Sway Bar Rate Calculator
This calculator shows you the spring rate of a sway bar. It is accurate for mild, spring, and chromoly steels since they all have a very similar stiffness. Nearly all sway bars are made from these materials.
The measurements needed for this calculation are quite easy to take, especially if the sway bar is off the car. Since very many sway bar manufacturers do not provide this information themselves (or perhaps do not even have the information to share), it can be very worthwhile to measure for yourself prior to installation or purchase.
Many readers might be surprised at how incredibly stiff their sway bars are. It is not uncommon to have a sway bar many, many time stiffer than your main springs. In these cases, that's where all your roll resistance on a road car (and many race cars) comes from- the sway bars!
Car manufacturers- and even race cars- use large sway bars to keep body roll minimized while keeping the main springs soft enough to absorb bumps. For example, a Subaru Impreza gets roughly twice as much roll resistance from its sway bars than it does its main springs. Many owners upgrade their sway bars to units that are two or four times stiffer than stock! In such a case, nearly all body roll is handled by the sway bars instead of the springs. The driver will also begin to notice the lack of independence in the suspension as now the left and right are linked pretty rigidly.
However, equivalent main spring rates equaling that of a sway bar are not practical, so most drivers consider this trade-off quite worth it.
The Math:
The equation is taken from How To Make Your Car Handle by Fred Puhn and has proven itself fairly accurate:
500,000 D^4
K (lbs/in) = -------------------------------------
(0.4244 x A^2 x B) + (0.2264 x C^3)
B
_________________
A| / \ C
| /
A - Length of end perpendicular to B (torque arm - inches)
B - Length of center section (inches)
C - Length of end (inches)
D - Diameter bar (inches)For hollow bars, we calculate the rate of a solid bar of the outer diameter and the rate of a solid bar of the inner diameter. Then, the rate of the smaller bar is subtracted from the larger bar.
There is a checkbox for whether the calculator gives the result for a one wheel bump or body roll situation. The equation above gives us a one-wheel bump rate, where one side of the sway bar is assumed to stay stationary. (Recall that for two wheel bumps, a sway bar's rate is always zero, which is why sway bars have minimal impact on ride quality.) The body roll spring rate is more realistic of the sway bar's intended purpose, and it is twice as high as the one wheel rate. This is because one side of the car compresses while the other extends in an equal but opposite direction. So, for each inch of compression on the outside suspension, there should be an inch of extension on the inside suspension. Thus, twice the stress is exerted on the sway bar, and both wheels get that full resistance. This is where the doubling comes from compared to a one wheel bump.
The motion ratio converts the sway bar rate into the wheel rate. Recall that the motion ratio is simply the ratio of how much wheel movement is generated for a given amount of movement where your sway bar endlink attaches. A motion ratio of 1 means they move the same amount, and your wheel rate is equal to the raw sway bar rate. Most cars use a value smaller than one, where an inch of wheel movement may only result in half an inch of sway bar arm movement (a motion ratio of 0.5). This ratio is determined mostly by where the sway bar endlinks connect on the suspension's control arm.
For those curious, the equation for converting from sway bar rate to wheel rate is:
wheel rate = sway bar rate * motion ratio ^ 2