Automotive, Diesel & Motorsports Suspension, Chassis, Wheels & Loads SAE J670 vehicle dynamics terminology; NHTSA static stability factor

Weight Transfer Calculator — Lateral & Longitudinal

Weight transfer is what a vehicle's centre of gravity does to its tire loads the moment it accelerates in any direction, and it is governed by three numbers: CG height, track width and wheelbase. Enter those with the vehicle's weight, its static front bias and the lateral and longitudinal g you are asking for, and this calculator returns the load transferred side to side and end to end, the dynamic load on each axle, all four corner loads with a lateral load transfer distribution you set, and the static rollover threshold the geometry allows.

Calculator

This calculator runs in your browser. Enable JavaScript for live results — the inputs, formula and worked example below remain fully readable without it.

Inputs this calculator takes, with typical values
InputWhat to enterExample
Total vehicle weightWeight as raced or as driven, with driver and fuel aboard — the sum of the four corner scale readings.3200 lb
Centre of gravity heightHeight of the whole vehicle's CG above the ground. Measure it by raising one axle a known amount and reweighing, or estimate from a similar vehicle.18 in
Track widthCentre-to-centre distance between the left and right tire contact patches. Use the average if front and rear differ.61 in
WheelbaseFront axle centreline to rear axle centreline.105 in
Static front weightShare of total weight on the front axle at rest, from corner scales or a two-pad weigh.52 %
Lateral accelerationCornering acceleration you want the loads for, from a data logger, a skidpad time or a grip estimate.1 g
Longitudinal eventChooses which way the longitudinal transfer acts. Set the magnitude below.Braking — transfers load to the front
Longitudinal accelerationMagnitude of braking or acceleration, entered as a positive number; the selector above sets its direction.0.9 g
Front lateral load transfer distributionShare of the total lateral transfer taken by the front axle, set by roll stiffness and roll centre heights. 50% splits it evenly.55 %

It returns

  • Lateral weight transfer — Load moved from the inside pair of wheels to the outside pair at the entered lateral g.
  • Longitudinal transfer onto the front axle — Positive under braking, negative under acceleration.
  • Dynamic front axle load
  • Dynamic rear axle load
  • Outside front corner load
  • Inside rear corner load — The corner that unloads first. Zero or below means that wheel has lifted.
  • Static rollover threshold — Track ÷ (2 × CG height). Lateral g at which a rigid vehicle would tip rather than slide.

The formula

ΔWlat=Walatht
SSF=t2h
FOF=Wf,dyn2+λΔWlat

In plain text: ΔW_lat = W · a_lat · h / track and ΔW_long = W · a_long · h / wheelbase

  • ΔW_latLoad transferred from the inside pair of wheels to the outside pair (lb)
  • WTotal vehicle weight (lb)
  • a_latLateral acceleration (g)
  • hCentre of gravity height above ground (in)
  • tTrack width, contact patch centre to contact patch centre (in)
  • a_longLongitudinal acceleration, braking or driving (g)
  • LWheelbase (in)

Both expressions are moment balances. The inertial force W·a acts at the CG height h and must be reacted by a couple across the contact patches, whose lever arm is the track for cornering and the wheelbase for braking or acceleration. Springs, dampers and roll bars change the timing and the front-to-rear split of the transfer, not the total.

Updated Category Suspension, Chassis, Wheels & Loads Verified against published test cases Reading time 13 min

What weight transfer is, and what it is not

Weight transfer is the redistribution of vertical tire loads caused by an inertial force acting at a centre of gravity that sits above the ground. Nothing physically moves. The vehicle's mass and its total weight are unchanged; what changes is how that weight is shared between four contact patches, because the inertial force at the CG and the friction forces at the ground form a couple that has to be balanced by a difference in vertical load.

The consequences are everything. Tire grip is not proportional to load — it rises with load but at a falling rate, so a pair of tires carrying 1,000 lb and 200 lb generates less total grip than the same pair carrying 600 lb each. Weight transfer therefore costs grip on the axle that experiences more of it, and the whole discipline of chassis tuning is largely about choosing which axle pays.

The three geometric terms carry different weight. CG height is the only one that appears in both formulas and it is the one you can actually change: lowering the CG by 2 in on an 18 in car cuts every transfer by 11.1%, because 16/18 = 0.889. Track divides the lateral transfer, so a wider car transfers less side to side. Wheelbase divides the longitudinal transfer, which is why short-wheelbase cars lift the inside front under braking and long trucks do not.

