# Maximum Spring Force (Fully Compressed)

## Description

A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication.

Hooke’s law of elasticity states that the extension of an elastic rod (its distended length minus its relaxed length) is linearly proportional to its tension, the force used to stretch it.

Hooke’s law is a mathematical consequence of the fact that the potential energy of the rod is a minimum when it has its relaxed length. Any smooth function of one variable approximates a quadratic function when examined near enough to its minimum point as a result of the Taylor series. Therefore, the force—which is the derivative of energy with respect to displacement—will approximate a linear function.

The formula shown here calculates the maximum force of a compressed spring.

Related formulas## Variables

F_{max} | force of fully compressed spring (N) |

E | Young's modulus (pascal) |

d | spring wire diameter (m) |

L | free length of spring (m) |

n | number of active windings (dimensionless) |

ν | Poisson ratio (dimensionless) |

D | spring outer diameter (m) |