**In reply to Driven5 :**

A coil spring is just a torsion bar that's been wound around into cylinder.

The spring rate formula given is for a perfect theoretical spring, and ignores a multitude of practical real world factors:

d - Spring wire is NEVER perfectly round, just winding it into a coil distorts the cross section. What about surface effects, rust, paint, surface finish? And since it's raised to the FOURTH power, so any small variation in size, cross section, or measurement is magnified. (a 5% variation yields over 20% difference result when ^4)

G - Note that this 'constant' is specified with leading '~', meaning it's approximate to only 3 digits, but plus/minus how much by actual alloy, by processing of the batch, by operating temperature, etc.

D - Again, how precise is the measurement, and how does the dimension change when the spring is compressed or extended (yes they do that), and it's to the THIRD power, any small variation in measurement is magnified. (a 5% variation yields over 15% result difference when ^3)

N - How do you precisely determine active coils? Are the ends 'dressed', ie end coil pitch is decreased and ground flat? Do the ends touch the next coil and bind when the spring is compressed? If not dressed, how well do the fitted spring end pockets fit, ie where and to what length does the pigtail end 'bottom out' against the pocket when compressed? Certainly more center coils improve accuracy, but with N <10, expect about 10% variation.

Given all that, I'll take an actual measurement over a theoretical calculation any day.