Tire Crown Radius: Meaning, Measurement and Calculation

Tire crown radius is the radius of curvature of the tread surface when the tire is cut across its width. In a cross-sectional profile, the tread is not flat. It forms a gentle arc from shoulder to shoulder. The radius of the circle that best fits that arc is the crown radius, usually stated in millimetres. A large crown radius means a flat tread. A small one means a rounded tread.

The crown radius is not printed on the sidewall. You can work it out from two measurements: the chord length across the tread and the sagitta, which is how far the arc drops from its centre to its edges. The crown radius formula is R = c² ÷ (8s) + s ÷ 2.

The sidewall size tells you the tire's overall dimensions, but it does not reveal the crown shape. That is why this article starts with what the sidewall does and does not tell you.

What do the numbers on the tire sidewall mean?

A tire sidewall marking such as 225/45R17 94W mixes three kinds of information:

• Dimensions: width and rim diameter.
• A ratio: the aspect ratio.
• Ratings: load capacity and speed capability.

The units also differ. Width is in millimetres, rim diameter is in inches, and the aspect ratio is a percentage.

Other common sidewall markings include:

• The DOT code, with a manufacturing date.
• Maximum load and maximum inflation pressure.
• In the United States, UTQG grades for treadwear, traction and temperature.

Some light-truck sizes use an inch-based format, such as 31x10.50R15. In this format, 31 is the overall diameter, 10.50 is the section width, and 15 is the rim diameter, all in inches.

No standard sidewall marking states the tread width, the tread crown shape or the crown radius. These are design features of the tire mould, set by each manufacturer.

How do width, aspect ratio and rim diameter determine tire size?

Three of the sidewall values let you calculate a tire's nominal size:

• Sidewall height = section width × aspect ratio ÷ 100
• Overall diameter = rim diameter × 25.4 + 2 × sidewall height
• Circumference = π × overall diameter

The rim diameter is multiplied by 25.4 to convert inches to millimetres. All results are in millimetres.

Worked example: 225/45R17

1. Sidewall height: 225 × 0.45 = 101.25 mm.
2. Rim diameter in millimetres: 17 × 25.4 = 431.8 mm.
3. Overall diameter: 431.8 + 2 × 101.25 = 634.3 mm.
4. Circumference: π × 634.3 ≈ 1,992.7 mm.
5. Revolutions per kilometre: 1,000,000 ÷ 1,992.7 ≈ 502.

Comparing tire sizes

Changing one sidewall number changes the others' effect. A wider tire with the same aspect ratio has a taller sidewall. A larger rim with a lower aspect ratio can keep the overall diameter similar.

The 205/55R16 and 225/45R17 sizes are almost identical in overall diameter, even though their sidewalls differ by 11.5 mm. The 245/40R18 size is about 3% larger in diameter and circumference.

A 3% difference means the tire covers about 3% more distance per revolution. On a vehicle calibrated for the reference size, the true road speed would be about 3% higher than the speedometer shows, for example about 103 km/h at an indicated 100 km/h.

Why calculated tire dimensions differ from actual dimensions

Calculated tire dimensions are nominal geometry, not measured values. Real tires differ from them for several reasons:

• Rim width: section width depends on the rim. A tire on a wider rim measures wider than the same tire on a narrower one.
• Brand and model: two tires with the same size marking can differ by a few millimetres in diameter and width. Manufacturers publish measured dimensions in their technical data.
• Load: a loaded, rolling tire deflects. Its effective rolling circumference is smaller than the calculated unloaded circumference.
• Inflation and wear: pressure changes the inflated shape, and tread wear reduces the diameter over time.

A size calculation shows how two sizes compare on paper. It does not confirm that a tire fits a vehicle. Vehicle fitment also depends on:

• Approved sizes on the vehicle placard or in the owner's manual.
• Load index and speed rating.
• Clearance to suspension and bodywork.
• Rim width compatibility.

What is the crown of a tire?

