# How do these tire sizes compare?

Computes the overall diameter, sidewall height, circumference and revolutions per mile of two metric tire sizes, the difference between them, and how a speedometer reading changes.

- Page: https://www.acalculator.org/everyday-life/tire-size-calculator
- JSON spec: https://www.acalculator.org/everyday-life/tire-size-calculator.json
- Version: 246b960fdc95

## Default answer

Example with the default inputs (Current width (mm) 225, Current aspect ratio (%) 45, Current rim (in) 17, New width (mm) 235, New aspect ratio (%) 40, New rim (in) 18, Speedometer reading 60 mph): The new tire’s diameter differs by 1.72%; at a reading of 60 mph you are going 61 mph.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| w1 | Current width (mm) | The section width of the current tire, the first number of its size, in millimetres. |
| a1 | Current aspect ratio (%) | The sidewall height of the current tire as a percent of its width, the second number. |
| r1 | Current rim (in) | The rim diameter of the current tire in inches, the number after the R. |
| w2 | New width (mm) | The section width of the new tire, in millimetres. |
| a2 | New aspect ratio (%) | The sidewall height of the new tire as a percent of its width. |
| r2 | New rim (in) | The rim diameter of the new tire in inches. |
| speed | Speedometer reading | A speed shown on the speedometer, set up for the current tires. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| difference | Diameter difference | How much larger (or smaller, if negative) the new tire’s diameter is, as a percent of the current one. |
| diameter | Current diameter | The overall diameter of the current tire: rim + 2 × sidewall. |
| newDiameter | New diameter | The overall diameter of the new tire: rim + 2 × sidewall. |
| sidewall | Current sidewall | The sidewall height of the current tire: width × aspect ratio ÷ 100. |
| newSidewall | New sidewall | The sidewall height of the new tire: width × aspect ratio ÷ 100. |
| circumference | Current circumference | The distance around the current tire: π × diameter. |
| newCircumference | New circumference | The distance around the new tire: π × diameter. |
| revs | Current revolutions per mile | How many times the current tire turns in one mile: 1 mile ÷ circumference. |
| newRevs | New revolutions per mile | How many times the new tire turns in one mile: 1 mile ÷ circumference. |
| actualSpeed | Actual speed on the new tires | The true speed when the speedometer shows the reading above: reading × new diameter ÷ current diameter. |

## Method

sidewall = width × aspect ÷ 100; diameter = rim + 2 × sidewall; circumference = π × diameter; revolutions per mile = 1 mile ÷ circumference; true speed = reading × new diameter ÷ current diameter

## Assumptions

- Sizes are metric tire codes such as 225/45R17: section width in millimetres, aspect ratio in percent, rim diameter in inches.
- The diameter is the unloaded design diameter. A tire under load, worn, or at a different pressure is a little smaller.
- The speedometer is assumed to read true on the current tires.

## Worked examples

1. w1 = 225, a1 = 45, r1 = 17, w2 = 235, a2 = 40, r2 = 18, speed = 26.8224 gives sidewall = 0.10125, diameter = 0.6343, newSidewall = 0.094, newDiameter = 0.6452, difference = 1.71843%, revs = 807.61486, actualSpeed = 27.283324. Source: hand calculation in content.mdx: sidewall 225 × 0.45 = 101.25 mm; diameter 431.8 + 202.5 = 634.3 mm (24.97 in); new 457.2 + 188 = 645.2 mm (25.40 in); +1.72%; 60 mph reads 61.03 mph true.
2. w1 = 205, a1 = 55, r1 = 16, w2 = 205, a2 = 55, r2 = 16, speed = 27.777778 gives difference = 0%, diameter = 0.6319, revs = 810.682237, actualSpeed = 27.777778. Source: hand calculation in content.mdx: 205 × 0.55 = 112.75 mm; 406.4 + 225.5 = 631.9 mm; 1,609,344 ÷ (π × 631.9) = 810.7 revolutions a mile.

## FAQ

### What do the numbers in a tire size mean?

In 225/45R17, 225 is the section width in millimetres, 45 is the aspect ratio (the sidewall height is 45% of the width), R means radial construction, and 17 is the rim diameter in inches.

### How do I work out a tire’s diameter?

Sidewall = width × aspect ratio ÷ 100. Diameter = rim + 2 × sidewall, with the rim converted to millimetres (× 25.4). For 225/45R17: 225 × 0.45 = 101.25 mm; 17 × 25.4 + 2 × 101.25 = 634.3 mm, or 24.97 in.

### How much can the diameter change?

The calculator shows the change; it does not set a limit. Check your vehicle maker’s and tire maker’s fitment guides: clearance in the wheel well, the load index and the speed rating all matter, not only the diameter.

### Why does a bigger tire make my speedometer read low?

The speedometer counts wheel turns. A larger tire covers more ground each turn, so at the same count you travel farther and faster. True speed = reading × new diameter ÷ old diameter.

### Does the width change the speedometer?

Only through the sidewall. The sidewall height is the width × the aspect ratio, so a wider tire with the same aspect ratio also has a taller sidewall and a larger diameter.

### Why do published diameters differ a little from this one?

This is the design diameter from the size code. Each tire maker publishes a measured diameter for each model, which can differ by a few millimetres, and a loaded tire is shorter than an unloaded one.

## Sources

- Wikipedia, Tire code: the metric size designation (width in mm, aspect ratio in percent, rim in inches) and the overall diameter (2 × W × A ÷ 100) + (R × 25.4) mm. https://en.wikipedia.org/wiki/Tire_code
- NIST SP 811 (2008), Appendix B: 1 in = 25.4 mm exactly; 1 mi = 1,609.344 m exactly.