Suspension kinematics calculator

Suspension kinematics calculator: double wishbone and McPherson geometry

7 paź 2026 · @Sławek Muraszko

This free calculator shows how a double wishbone or McPherson front suspension moves: camber, roll centre, track change, KPI, scrub radius, caster, anti-dive, bump steer and roll steer, all live as the wheel travels and the body rolls. Change a pivot point, drag a node on the diagram or load an example, and every curve updates instantly. The kinematics have been checked against an Autodesk Inventor kinematic model.

It is built for Formula Student teams, kit car and off-road builders, engineering students and anyone who wants to understand what a suspension change really does before cutting metal.

Key parameters at a glance

How to use the calculator

Start from an example and change one parameter at a time; every curve shows the effect immediately.

1. Pick an example: double wishbone for a sports car, a Formula Student car, parallel equal-length wishbones (a useful reference case) or a McPherson strut for a compact car.
2. Move the sliders: Wheel travel moves both wheels up and down together (heave); Roll tilts the body as it does in a corner. Roll to the right (+) corresponds to a left-hand turn, so the right wheel is the outer one.
3. Switch views: Front shows the full axle with the instant centres and the roll centre, Side shows the right wheel with caster, trail and the anti-dive line, Isometric shows the whole axle in 3D.
4. Change the geometry: type new coordinates in the form, enter a new link length in Link lengths, or press Edit nodes on the diagram and drag points A–F with your finger or mouse.
5. Read the results: each result card has a short What it means explanation, and the charts below show how every parameter changes over the whole travel and roll range.

All coordinates are in millimetres. In the form, x runs outwards from the vehicle centreline, y up from the ground, and z (tie rod only) forwards. Press Show link dimensions to see link lengths and the current position of every node on the diagram.

[Screenshot: front view with link dimensions shown]

Front view geometry

In the front view, almost everything follows from one point: the instant centre.

Instant centre and virtual swing arm

Extend the line of the lower wishbone and the line of the upper wishbone until they meet. That point is the instant centre (IC): at this moment the wheel and upright rotate about it, as if the wheel sat on a single swing arm. The distance from the tyre contact patch to IC is the virtual swing arm length. On a McPherson strut, the second line is drawn through the strut top mount, perpendicular to the strut.

A short swing arm means fast changes in camber and roll centre as the wheel moves. A long one means small changes. Parallel, equal-length wishbones give an infinitely long arm.

Camber and camber gain

Camber is the wheel’s tilt from vertical; negative camber means the top leans inwards. Camber gain is how camber changes as the wheel moves into bump. A suspension that adds negative camber in bump keeps the outer tyre flatter on the road in a corner and gives more grip. A shorter upper wishbone, or a shorter virtual swing arm, gives more gain. Too much gain wears the tyres on straight roads and hurts braking over bumps.

Roll centre and its migration

Draw a line from the tyre contact patch through IC. Where it crosses the vehicle centreline is the roll centre (RC), the point about which the body momentarily rolls. A higher RC means less body roll, but more of the cornering force goes through the links, and the body can be jacked up. Just as important as its height is how much RC moves as the suspension works; a roll centre that migrates a lot makes the car less predictable.

Track change

As the wheel moves up and down, the contact patch moves sideways. The tyre must scrub across the road to follow it, which creates side forces and wear and can make the car follow ruts and grooves. A high roll centre usually means more track change.

KPI and scrub radius

The steering axis runs through the two ball joints (or, on a McPherson, through the lower ball joint and the strut top mount). Its tilt from vertical in the front view is the kingpin inclination (KPI). Where the axis meets the road, its distance to the contact patch centre is the scrub radius. A large positive scrub radius lets bumps and split-friction braking tug at the steering wheel; a small or negative one improves braking stability but reduces feel. More KPI reduces scrub and helps the steering self-centre, but it also tilts the wheel towards positive camber when it is steered.

[Screenshot: front view with IC construction lines and roll centre]

Body roll: what the tyre actually sees

For grip, camber relative to the road matters, not camber relative to the body. When the body rolls, the outer wheel tilts with it towards positive camber by the full roll angle. Camber gain in bump works against this, and the result is the camber the tyre really runs at.

