# Mechanical

Compression Spring Forces and Deflection

F = k (Lf - Ld)

or

L= 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.
Lf is the length of the spring with zero deflection, ie, no force applied. Often called "free length" (inches).

Ld is the length of the spring with the force F applied. (inches).

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

Spring Rate (calculated)

k = (G d4) / (8 n D3)

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).
is the Poisson ratio of the material
.