Scrub Radius Calculator finds signed scrub radius from tire diameter, hub-face-to-steering-axis distance, wheel offset, and SAI. Formula: scrub radius = (hub axis − ET) − tire radius × tan(SAI).
Definition and Mechanical Function
Scrub radius is the lateral distance at ground level between the center of the tire contact patch and the point where the steering axis intersects the road surface. It is a fundamental suspension geometry parameter that governs how tire forces feed into the steering wheel and how the vehicle responds to braking on surfaces with unequal grip.
The sign convention is critical. A positive scrub radius exists when the steering axis meets the ground inboard of the tire centerline—the tire patch center sits laterally outward from the pivot point. A negative scrub radius occurs when the steering axis intersection lies outboard of the tire centerline. Zero scrub radius means the two points coincide.
Most modern front‑wheel‑drive cars use a small negative scrub radius, while many rear‑wheel‑drive platforms traditionally run slightly positive values. The direction and magnitude of scrub radius directly influence steering kickback, straight‑line stability during tire failure, and the self‑centering feel of the steering system.
Scrub radius is not a direct measurement but a derived geometric quantity. It depends on the steering axis inclination (SAI), the wheel offset, the hub‑face distance to the steering axis, and the tire’s rolling radius. Small production tolerances in any of these dimensions can shift scrub radius by several millimeters, which is enough to alter on‑center steering precision and braking stability.
Geometry of the Steering Axis and Tire Contact
The steering axis is the line through the upper and lower pivot points of the front suspension—typically the center of the top strut mount and the ball joint on a MacPherson strut, or the upper and lower ball joints on a double‑wishbone system.
Inclination of this axis, known as steering axis inclination (SAI) or kingpin inclination (KPI), is the angle between the steering axis and a true vertical line when viewed from the front of the vehicle. SAI typically ranges from about 7° to 15° on production cars.
As the steering axis inclines, its intersection with the ground plane moves laterally. The distance from the wheel center plane to that intersection point is equal to the tire’s rolling radius multiplied by the tangent of the SAI angle. This offset is entirely geometric and would exist even if the wheel were a thin disc centered on the hub face.
The tire centerline at ground level is determined by the wheel’s mounting face offset and the tire’s symmetry. The distance from the steering axis to the tire centerline at the hub plane is the net lateral offset of the hub face relative to the steering axis.
When combined with wheel offset—the distance between the hub‑mounting face and the wheel’s geometric centerline—this defines where the tire centerline sits relative to the steering axis at the wheel plane. Projecting that down to the ground yields the scrub radius.
Because the tire contact patch is a deformable area, not a point, scrub radius describes the center of the patch under static, straight‑ahead conditions. In practice, the effective scrub radius can shift slightly under cornering loads as the tire carcass deforms, but the geometric static value remains the primary design target.
Formula for Scrub Radius
The geometric scrub radius is calculated from four primary inputs: the tire rolling radius, the steering axis inclination, the lateral distance from the hub face to the steering axis, and the wheel offset (ET). The formula, expressed in a length unit, is:
Scrub Radius = (D_HubAxis − ET) − (R_Tire × tan(SAI))
Where:
- D_HubAxis is the perpendicular distance from the wheel hub mounting face to the steering axis, measured in the transverse direction at the wheel center height.
- ET is the wheel offset, defined as the distance from the wheel’s mounting face to the centerline of the wheel rim. Positive offset places the mounting face outboard of the rim centerline.
- R_Tire is the static loaded tire rolling radius, or more commonly for design purposes the undeflected radius from the tire’s overall diameter divided by two. Minor tire deflection can be added as a correction.
- SAI is the steering axis inclination angle, in degrees, measured from the vertical in front view.
All linear dimensions must be in the same unit system. If tire radius and offset are given in millimeters and the hub‑axis distance in inches, conversion is required.
Worked Example (Imperial Units):
Assume an overall tire diameter of 26.0 inches (giving a radius of 13.0 inches), a hub‑face to steering‑axis distance of 3.0 inches, a wheel offset of 40 mm (which converts to 1.575 inches, using 1 inch = 25.4 mm), and an SAI of 12.0°.
First, compute the tire centerline offset at the hub plane: 3.0 in − 1.575 in = 1.425 in.