Notice what is absent from the formulas: springs, dampers, anti-roll bars and roll centres. None of them appears. Suspension governs how much the body rolls, how quickly the transfer arrives, and how it splits between the front and rear axles — but the total transfer at a given g is fixed by CG height and track alone. A car with no suspension at all transfers exactly the same total.

Deriving both expressions from one moment balance

Consider a car cornering steadily at a g. The tires supply a total lateral force W·a at ground level. The inertia of the body resists it with an equal force at the CG, a height h above the ground. Those two forces are equal, opposite, and separated by h, so they form a couple of magnitude W·a·h. The only thing available to balance it is a difference in vertical load between the left and right contact patches, separated by the track t. Setting the two moments equal gives ΔW × t = W·a·h, hence ΔW = W·a·h/t.

The longitudinal case is identical with the wheelbase substituted for the track: ΔW = W·a·h/L. Braking moves load onto the front axle, driving moves it onto the rear. Both transfers act on top of the static axle split, so a 52% front car braking at 0.9 g does not merely bias forward — it may well arrive somewhere near 67% front, which is why brake bias is set for the dynamic distribution and not the static one.

The two transfers superimpose. Braking in a corner adds the longitudinal transfer to each axle and the lateral transfer to each side, and the outside front corner receives both. That corner routinely carries more than half the whole vehicle's weight in a hard trail-braked entry, which is why front outside tire temperature and wear tell you so much about a setup.

The lateral load transfer distribution is where suspension enters. The total lateral transfer is fixed, but its split between the front and rear axles depends on the roll stiffness of each end and on the roll centre heights. Stiffening the front anti-roll bar raises the front's share, which unloads the inside front further and reduces front grip relative to rear — the standard cure for oversteer. This calculator takes that split as an input rather than deriving it, because a rigorous derivation needs roll centre heights and measured roll rates. Get the wheel rates first with the wheel rate and motion ratio calculator.

Worked example: 3,200 lb car braking at 0.9 g in a 1.0 g corner

A 3,200 lb car has an 18 in CG height, a 61 in track, a 105 in wheelbase and 52% static front weight. It is trail-braking at 0.9 g while pulling 1.0 g laterally, with 55% of the lateral transfer taken at the front.

  1. Lateral transfer. 3,200 × 1.0 × 18 ÷ 61 = 57,600 ÷ 61 = 944.3 lb moves from the inside pair to the outside pair.
  2. Longitudinal transfer. 3,200 × 0.9 × 18 ÷ 105 = 51,840 ÷ 105 = 493.7 lb moves onto the front axle.
  3. Static axles. Front 0.52 × 3,200 = 1,664 lb; rear 3,200 − 1,664 = 1,536 lb.
  4. Dynamic axles. Front 1,664 + 493.7 = 2,157.7 lb; rear 1,536 − 493.7 = 1,042.3 lb. The car is now 67.4% front, since 2,157.7 ÷ 3,200 = 0.674.
  5. Split the lateral transfer. Front 0.55 × 944.3 = 519.4 lb; rear 0.45 × 944.3 = 424.9 lb.
  6. Corner loads. Outside front 2,157.7 ÷ 2 + 519.4 = 1,598.2 lb; inside front 1,078.9 − 519.4 = 559.5 lb; outside rear 1,042.3 ÷ 2 + 424.9 = 946.1 lb; inside rear 521.1 − 424.9 = 96.2 lb.
  7. Rollover threshold. 61 ÷ (2 × 18) = 61 ÷ 36 = 1.694 g, well above the 1.0 g requested.

The outside front carries 1,598.2 of the 3,200 lb total — 49.9% of the whole car on one tire. The inside rear is down to 96.2 lb and is about to leave the ground; at 1.05 g lateral with the same braking it would lift. That is the single most useful thing this calculation tells a setup engineer, because a lifted inside rear means the rear axle's total grip is now whatever one tire can produce.

What the numbers tell you to change

Compare lateral transfer against total weight. Transfer divided by weight is just a·h/t, so at 1 g it equals the ratio of CG height to track. Our example is 18/61 = 0.295, meaning 29.5% of the car's weight crosses the centreline at 1 g. Anything much above 0.35 at 1 g is a tall vehicle and will feel like one; below 0.25 is a low, wide car.

Watch the inside rear. It is the first corner to reach zero in almost every road-car geometry, because braking already removed load from that axle before the corner takes more. Once it lifts, further lateral transfer at the rear does nothing — the model's assumption of two contact patches per axle no longer holds and rear grip stops responding to bar changes.

