# Variation in spring constant with respect to the length and no. of coils

Do the spring constant depend upon the length of the spring? No. of coils? Like what happens to the spring constant if you cut it in the half?

• Instead of cutting the spring in half, imagine what happens if you paint a red dot on the middle. That thought experiment should tell you what happens to the halves above and below the dot. – MSalters Apr 8 '15 at 12:17
• Half the length equals double the stiffness generally. As commented above the displacement of the middle is half of the displacement of the end. – ja72 Apr 8 '15 at 14:53

In the standard approximation it does not depend on the length but on the number of active windings. As you can find e.g. here, the spring constant $k$ is
$$k=\frac{G d^4}{8 n D^3}$$
whre $d$ is the wire diameter, $D$ the coil diameter, $n$ the number of active coils, and $G$ the shear modulus. So if you cut it in half $n \rightarrow n/2$ the spring constant doubles $k\rightarrow 2k$. The maximum length decreases of course and you get into the non-linear regime with less displacement.