The calculator simulates roll the way kinematics software does: the wheels on the two sides move in opposite directions until the contact patches give the chosen roll angle. Two reference cases show the range:

• Parallel, equal-length wishbones: 2° of body roll puts the outer wheel at exactly +2° to the road. There is no compensation at all, and in roll the roll centre is at infinity: the body slides sideways instead of rotating.
• Sports car double wishbone example: 2° of body roll changes the outer wheel’s camber by about +1.3°, so the geometry compensates roughly a third of the roll. The roll centre moves sideways by about 28 mm.

Watch the roll centre in roll, too. It is no longer on the centreline but where the two CP–IC lines cross, and it can move sideways a long way: about 300 mm at 2° of roll in the McPherson example.

[Screenshot: isometric view of the axle in roll]

Side view geometry

The side view decides how the car steers, brakes and rides over bumps.

Caster and trail

Caster is the rearward tilt of the steering axis in the side view. It gives self-centring and straight-line stability, and when the wheels are steered it adds negative camber to the outer wheel, which helps in corners. Mechanical trail is the distance on the road from where the steering axis meets the ground to the contact patch centre. It is the lever arm on which the tyre’s side force creates the aligning moment, so it largely sets steering feel and weight.

Anti-dive and anti-lift

In the side view the wishbone pivot axes can be inclined. Lines drawn through the ball joints parallel to those axes meet at the side-view instant centre. The angle of the line from the contact patch to this point decides how much of the brake dive is carried by the links rather than the springs:

\text{anti-dive} = \frac{\tan\theta}{h/L} \cdot b_f \cdot 100\%

where θ is the angle of the contact patch–IC line, h the centre of gravity height, L the wheelbase and b_f the front share of braking (outboard brakes). For front-wheel drive with half-shafts, anti-lift uses the line from the wheel centre instead. 100% means no dive at all, but the suspension then absorbs bumps under braking poorly and the steering can feel hard.

Wheel recession

When the side-view IC lies above the wheel centre, the wheel moves forwards as it rises; below it, rearwards. A wheel that moves back when it hits a bump absorbs impacts better. Strong anti-dive needs a high IC, so it usually costs ride comfort: one of the classic side-view trade-offs.

Fig.4 Side view with anti-dive line and trail

Steering: bump steer and roll steer

Bump steer is a toe change as the wheel moves up and down. It happens when the tie rod swings on a different arc than the upright: the tie rod pulls or pushes the steering arm, and the car steers itself over bumps.

The classic rule for avoiding it is simple. In the front view, the tie rod extended should point at the instant centre IC, and its length should match the virtual swing arm. The calculator uses the first part of this rule to suggest the height of the inner tie-rod joint: the point on the line from the outer joint to IC.

The sensitivity is high: in the McPherson example, moving the inner tie-rod joint 50 mm off the recommended height gives about ±4° of toe change over ±80 mm of wheel travel.

Roll steer is the same effect in a corner: the outer wheel goes into bump and the inner into rebound, so both change toe. If the front wheels steer towards the outside of the turn, the car tends to understeer; towards the inside, to oversteer. Values close to zero are the usual aim, with any deliberate roll steer chosen, not inherited.

[Screenshot: bump steer chart before and after correcting the inner joint height]

Double wishbone vs McPherson

Double wishbones give the designer more control over the geometry; the McPherson strut wins on cost, space and part count. The calculator’s two examples show where the difference lies.

The example geometries are indicative, not taken from specific vehicles. Load both in the calculator to compare the full curves.

This is why double wishbones dominate racing and many sports cars, and the McPherson strut dominates everyday cars.

Worked example: shortening the upper wishbone

Shortening the upper wishbone is the classic way to get more camber gain, and the calculator shows exactly what it costs. Load the Wishbones – sports car example and move the upper inner pivot C outwards from x = 430 mm to x = 520 mm; the upper wishbone shortens from 247 mm to 158 mm.

Result: in 2° of roll the outer tyre runs at −0.12° to the road instead of +0.32°, so it keeps more of its contact patch. Cost: the roll centre rises by 21 mm, shifts 221 mm sideways in roll, and track change in bump grows fourfold. Whether the trade pays off depends on the car’s roll stiffness and tyres.

Limitations of the model

The calculator computes rigid-link kinematics: where the parts go, not what forces they carry. Within that, it is exact for the front view and checked against an Autodesk Inventor kinematic model. It does not include:

• bushing compliance (elastokinematics): real rubber bushings deflect under load, so camber and toe in a real car differ somewhat from the kinematic values;
• forces, springs and dampers: there is no load transfer, tyre model or handling simulation;
• full 3D wishbone axes: the front view is solved exactly in its plane, while the side view (caster, anti-dive) and toe are solved as a first-order coupling to it. This is accurate for learning and concept work but is not a replacement for a full 3D multibody model;
• multi-link and rear suspensions, which need a different model.