The static rollover threshold is a geometry limit, not a prediction. SSF = t/(2h) is the lateral g at which a rigid vehicle's resultant force line passes outside the contact patch. NHTSA uses exactly this measure in its rollover resistance ratings. A car whose tires peak at 0.9 g and whose SSF is 1.69 will slide long before it tips on flat pavement. A vehicle whose SSF is close to or below its available grip — a loaded van, a lifted truck, a top-heavy trailer — can tip on smooth pavement, and tripping over a kerb reduces the effective threshold much further. Suspension roll lowers the real threshold below the rigid-body figure, so treat SSF as an optimistic ceiling.

Use the dynamic axle split to set brake bias. Our example arrives at 67.4% front under braking. Brake torque distribution should track that, not the 52% static figure, which is why front brakes on almost every vehicle are much larger than rear. See the brake bias and brake torque calculator for turning that into master cylinder and caliper sizes, and the braking and stopping distance calculator for what the resulting deceleration achieves.

Static rollover threshold by track width and CG height

SSF = track ÷ (2 × CG height), in g. Divide track by twice the CG height to read the lateral acceleration at which a rigid vehicle would tip.
CG height (in)56 in track60 in track64 in track68 in track72 in track
151.8672.0002.1332.2672.400
181.5561.6671.7781.8892.000
201.4001.5001.6001.7001.800
221.2731.3641.4551.5451.636
251.1201.2001.2801.3601.440
281.0001.0711.1431.2141.286

The same ratio inverted gives lateral transfer as a fraction of vehicle weight per g: h/t. A 20 in CG on a 60 in track transfers 20/60 = 33.3% of the vehicle's weight at 1 g.

Measuring CG height, the input that matters most

CG height appears in every formula on this page and it is the one number nobody has on a spec sheet. Measure it by weighing the vehicle level on corner scales, then raising one axle a measured height and reweighing. The change in the other axle's load, the wheelbase, the raised height and the wheel radius give the CG height directly. Do it with the fuel level, driver and ballast you actually run, secure everything that could move, and lock out the suspension or account for the body's rotation — an unrestrained suspension lets the sprung mass settle as you tilt and biases the answer low. Repeat at two different lift heights; if the two answers disagree by more than about half an inch, something moved.

Assumptions and limits of this model

  • It is a steady-state result. The formulas give the transfer once the manoeuvre has settled. During turn-in the transfer builds at a rate set by the dampers, and a stiff, well-damped car reaches the steady value far sooner than a soft one.
  • It assumes a rigid body. Real body roll moves the CG laterally by a small amount, which adds a little more transfer than the rigid figure. The correction is second order for a car with a few degrees of roll, and significant for a tall vehicle on soft springs.
  • It assumes level ground. Banking, crowned roads and elevation change all alter the direction of the resultant and hence the transfer. A banked corner reduces the lateral transfer at a given speed, which is part of why banking raises cornering speed — see the cornering speed and lateral g calculator.
  • Unsprung mass is lumped in. Rigorously, unsprung mass transfers about its own CG height and the sprung mass about the roll centre. The single-CG treatment is standard for setup work but slightly overstates the transfer that the springs and bars actually control.
  • The lateral split is an input, not a derivation. Front lateral load transfer distribution follows from roll stiffness and roll centre heights. Entering a number you have not measured makes the corner loads an illustration rather than a measurement.
  • Aerodynamic load is not included. Downforce adds vertical load without adding mass, so it raises tire loads without adding transfer. The downforce and drag calculator quantifies it separately.

Using transfer numbers to make setup decisions

The practical value of these numbers lies in the differences, not the absolutes. Change one thing and recompute.

To reduce total transfer, you have exactly two levers: lower the CG or widen the track. Springs and bars cannot help, because they do not appear in the formula. This is why a lowered, wide car is fundamentally quicker in a corner regardless of how it is sprung.

To move grip between axles, change the split. Raising front roll stiffness relative to rear increases the front's share of lateral transfer, which unloads the inside front further, reduces total front grip, and pushes the balance toward understeer. Lowering it does the reverse. The total is unchanged; you are choosing which end pays.

To read tire data, work in corner loads rather than axle loads. A tire's grip coefficient falls as load rises, so the outside front at 1,598 lb is generating less grip per pound than it would at 800 lb. That load sensitivity is precisely why transfer costs performance and why an evenly loaded pair beats a lopsided one.

