Compression Spring Forces and Deflection F=k(Lf-Ld) or Ld=Lf-(F/k)

Where;

F is the force applied to the compression spring (lbs)
k is the spring rate, often specified in catalogs. (lbs/inch) Also, see below for calculation of spring rate.
L_f is the length of the spring with zero deflection, ie, no force applied. Often called "free length" (inches).
L_d is the length of the spring with the force F applied. (inches).

There is a comprehensive compression spring calculator/designer here at efunda.

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Spring Rate (calculated)

Where;

k is the spring rate. (lbs/inch)
G is the modulus of rigidity (also called shear modulus) of the spring material (psi), See below.
d is the spring wire diameter (inches)
n is the number of active coils (less than the total number of coils)
D is the mean spring coil diameter.(inches). = Spring dia. - wire dia.

G=E/(2(1+v))

E is the elastic modulus of the spring material (psi).
v is the Poisson ratio of the material.