# 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

## formulas that use Spring Constant

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

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

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

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

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

\(\large{ k_s = \frac {G \; d^4} {8 \; n_a \; D^3} }\) |

### Where:

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

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

\(\large{ D }\) = mean coil diameter

\(\large{ n_a }\) = number of active coils

\(\large{ G }\) = shear modulus of material

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

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

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

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

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

\(\large{ d }\) = wire size

\(\large{ D/N }\) = index correction

- \(\large{ G }\) value for common spring materials
- Copper = 6.5 x 10^6
- Beryllium Copper = 6.9 x 10^6
- Inconel = 11.5 x 10^6
- Monel = 9.6 x 10^6
- Music Wire = 11.5 x 10^6
- Phospher Bronze = 5.9 x 10^6
- Stainless Steel = 11.2 x 10^6

Tags: Equations for Force Equations for Constant Equations for Spring