Next, compute the steering axis lateral shift at the ground: R_Tire × tan(SAI) = 13.0 in × tan(12°) = 13.0 in × 0.21256 ≈ 2.763 in.
Then, scrub radius = 1.425 in − 2.763 in = −1.338 in. The result is negative, meaning the steering axis hits the ground outside the tire centerline.
Metric Example:
Use the same geometry converted to millimeters. Tire radius = (26.0 × 25.4)/2 = 330.2 mm. Hub‑axis distance = 3.0 × 25.4 = 76.2 mm. Offset = 40 mm. SAI = 12°.
Tire centerline offset at hub = 76.2 − 40 = 36.2 mm.
Steering axis ground offset = 330.2 × tan(12°) ≈ 70.17 mm.
Scrub radius = 36.2 − 70.17 = −33.97 mm, which equals −1.338 in.
The formula is linear in offset: a change of 1 mm in wheel offset changes scrub radius by exactly 1 mm in the opposite direction. SAI changes have a nonlinear effect because they alter the tan(SAI) term; a 0.5° increase in SAI typically moves scrub radius several millimeters in the negative direction, depending on tire radius.
Key Variables and Their Influence
The four primary variables each affect scrub radius in a distinct way, and their interactions are what make suspension tuning a deliberate balancing act.
Steering Axis Inclination (SAI): Increasing SAI tilts the steering axis more inward at the top, moving the ground intersection point outward. Because tan(SAI) grows faster than the angle itself, a given degree change has a larger effect on scrub radius when SAI is already high. For a typical passenger car tire radius, each additional degree of SAI shifts scrub radius by roughly 5–8 mm in the negative direction. SAI is largely set by the suspension hard points and is rarely adjustable without changing uprights or control arms.
Wheel Offset (ET): Offset directly sets the lateral position of the tire centerline. Reducing offset (moving the wheel outward, common with aftermarket wheels) shifts scrub radius in the positive direction. A 10 mm lower offset adds exactly 10 mm to the scrub radius. This one‑to‑one sensitivity means that seemingly modest wheel spacer or offset changes can completely alter the scrub radius from its factory‑engineered value.
Hub‑Face to Steering‑Axis Distance: Sometimes referred to as kingpin offset at the wheel center, this dimension is built into the steering knuckle and defines how far the hub face sits from the steering axis. A larger distance pushes the tire centerline outward, increasing scrub radius positively. Many production knuckles are designed to place the hub face inboard of the steering axis, so this value can be negative in sign conventions, but the net effect remains consistent: it directly offsets the tire centerline.
Tire Rolling Radius: A larger tire radius magnifies the effect of SAI because the tan(SAI) term is multiplied by a larger number. Switching from a 25‑inch to a 27‑inch overall tire diameter can shift scrub radius several millimeters negative without any other changes. This means tire upsizing must be evaluated alongside wheel offset to preserve the intended scrub radius.
Typical Values in Production Vehicles
Automakers target scrub radius within narrow ranges depending on the vehicle’s drivetrain layout and intended handling character. The following table summarizes common design windows, though individual models can vary.
| Vehicle Type | Typical Scrub Radius | Common Sign | Reason |
|---|---|---|---|
| Front‑wheel‑drive passenger car | −10 mm to 0 mm | Negative | Braking stability on split‑mu surfaces; torque steer management |
| Rear‑wheel‑drive sedan | −5 mm to +15 mm | Slightly positive or near zero | Steering feel, reduced sensitivity to offset variation |
| Performance sports car (mid‑engine or front‑engine RWD) | 0 mm to +10 mm | Positive or zero | Steering precision, feedback, and linearity |
| Off‑road truck or SUV with solid axle | +20 mm to +50 mm | Positive | Large tire scrub diameter aids steering geometry with manual steering boxes |
| Heavy‑duty commercial vehicle | +50 mm and above | Strongly positive | Reduce steering effort in low‑speed maneuvers with high vertical loads |
Values near zero are increasingly common on modern vehicles with electric power steering, as they allow engineers to tune steering feel through software rather than relying on geometric feedback alone. Negative scrub radius was a hallmark of front‑drive vehicles with diagonal split braking systems, where it inherently counters yaw during a front brake circuit failure. Vehicles with stability control can manage such events electronically, making small positive scrub more acceptable today.
