The spring constant \(k\) of a spring quantifies its stiffness and is determined by the material and shape of the spring. It does not depend on the applied force or the amount of elongation.

Mathematically, the spring constant \(k\) is related to the force \(F\) and elongation \(x\) of the spring according to Hooke's law:

$$F = kx,$$

Where:

- \(F\) is the force applied to the spring (in newtons, N)

- \(k\) is the spring constant (in newtons per meter, N/m)

- \(x\) is the elongation of the spring (in meters, m)

In this equation, \(k\) is constant for a given spring. It remains the same regardless of the applied force or the amount of elongation.