Spring Rate Calculator

Where a coil spring's rate comes from

A coil spring is a torsion bar wound into a helix. Push the ends together and the wire barely bends, it twists, and the rate that comes out of that is G times the wire diameter to the fourth power, divided by eight times the mean coil diameter cubed times the number of active coils. Two things in that sentence do the damage. Wire diameter is raised to the fourth, so a wire measured 2% fat gives a rate 8% high. Mean coil diameter is cubed in the denominator, so a wider spring of the same wire is softer, and mean diameter is measured centre of wire to centre of wire, which is outer diameter minus one wire diameter, not the outer diameter you can reach with a tape measure. The tool wants outer diameter and does that subtraction itself.

Active coils are the third trap and the one that separates a calculation from a catalogue. Only the coils that are free to twist count. On a closed-and-ground spring, the two end coils sit flat against the seats and do almost nothing, so active coils are total coils minus two. On a plain-ended spring, close to all of them work. Nobody grinds an end perfectly, so the true figure sits somewhere either side of that rule, and a spring maker publishes a rate they measured on a press rather than one they calculated. That is why a catalogue number and a geometry number rarely agree exactly, and why the sensitivity table above is there: on the six-coil default spring, one active coil either way moves the rate by 14 to 20 percent.

Motion ratio, and the word that gets it backwards

The spring almost never sits on the wheel. It sits inboard on a wishbone, or at an angle on a strut, so the wheel moves further than the spring does and pushes on it with more force than it returns. The motion ratio here is spring travel divided by wheel travel, and it enters the wheel rate squared, because the linkage works on both terms at once: it divides the travel the spring sees, and it divides the force the spring can send back. Multiply those two and you get the square. If the spring also leans, only the vertical part of its force holds the corner up and only the vertical part of the mount's motion compresses it, so the same argument gives a second squared term, cosine of the angle squared.

The trap is that the phrase "motion ratio" is used both ways round in print. OptimumG's own published tech tip on springs and dampers defines it as wheel travel over spring travel, the inverse of the definition used here and by most spring suppliers, and articles exist that state one definition and then use the other in the arithmetic below it. It matters more than it sounds: the ratio is squared, so typing the inverse squares the wrong number, and the error is a factor of one over the ratio to the fourth power. Type 1.43 where 0.70 belongs and the wheel rate comes out 4.2 times too high. That is why the second dropdown in step two is a choice you make rather than something this tool guesses from whether your number is above or below one.

Ride frequency and the published bands

Ride frequency is the undamped natural frequency of one corner: the wheel rate divided by the sprung mass it holds up, square-rooted, divided by two pi. It is the number setup people compare across cars, because it normalizes stiffness against weight, and a 500 lb/in spring means nothing until you know what it is carrying. The bands in the table come from OptimumG's published tech tip Springs and Dampers, Part One, which lists 0.5 to 1.5 Hz for passenger cars, 1.5 to 2.0 Hz for sedan racecars and moderate downforce formula cars, and 3.0 to 5.0 Hz and up for high downforce racecars. Those are descriptions of what cars in each class run, with a gap between 2.0 and 3.0 Hz that the source simply does not name, and they are printed here as labels rather than targets.

Two limits on that number, both real. The tire is a spring too, in series with the suspension, so the frequency a car actually shows on a rig is a little lower than this figure, and the softer the sidewall relative to the wheel rate the bigger the gap. And this is an undamped frequency: dampers are not in the model at all. For the sprung mass to put in, weigh the car first. The corner weight calculator handles the scale readings and the cross-weight; subtract the unsprung parts from the corner figure it gives you and that is the mass this tool wants. Choosing a front-to-rear frequency split is a setup conversation with its own arguments, and this tool stays out of it.

What this tool will not do

It will not tell you what spring to buy. There is no target of its own in here, no recommendation, and no judgement about whether a number is right for your car; the target frequency in step four is one you bring, and the tool only runs the same formula backwards from it, because that depends on the track, the tire, the aero and the driver, and a calculator that guessed would be inventing confidence it has not earned. The geometry formula also has a scope: it describes a cylindrical, constant-pitch coil of round wire. Progressive, barrel and beehive springs change diameter or pitch along their length by design, so a single rate does not describe them and this formula does not apply. And nothing here covers roll: anti-roll bars, roll centres and load transfer all sit on top of the wheel rate, and none of them are modelled.