The value of the spring constant k is determined by:

The force required to stretch a string from its equilibrium position in an ideal spring is directly proportional to the spring's extension.

Hooke's law for springs states as follows:

${\mathrm{F}}_s=-\mathrm{kx}$

Here $F_s$ is the spring force, $x$ the displacement from the equilibrium position, and $k$ the spring constant.