The crown of a tire is the tread region centred on the tire's circumferential centreline. It runs around the tire and spans the tread from shoulder to shoulder. In tire construction, the crown includes the tread rubber and the belt package beneath it.

Viewed in cross-section, the crown is the outer arc of the profile. This arc is the shape that crown radius describes. The point where the arc is highest, on the centreline, is the crown centre. The tread edges where the arc meets the sidewall are the shoulders.

The shape of the tread crown affects how the tread meets the road. A flatter crown tends to spread contact more evenly across the tread width. A more rounded crown concentrates contact towards the centre. Motorcycle tires, which lean into corners, have a much more rounded crown than typical passenger-car tires.

What is the crown radius formula?

The crown radius formula treats the tread profile as an arc of a circle. It calculates that circle's radius from the arc's chord length and sagitta:

R = c² ÷ (8s) + s ÷ 2

• R is the crown radius.
• c is the chord length: the straight-line distance between two points on the tread surface, usually the two tread edges.
• s is the sagitta: the perpendicular distance from the middle of the chord to the arc. In practice, this is how much the tread edges sit below the crown centre.

Use the same unit, normally millimetres, for all three values. This formula comes from circle geometry and is exact for a true circular arc.

Example calculation

Suppose a tread profile has a chord length of 180 mm and a sagitta of 6 mm. These are illustrative numbers, not data for any specific tire.

1. Square the chord: 180² = 32,400.
2. Divide by 8 times the sagitta: 32,400 ÷ 48 = 675.
3. Add half the sagitta: 675 + 3 = 678 mm.

With the same 180 mm chord but a sagitta of only 3 mm, the result is 32,400 ÷ 24 + 1.5 = 1,351.5 mm. Halving the drop roughly doubles the crown radius. This shows how sensitive the result is to small sagitta measurements.

Reverse formula: sagitta from a known crown radius

If you know the crown radius and want the expected drop across a given chord, use:

s = R − √(R² − (c ÷ 2)²)

For R = 678 mm and c = 180 mm, the result is s ≈ 6 mm, which confirms the example above.

How do you measure tire crown radius?

You measure tire crown radius by finding the sagitta of the tread arc over a known chord length, then applying the crown radius formula. A straightedge and a depth gauge or feeler gauges are enough for a basic measurement.

1. Mount the tire on its rim and inflate it to the pressure you want to evaluate. Keep it unloaded, or record the load if it is on the vehicle.
2. Choose the chord. Measure the tread width between the two points you will use, such as the outer edges of the tread blocks. Record this as c.
3. Lay a rigid straightedge across the tread, perpendicular to the direction of rotation, so it touches the crown centre on a tread block rather than a groove.
4. At each chosen edge point, measure the gap between the straightedge and the tread surface. Average the two readings and record this as s.
5. Calculate R = c² ÷ (8s) + s ÷ 2.
6. Repeat at several positions around the circumference and average the results. This reduces the effect of tread pattern and local irregularities.

A contour gauge can capture the cross-sectional profile so you can measure it from a tracing. Laser or optical profilometers give a much denser profile, from which a radius can be fitted.

What are the limits of a single crown radius?

A single crown radius is a circular arc approximation, and real tread profiles are often more complex. Many tires use different radii across the tread, such as a flatter centre section and tighter curvature towards the shoulders. One radius calculated from edge-to-edge measurements smooths over that detail.

Several factors change the measured value:

• Chord choice: measuring over the full tread width or over the centre section alone can give different radii on a multi-radius profile.
• Inflation pressure and rim width: both change the inflated cross-sectional profile, so the mould shape and the in-service shape are not identical.
• Load: under load the crown flattens into the contact patch, so an unloaded measurement does not describe the shape on the road.
• Wear: uneven wear across the tread alters the profile over the tire's life.
• Measurement resolution: sagitta values are small, so an error of a fraction of a millimetre noticeably changes the result.

Crown radius is best used to compare profiles measured the same way, under the same conditions. It is a description of shape, not a rating. Like the calculated size geometry from the sidewall, it does not by itself say whether a tire suits a particular vehicle.