For road vehicles and load carriers, the SSF and the transfer fraction are the numbers that matter, and they are why load placement is a safety issue. A high load raises h directly, and every transfer scales with it. The same arithmetic drives trailer tongue weight and the axle loads checked with the truck axle weight calculator.

Key terms

Weight transfer
The change in vertical load at each tire caused by an inertial force acting at a centre of gravity above the ground. Total vehicle weight does not change.
Lateral load transfer distribution (LLTD)
The share of total lateral transfer taken by the front axle, set by front-to-rear roll stiffness and roll centre heights. The primary balance adjustment on a race car.
Static stability factor (SSF)
Track width divided by twice the CG height. The lateral acceleration at which a rigid vehicle's weight vector passes outside the contact patch.
Tire load sensitivity
The tendency of a tire's grip coefficient to fall as vertical load rises. It is the reason weight transfer reduces the total grip an axle can produce.
Corner weight
The vertical load on one individual wheel. Four corner weights sum to vehicle weight and are what scales measure directly.

Frequently asked questions

Does a stiffer spring reduce weight transfer?

No. Total weight transfer depends only on vehicle weight, acceleration, CG height and track or wheelbase — springs appear nowhere in the formula. Stiffer springs reduce body roll and make the transfer arrive faster, and they change how much of the lateral transfer each axle takes, but the total crossing the car is identical. Only lowering the CG or widening the track reduces it.

How do I measure centre of gravity height?

Weigh the vehicle level on corner scales, then raise one axle by a measured height and weigh again. The change in the unraised axle's load, together with the wheelbase, the lift height and the loaded wheel radius, solves for CG height. Do it at the running weight with driver and fuel aboard, restrain anything that could shift, and take readings at two lift heights as a cross-check.

Why does the inside rear wheel lift first?

Because braking has already taken load off the rear axle before the corner takes more from the inside. In the worked example the rear axle drops from 1,536 lb static to 1,042 lb under 0.9 g braking, so each rear corner starts at 521 lb, and 425 lb of lateral transfer leaves just 96 lb inside. A front-biased lateral transfer split makes it worse at the front and better at the rear, which is one reason rear anti-roll bars are usually the smaller of the pair.

What lateral g can a road car actually pull?

Grip, not this calculator, sets that: peak lateral acceleration equals the tire's effective friction coefficient. Enter a figure you have measured on a skidpad or logged in a corner rather than one you hope for. What this page tells you is the consequence of whatever g you achieve, and whether the geometry — through the static rollover threshold — allows it at all.

Is longitudinal transfer under braking the same as under acceleration?

The magnitude is identical for the same g: W·a·h/L in both cases, just in opposite directions. What differs in practice is the achievable g. Braking uses all four tires so it can reach the tires' full friction limit, while acceleration on a two-wheel-drive car is limited by what the driven axle can transmit, which is why braking decelerations are typically far larger than accelerations.

What is a good static rollover threshold?

Higher than the vehicle's peak lateral grip, with margin. A sports car at 1.6–2.0 g will always slide before tipping on flat pavement. A tall SUV or a loaded van nearer 1.1–1.3 g has much less margin, and a tripped rollover — hitting a kerb or soft ground sideways — can occur well below the untripped threshold. Suspension roll shifts the CG outboard slightly and lowers the real threshold below the rigid-body number.

How does aerodynamic downforce interact with weight transfer?

Downforce adds vertical tire load without adding mass, so it increases grip while adding no inertial force and therefore no extra transfer. That is why aerodynamic grip is so valuable: the tires carry more load but the car does not have to transfer any more of it. The downforce itself does load the axles according to its centre of pressure, so aero balance shifts the static distribution at speed.

Should I use average track width if front and rear differ?

For a single-figure answer, yes, and the error is small when the two tracks are within an inch or two. Strictly, the lateral transfer at each axle divides by that axle's own track, so a car with a markedly wider front will transfer proportionally less at the front for the same share of the roll couple. If the difference exceeds about 3%, calculate each axle separately using its own track.

References

  • Race Car Vehicle Dynamics — William F. Milliken & Douglas L. Milliken, SAE International
  • Fundamentals of Vehicle Dynamics — Thomas D. Gillespie, SAE International
  • SAE J670 — Vehicle Dynamics Terminology — SAE International
  • Rollover Resistance Ratings and the Static Stability Factor, New Car Assessment Program — National Highway Traffic Safety Administration