Wheel Rate Calculator

Spring rate (k_spring)

Motion ratio (MR)

Wheel rate (k_wheel)

Enter any two values and the third is solved for you. Most often you have the spring rate and motion ratio and want the wheel rate — leave that field blank.

Show pounds per inch (lbf/in)

Add the wheel and spring rate in pound-force per inch alongside the metric answer.

Add corner weight (ride frequency and sag)

Enter the sprung corner mass to get the natural ride frequency, a street/track verdict, and the static ride sag at the wheel.

Please input values into the fields

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Show the motion-ratio graph

Plot wheel rate against motion ratio to see the square-law curve.

Show the motion-ratio table

List wheel rate and the share of spring stiffness across a range of motion ratios.

Spring rate and wheel rate are not the same thing. Confusing these two values is one of the most common causes for incorrect suspension tuning. Spring rate is a value specified on the spring. Wheel rate, on the other hand, is the actual stiffness that the tire experiences due to the effects of suspension geometry. This calculator does this conversion by including the motion ratio of the suspension geometry into the calculation and can also back calculate wheel rate, spring rate or motion ratio if desired.

What is wheel stiffness?

Wheel stiffness is the actual stiffness experienced by the wheel. It differs from the original spring stiffness because almost all suspensions have a lever arm between the wheel and the spring - such as A-arms, wishbones or struts.

The motion ratio is used to quantify this leverage effect. For example, if the motion ratio is 0.6, then a wheel moves by 100 mm when the spring compresses by 60 mm. Intuitively one might assume that the stiffness of the spring at the wheel would be 60% of the original stiffness. In fact it is only 36% lower since this value is squared.

The path and the load of the wheel are lower, so the motion ratio appears twice in the mathematical calculation. This quadratic term is exactly why this calculator exists - it has a big impact and is often underestimated.

How do I use this calculator?

Enter two of the three values and the third value will be automatically calculated. The spring constant can either be taken from manufacturer specifications or directly from the spring itself.

The motion transmission ratio can be found in the records of a suspension designer or measured yourself: let the wheel suspension travel a known distance and then check how far the spring has moved on the same arc. The units automatically switch between metric and imperial, and the result is also shown in pounds per inch which is convenient for users of the imperial system.

Understanding of the formula:

The wheel stiffness is the spring constant multiplied by the square of the motion transmission ratio:

k_{wheel} = k_{spring} \times (MR)^2

Example: You install a set of coilover springs with a nominal spring constant of 50 N/mm and a motion ratio of 0.6 on your race car. Plug the values in to calculate:

k_{wheel} = 50 \times (0.6)^2 = 50 \times 0.36 = 18\ \text{N/mm}

The wheel stiffness is 18 N/mm which equates to about 103 pounds per inch. The actual spring rate that the tire feels is much less than the spring installed on the vehicle. This is one of the reasons race cars often use such high spring rates in their specs - some of it gets absorbed by the suspension geometry.

Quadratic terms also magnify small changes in geometry. Using the same spring, increasing the travel ratio from 0.6 to 0.7 increases wheel stiffness from 18 to 24.5 N/mm. While the change in travel ratio is about 17%, the increase in wheel stiffness is 36%.

Estimation of motion ratio by type of suspension system

The typical range of the rate ratio is between 0.5 and 1.0 depending on the type of suspension. If you cannot measure your own rate ratio these are sufficient ranges to perform a reasonable check of your spring selection.

Suspension type	Typical motion ratio	Notes
MacPherson strut	0.8 – 1.0	Spring sits almost in line with the strut
Double wishbone (outboard)	0.6 – 0.8	Spring on the lower arm near the wheel
Double wishbone (inboard / pushrod)	0.5 – 0.7	Spring tucked inboard for packaging and aero
Multi-link	0.6 – 0.9	Depends on where the spring picks up
Live axle / leaf spring	≈ 0.9 – 1.0	Spring close to or at the wheel line

A lower ratio allows designers to position the spring further inboard to accommodate wider tires, but to achieve the same wheel stiffness the spring rate must be increased proportionally - and due to the quadratic relationship, "proportionally increase" means a significant increase.

Why wheel stiffness is important: natural frequency of the vehicle

Racing teams value wheel stiffness as it directly affects the natural frequency of the vehicle. Natural frequency is how engineers compare different suspension configurations on various vehicles and loads.

This is the natural frequency at which the spring load oscillates up and down due to the stiffness of the wheel.

f = \frac{1}{2\pi}\sqrt{\frac{k_{wheel}}{m}}

where k is the wheel stiffness in Newtons per meter and m is the sprung mass of the vehicle. If you enable the "Suspension natural frequency" option and enter the sprung mass, then this tool will calculate the frequency and its range.

