Radius Matters
Rolling radius links wheel rotation to road distance. When the radius grows, the vehicle travels farther per revolution. Engine speed drops at the same road speed. The speedometer may read lower than the real speed. When the radius shrinks, the opposite happens. This is important for replacement tyres, off road builds, fleet checks, and race setup work.
What This Tool Estimates
The calculator starts with section width, aspect ratio, and rim diameter. It finds the sidewall height and the theoretical unloaded radius. Then it applies a static deflection percentage. This models how the tyre compresses under load. A growth value can be added for speed related expansion. A slip value can reduce the effective distance moved per rotation. These inputs create a practical rolling radius and rolling circumference.
Physics Behind The Output
The key relationship is simple. Distance per wheel turn equals two times pi times rolling radius. Revolutions per kilometre are found by dividing one kilometre in millimetres by that circumference. Wheel rpm comes from road speed divided by circumference. Gear ratio and final drive convert wheel rpm into engine rpm. These linked outputs make the result useful beyond tyre sizing alone.
Good Input Practice
Use measured data when accuracy matters. Real tyres vary by brand, tread, pressure, load, and temperature. New tyres have taller tread than worn tyres. Low pressure increases deflection. Heavy load reduces static radius. High speed can increase dynamic radius. Treat the result as an engineering estimate, not a certified measurement. For legal speedometer calibration, confirm with GPS, road tests, or workshop equipment.
Useful Planning Notes
Changing tyre size affects clearance, acceleration, braking feel, odometer readings, and traction control behavior. Compare the new radius against the original setup before buying parts. Small differences are often manageable. Large differences may need recalibration, alignment checks, or gearing changes. Always leave space for suspension travel and steering lock under load.
FAQs
What is tyre rolling radius?
Tyre rolling radius is the effective radius that links wheel rotation to road distance. It is usually smaller than the unloaded radius because the tyre compresses under vehicle load.
Is rolling radius the same as tyre radius?
No. Tyre radius often means theoretical unloaded radius. Rolling radius considers compression, motion, and slip. It better represents how far the vehicle travels per wheel revolution.
Why does static deflection matter?
Static deflection models the tyre flattening at the road contact patch. More load or lower pressure usually increases deflection and reduces the practical rolling radius.
What is dynamic growth?
Dynamic growth is tyre expansion during motion. It may happen at higher speed because rotating forces slightly increase tyre size. The amount depends on tyre construction and conditions.
How does slip affect rolling radius?
Slip reduces the useful distance travelled per revolution. This calculator applies slip as a percentage reduction after loaded and dynamic radius adjustments.
Can this calculate speedometer error?
Yes. Enter the original or reference rolling radius. The calculator compares the new radius against it and estimates speedometer error and true speed.
Are the results exact?
No. The result is an engineering estimate. Actual rolling radius depends on tyre brand, tread depth, pressure, load, temperature, road surface, and speed.
Can I export the result?
Yes. After calculation, use the CSV button for spreadsheet work. Use the PDF button for a simple saved report of the result table.