Use it to understand geometry and compare concepts; confirm the final design in a full 3D model.

FAQ

What is camber gain and how much is ideal? Camber gain is the change in camber as the wheel moves into bump, usually given in degrees per 10 mm or per inch. There is no single ideal: the right amount depends on how much the car rolls and on the tyres. The aim is to keep the loaded outer tyre close to its best camber relative to the road in a corner.

How do you find the roll centre of a double wishbone suspension? Extend both wishbone lines to their intersection, the instant centre. Draw a line from the tyre contact patch through it. Where that line crosses the vehicle centreline is the roll centre. The calculator does this in every position.

Why does a McPherson strut have a high roll centre? Its instant centre is set by the lower arm and a line through the strut top mount perpendicular to the strut. With a tall, nearly vertical strut this point usually sits high and fairly close, which lifts the roll centre and makes it move a lot with travel.

What causes bump steer and how do you fix it? The tie rod and the upright swing on different arcs, so wheel travel changes toe. The fix is to place the tie rod so that, in the front view, its extension points at the instant centre and its length matches the virtual swing arm. The calculator suggests the inner joint height.

What is the difference between caster and trail? Caster is an angle: the rearward tilt of the steering axis. Trail is a distance on the road: from where the steering axis meets the ground to the contact patch. Caster creates trail, but trail also depends on the fore-aft position of the axis relative to the wheel centre.

What does anti-dive percentage mean? It is the share of front-end dive under braking that the suspension geometry carries instead of the springs. 0% means all dive goes into the springs; 100% means none does.

Is this calculator accurate enough for Formula Student? For concept work and learning, yes: the front-view kinematics are exact and were checked against Autodesk Inventor. For the final design, confirm the geometry in a full 3D model that includes the real wishbone pivot axes.

A short history of suspension design

Suspension geometry grew from carriage axles into a discipline of its own, one problem at a time.

The steering problem came first. In 1817 the Munich carriage builder Georg Lankensperger worked out how to turn the two front wheels through different angles so that both roll around a common centre. Rudolph Ackermann patented the idea in England in 1818, and “Ackermann geometry” is still its name.

Early cars borrowed the rigid axle and leaf springs from horse-drawn carriages. It was simple and strong, but a bump under one wheel tilted the other, and the whole axle shook the steering. Independent front suspension appeared in the 1920s; the Lancia Lambda of 1922 was one of the first production cars to use it.

The 1930s turned suspension into engineering. At General Motors, Maurice Olley and his colleagues studied ride and handling systematically, describing understeer and oversteer and introducing independent front suspension to mass production. The short-long arm, or double wishbone, became the standard American front suspension for decades.

After the Second World War, Earle S. MacPherson designed the strut that carries his name. It entered production in the late 1940s on the French Ford Vedette and then on the British Ford Consul and Zephyr. Cheap, compact and with few parts, it went on to dominate small and medium cars, and it still does.

Racing pushed the theory further. As tyres grew wider and grip increased, engineers learned to shape camber gain, roll centre height and anti-dive deliberately rather than accept what the packaging gave them. Colin Chapman adapted the strut to the rear of the Lotus Elite in 1957, and the 1980s brought multi-link suspension to production cars.

For most of this history, geometry was found on the drawing board: the wishbone lines were extended by hand to the instant centre, and the roll centre was drawn from the tyre contact patch. Every new wheel position meant a new drawing. Multibody software later moved this into the computer, and in 1995 William and Douglas Milliken’s Race Car Vehicle Dynamics gave students and engineers a common language for it. Student competitions such as Formula SAE, started in 1981, brought a new generation back to designing suspensions from first principles.

This calculator does what the drawing board did, in every wheel position at once.

Further reading

• William F. Milliken and Douglas L. Milliken, Race Car Vehicle Dynamics, SAE International, 1995: the reference on suspension geometry and vehicle dynamics.
• Jörnsen Reimpell, Helmut Stoll and Jürgen W. Betzler, The Automotive Chassis: Engineering Principles: geometry, components and design practice of production chassis.
• Thomas D. Gillespie, Fundamentals of Vehicle Dynamics, SAE International: a compact introduction to handling, ride and braking.

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