where G is shear modulus of elasticity, d is wire diameter, D is mean spring diameter, N is number of active coils which is the number of complete coils plus a fraction that depends on the types of ends the spring has...plain, plain and ground, squared, closed, squared and ground.
Squared and ground? For a coil over.
G(modulus of rigidity) is 30 x 10E6 for all spring steels. Just counting the number of active coils and not worrying too much about the "fractions" at the ends will get you in the ballpark. The "lb." rating on coils is actually their rate, lb./in., rating.
yes...but a lot of times spring manufacturesr like to give you a spring rate at mid stroke and back out an average or many other stupid ways of doing it, but if you actually measure it and also calculate it...you should be within +/-10-12% without considering the spring ends and +/-3-4% with allowance for the ends in your calcs.
If you're dealing with absolutes...The rate of a coil spring is not exactly linear. On average, it is very close to linear only through about 85 percent of its total travel. The only way to know the exact rate throughout the entire travel is to measure it throughout the entire travel.