# Spring Constant

Spring force constant, abbreviated as \(k_s\), also called spring constant, is the ratio of opposing force to the displacement from the origional position or how much force is needed to change a springs distance.

- See Hooke's law

### Spring Constant formula

\(\large{ k_s = - F \; d_s }\)

\(\large{ k_s = \frac {F} {d_s} }\)

\(\large{ k_s = \frac {2 \; E}{ d^2 } }\)

\(\large{ k_s = \frac { F }{ x \;-\; x_0 } }\)

\(\large{ k_s = \frac { 2 \; PE_s }{ x^2 } }\)

Where:

\(\large{ k_s }\) = spring force constant

\(\large{ x }\) = distance from equilibrium

\(\large{ F }\) = force

\(\large{ d_s }\) = spring displacement

\(\large{ E }\) = spring energy

\(\large{ F }\) = spring force (applied force)

\(\large{ x_0 }\) = spring equilibrium position

\(\large{ PE_s }\) = spring potential energy

Tags: Equations for Force Equations for Constant Equations for Spring