Effects on Steering and Handling
Scrub radius acts as a lever arm through which longitudinal tire forces produce a torque about the steering axis. The magnitude and direction of this torque depend on the sign and size of the scrub radius.
With positive scrub radius, a braking force on one front wheel generates a moment that tries to steer that wheel outward, turning the vehicle toward the side with less grip. This is unfavorable during split‑mu braking (one tire on ice, the other on dry pavement), as the driver must actively correct the steering.
With negative scrub radius, the braking force pulls the wheel inward, steering the car away from the low‑grip side—a self‑stabilizing effect that many front‑drive cars exploited before electronic stability control became ubiquitous.
Positive scrub radius can enhance steering feedback and on‑center feel, transmitting road surface irregularities more directly to the steering wheel. That increased feedback is sometimes desirable in sports cars but can also amplify tramlining—the tendency to follow road grooves—and steering kickback over bumps. Near‑zero scrub radius isolates the steering from longitudinal force disturbances, providing a more relaxed feel but potentially reducing the sense of connection.
Scrub radius also affects steering effort in parking maneuvers. A larger positive scrub radius increases the resistance to turning when stationary because the tire must scrub across the pavement in a larger arc. The scrub radius defines the radius of the sweep circle that the contact patch center traces around the steering axis; a larger circle demands more displacement of the tire carcass and generates higher steering forces.
Common Misunderstandings
One frequent misconception is that the ideal scrub radius is always zero. While zero scrub radius eliminates the lever arm for longitudinal forces and theoretically minimizes kickback, it does not guarantee optimal steering feel or stability. Many vehicles deliberately run slightly positive or negative values to achieve specific dynamic behaviors, such as enhanced self‑centering or improved directional stability during braking.
Another misunderstanding confuses scrub radius with the turning circle scrub, which is the lateral slip of the tire during low‑speed cornering due to Ackermann geometry. Scrub radius is a static suspension parameter; turning circle scrub is a dynamic effect related to steering angle differences between the inner and outer wheels.
A related confusion arises when people treat scrub radius as independent of tire pressure or load. The calculation relies on the tire rolling radius, which changes slightly with load and inflation. In practice, the geometric scrub radius calculated with unloaded tire dimensions is adequate for design, but the effective scrub radius under hard braking, when the tire contact patch flattens and shifts rearward, can differ by a few millimeters.
Finally, some assume that scrub radius is purely a suspension hard‑point concern and ignore the role of wheel offset. Aftermarket wheel changes are the most common way that scrub radius departs from factory design.
A wheel with 15 mm less offset than stock can push a vehicle from negative scrub to positive, completely changing the braking stability behavior and steering feedback, often without the driver understanding why the car feels different.
Dynamic Considerations and Limitations of Static Geometry
The classic scrub radius formula assumes a rigid tire with a circular cross‑section and a static, straight‑ahead steering position. In reality, several dynamic effects alter the effective scrub radius in operation.
Tire deflection under vertical load reduces the effective rolling radius slightly, which in turn changes the tan(SAI) term. A typical radial tire with a 13‑inch unloaded radius may lose roughly 0.2–0.3 inch of radius when supporting the vehicle’s corner weight. This moves the steering axis intersection point inward by a small but measurable amount, typically shifting scrub radius 1–2 mm positive compared to the unloaded calculation.
Suspension travel also changes SAI in most independent suspension systems because the control arm angles alter the steering axis orientation. As the wheel moves into bump, the lower control arm angle may increase the effective SAI by a fraction of a degree, while rebound reduces it.
These dynamic changes mean that the scrub radius measured at design ride height is a nominal target; the actual value varies through the suspension stroke.
Camber angle adds a further nuance. While scrub radius is defined in the front view, changes in camber affect the tire contact patch shape and the lateral position of the force application point. Under hard cornering, the outer tire’s contact patch shifts inboard relative to the wheel centerline, altering the effective lever arm.
These second‑order effects explain why production suspension tuning often involves iterative testing with instrumented vehicles. A static geometric calculation provides the essential starting point, but final validation requires assessing steering precision, pull during braking, and feedback on real road surfaces.
Nonetheless, for aftermarket wheel fitment, suspension design, and understanding vehicle dynamics fundamentals, the simple geometric scrub radius remains an indispensable reference.