Roughly speaking, the natural frequency of a comfortable city car is about 1.0 to 1.5 Hz. For a sporty road car it's 1.5 to 2.0 Hz. Racing cars are in the range from 2.0 to 3.0 Hz, while vehicles with downforce have an even higher frequency due to the aerodynamic load to keep the vehicle height.

Static compression and spring travel

The corner weight also tells you how much the suspension will compress under the weight of the vehicle, so it is the spring travel. The wheel deflection is equal to the corner weight divided by the wheel stiffness:

\delta_{wheel} = \frac{W}{k_{wheel}} = \frac{m \cdot g}{k_{wheel}}

The compression of the spring itself is less than the movement of the wheel and the difference is a motion ratio. The spring travel equals the wheel drop multiplied by the motion ratio. Therefore, an apparently soft spring with a low motion ratio can still result in large vehicle droop because the droop value is determined by the wheel stiffness rather than the spring stiffness.

The suspension and the natural frequency of a vehicle are two different manifestations of the same physical law. When both formulas are combined, the spring stiffness coefficient completely falls away:

f = \frac{1}{2\pi}\sqrt{\frac{g}{\delta_{wheel}}}

This is a practical way to check: A static suspension deflection of about 25 mm corresponds to the natural frequency of the vehicle being around 1 Hz. A harder setup leads to less suspension deflection. By activating the "Mass distribution" option, you can display the suspension deflection and the frequency side by side for your values.

Areas of application:

A stiffer spring combined with a lower motion ratio can result in softer wheel behavior than the part being replaced, so comparing spring rates alone is misleading.

Suspension designers also use the same mathematical method to integrate all components in terms of spring rate and ride stiffness. This calculation is also used when changing the type of springs or designing a custom geometry as looking at the spring rates alone doesn't tell you much about how the car will feel to drive.

Chassis tuning tips.

First calculate the wheel stiffness and then compare the springs. Do not reverse the order. When replacing a spring strut you should also check the shock absorbers as different wheel stiffnesses require differing damping characteristics.

The handling depends on the wheel stiffness not the spring stiffness. Many sports cars have higher front wheel stiffness to reduce understeer. The optimal front and rear axle distribution depends on the weight distribution ratio and desired driving characteristics, not that both axles are exactly equal.

Frequently asked questions

Why is the ratio of motion squared in the formula for wheel stiffness?

This is because the motion ratio appears twice in the physics relationship. The spring travel is shorter than the wheel travel, which is one factor of the motion ratio; the force that the spring applies to the wheel is also less, which is the second factor. When these two factors are multiplied together, the motion ratio is squared. So with a motion ratio of 0.6, the wheel only feels 36% of the stiffness of the spring.

Can the wheel stiffness be higher than the spring stiffness?

This is only possible if the motion ratio is greater than 1.0, which is rare in production vehicles. Most designs have a motion ratio less than 1.0 so that the stiffness of the wheels is ultimately lower than the stiffness of the springs. If your values indicate a motion ratio greater than one, double check your measurements before trusting the results.

How do you measure a car's gearing?

Remove the spring and let the suspension travel a known distance on the wheel path. Then measure how far the spring seat has moved over that same distance. The ratio of spring movement to wheel movement is your motion ratio. Take this measurement near the static ride height, as the motion ratio varies with trail.

Does the motion ratio remain constant over the entire suspension travel?

Normally not. Most suspensions have progressive or regressive properties so the motion ratio changes as the wheel moves. The single value you enter here is an average or static ride height value and is used to select a spring that will be sufficient but not suitable for full kinematic analysis.

What body frequency should I aim for?

The natural frequency of the suspension on a comfortable road car is about 1.0 to 1.5 Hz, for a sporty coupe it's 1.5 to 2.0 Hz and for a race car 2.0 to 3.0 Hz. Downforce vehicles use higher frequencies in order to maintain vehicle height under aerodynamic loads. Enter the sprung mass at each corner to get appropriate values for your configuration and assess results.

Should I match front wheel stiffness to rear?

Automatic adjustment is not recommended. The optimal front-to-rear ratio depends on the weight distribution, vehicle itself and desired handling characteristics. Many high performance vehicles use a higher stiffness in the front to reduce understeer. So the balanced ratio is often the result of intentional tuning rather than just an adjustment.

How much will the suspension compress under the weight of the vehicle?

The deflection of a wheel is equal to the spring load divided by the wheel stiffness acting on the wheel. The compression of the spring is this result multiplied by the gearing ratio. As the deflection is mostly determined by the wheel stiffness, a soft spring with low gearing can still give significant deflection. Enable the mass option and enter the sprung mass to show the static deflection for your configuration.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

FSAE / Milliken: Race Car Vehicle Dynamics
Motion ratio, wheel rate, and how the ratio squares into the effective stiffness at the tyre.
Engineering ToolBox: Springs and Ride Frequency
Natural frequency of a sprung mass and the spring-rate relationships behind ride frequency.