Static loaded radius and effective rolling radius

Static loaded radius (often abbreviated SLR) is a stationary height. It is the distance from the wheel's axle center to the ground while the tire carries load and is not rolling. Effective rolling radius is a rolling quantity. It is the distance the wheel travels in one revolution divided by 2π. The two answer different questions and are measured in different ways, so one cannot stand in for the other. Neither can be read from the size marked on the sidewall. Both depend on load and inflation pressure. Rolling radius also depends on speed, on driving or braking torque, and on how much the tire slips.

The four quantities people mix up

Quantity	What it describes	How it is obtained	Typical use
Unloaded (free) radius	Outer radius of the tire when it carries no load and is not rolling	Measured on an unloaded tire, or estimated from the size designation	Comparing tire dimensions on paper
Static loaded radius	Height of the axle center above the ground under load, with the wheel stationary	Measured from the ground to the wheel center at a stated load and pressure	Stationary geometry such as ride height and ground clearance
Rolling circumference	Distance travelled per wheel revolution	Measured travel divided by revolutions, or taken from published revolutions-per-distance data	Speed, distance and gearing calculations
Effective rolling radius	The radius that would cover the rolling circumference in one revolution	Rolling circumference divided by 2π	Relating wheel rotation speed to vehicle speed

Load flattens the tire where it meets the road, and this lowers the axle directly. The distance covered per revolution behaves differently, because it depends on how the tread moves through the contact patch. A stationary height measurement therefore tells you nothing about the rolling quantity. The reverse is also true: rolling data does not give you the stationary height.

Why nominal tire size is not enough

A metric size designation lets you estimate a nominal unloaded diameter. The example below uses a 225/45R17 tire. The section width is 225 mm, the sidewall height is 45 percent of that width, and the rim diameter is 17 inches.

Sidewall height   = 225 mm × 0.45            = 101.25 mm
Rim diameter      = 17 in × 25.4 mm/in       = 431.8 mm
Overall diameter  = 431.8 + (2 × 101.25)     = 634.3 mm
Nominal radius    = 634.3 / 2                = 317.15 mm

The result is only a nominal free radius. Actual tires of the same size vary by model and by remaining tread depth. More importantly, the size code does not say how far the axle drops under a particular load, or how far the tire travels per revolution. Those depend on several factors: load, inflation pressure, the tire's own deflection characteristics (which come from its construction), torque and speed. In simulation models, effective radius is often calculated from vertical load and rotational velocity using coefficients specific to that tire, not from the size alone.

Calculating effective rolling radius from travel and revolutions

Rolling circumference   C   = L / N
Effective rolling radius r_e = L / (2 × π × N)   (equivalently C / (2 × π))
Vehicle speed            V   = r_e × Ω

L = distance travelled (m)
N = number of wheel revolutions
Ω = wheel angular speed (rad/s)

These relationships assume the wheel rolls without slipping. A wheel that is driving or braking develops slip, so the travel you measure includes the effect of that slip. Treat a result taken under drive or braking as valid for that condition only. Do not use it as a general property of the tire. The cleanest measurement comes from a free-rolling wheel with as little torque applied as possible.

Worked example (hypothetical numbers)

Suppose a wheel rolls 20 m without slipping in 10 revolutions. The rolling circumference is 20 / 10 = 2 m per revolution. The effective rolling radius is 2 / (2π) ≈ 0.3183 m. Now suppose you separately measured a static loaded radius of 0.300 m and an unloaded radius of 0.330 m on the same tire. In this example the rolling radius sits 0.0183 m above the static loaded radius and 0.0117 m below the unloaded radius. These are illustrative inputs only. They do not represent any real tire, and the gaps between them are not correction factors you can apply elsewhere.

Measuring each radius

Static loaded radius

• Park on a flat, level surface with the wheel straight.
• Set the tire to a known pressure and record it.
• Record the load condition: occupants, cargo and fuel, plus the axle or wheel load if you have scale data.
• Measure vertically from the ground to the center of the wheel hub.
• Note the units, and repeat the measurement to check that it is consistent.

Rolling circumference and effective rolling radius

• Mark the bottom of the tire sidewall and the matching spot on the ground.
• Roll the vehicle in a straight line, applying as little drive or brake torque as practical.
• Stop when the mark returns to the bottom after a whole number of revolutions. More revolutions reduce the effect of small marking errors on each revolution.
• Measure the distance between the start and end ground marks.
• Record the load, pressure and approximate speed, because the result applies to those conditions.
• Calculate C = L / N and r_e = C / (2π).

Using published circumference or revolutions-per-distance data

Where a tire maker publishes revolutions per mile, revolutions per kilometre or a rolling circumference, you can convert that figure directly. Keep the maker's stated test conditions attached to the number. Compare it only with figures measured on the same basis.

C (m) = 1609.344 / revolutions per mile
C (m) = 1000 / revolutions per kilometre
r_e (m) = C / (2 × π)

1 in = 25.4 mm   |   1 mile = 1609.344 m

Which radius to use for which job

• Ride height, ground clearance and other stationary geometry: static loaded radius at the relevant load and pressure.
• Vehicle speed from wheel speed, distance per revolution, gearing and speedometer comparisons: rolling circumference or effective rolling radius.
• Quick comparison of two sizes on paper: nominal unloaded dimensions, keeping in mind that loaded behavior will differ.
• Simulation work: the tire-specific model inputs, which may vary effective radius with load and speed.
• Comparing two tires: the same quantity, measured or published under matching load, pressure and speed.

These calculations only compare dimensions. They do not confirm that a tire fits a particular vehicle. For fitment, follow the vehicle and tire manufacturers' specifications.

Input worksheet

Copy this layout into a spreadsheet or printable sheet so every value keeps its definition and conditions.

Tire model / size:            ____________________
Rim:                          ____________________

Quantity            Value   Units   Source (measured/published)   Conditions
Unloaded radius     _____   _____   ___________________________   __________
Static loaded rad.  _____   _____   ___________________________   load ____ pressure ____
Travel L            _____   _____   ___________________________   speed ____ slip assumed? Y/N
Revolutions N       _____   -       ___________________________   drive/brake torque? Y/N
Rolling circ. C     _____   _____   = L / N
Rolling radius r_e  _____   _____   = C / (2π)

A radius found at one load, pressure and speed describes only that condition. If you need values for a different load or pressure, measure again or obtain data for that condition. Do not scale a single result.