Spring constants from the physical dimensions of a spring

[Alen_Esterling]

I’d like to know if anyone has formulas for calculating the spring constant (k) of coil springs, from their physical dimensions. I bought a coil spring, suspended a 0.6 kg mass to it, observed its oscillation period at very close to 0.6 seconds, and so believed the spring constant “k” to be about 65. The spring has a 19mm coil diameter, 22 active coils, the wire is 1mm diameter. Not sure of the shear modulus, but I believe it’s just spring steel. Can’t seem to find a formula that comes out even close to agreement, or even a place that tells the units of measure for their formulas.

 

[jrmichler]

Everything you want to know about spring design, and more, is in the Handbook of Spring Design from the Spring Manufacturers Institute: https://smihq.org/store/ListProducts.aspx?catid=550000&ftr=. It has a hundred pages of spring goodness. Here is an online calculator that should do the job for you: https://www.acxesspring.com/spring-stiffness-calculator.html.

Your spring alloy is most likely music wire.