Spring Constant Calculator

At a glance:The spring constant k (also 'stiffness' or 'spring rate') describes how stiff a spring is — the force needed to stretch (or compress) it by a unit length. It comes from Hooke's law (Robert Hooke, 17th century): within the elastic limit, the spring force (or applied force) is proportional to the deformation. Formally F=k·x, where F is the applied force (N), x is the deformation from natural length (m) and k is the spring constant (N/m). Rearranging gives k=F/x. Physically k is 'force per metre of stretch': larger k means a stiffer spring (more force for the same stretch), smaller k means softer. Example: apply F=20 N to stretch a spring x=0.1 m (10 cm) → k=20/0.1=200 N/m, meaning 200 N per metre. Hooke's law and k are widely used: (1) weighing and scales — a spring scale reads force from extension via F=kx; (2) suspension and damping — car/motorcycle springs absorb road shock, k sets softness; (3) mechanical devices — buttons, valves, clock springs; (4) simple harmonic motion — the period of a mass-spring oscillator is T=2π√(m/k), so larger k oscillates faster; (5) material elasticity. The elastic potential energy stored is E=½kx². Combined springs: parallel (side-by-side) add stiffness (k_total=Σk_i, stiffer); series (end-to-end) follow 1/k_total=Σ1/k_i (softer) — opposite to resistors. Note: (1) Hooke's law holds only within the elastic limit — overstretch causes permanent deformation; (2) use SI units (N, m → N/m; cm to m); (3) if hanging a mass, F=m·g; (4) this tool takes non-negative force and x>0. In short, it quickly gives the spring constant from force and extension — a practical tool for Hooke's law, scales and SHM.