Spring Constant & Hooke's Law Calculator

Hooke's Law and Springs Guide

Hooke's Law

F = kx. Where F = applied force (N), k = spring constant (N/m), x = extension from natural length (m). Spring constant k represents stiffness — higher k = stiffer spring. Steel coil spring (typical car): k ~30,000-50,000 N/m. Pen spring: k ~100-500 N/m. Bungee cord: k ~50-200 N/m. Elastic limit: beyond a certain extension, the spring no longer returns to its natural length (permanent deformation). Hooke's law only applies within the elastic limit. Most springs obey Hooke's law for extensions up

Elastic Potential Energy

Energy stored in a stretched (or compressed) spring: E = ½kx². The factor of ½ comes from the average force (zero to maximum) acting over the extension. This is the work done stretching the spring. Example: spring k=400 N/m, stretched 0.1m. E = ½ × 400 × 0.01 = 2 J. This energy is released when the spring returns to natural length — useful in: pinball plungers, mousetraps, spring guns, watch escapements, suspension systems. Springs in cars: store the kinetic energy of bumps and release it back g

Simple Harmonic Motion (SHM)

A mass on a spring oscillates with simple harmonic motion. Period: T = 2π√(m/k). Where m = mass, k = spring constant. Frequency: f = 1/T = (1/2π)√(k/m). Independent of amplitude (assuming Hooke's law holds). Heavier mass: longer period (lower frequency). Stiffer spring (higher k): shorter period. Example: 0.5kg mass on 400 N/m spring. T = 2π√(0.5/400) = 2π × 0.0354 = 0.222s. f = 4.5 Hz. The mass oscillates 4.5 times per second. Angular frequency: ω = 2πf = √(k/m). Equation of motion: a = -(k/m)x

Springs in Series and Parallel

Combining springs changes effective stiffness. Springs in parallel: stiffness adds. k_total = k₁ + k₂. Example: two 100 N/m springs in parallel: k_total = 200 N/m (stiffer). Springs in series: stiffness combines as: 1/k_total = 1/k₁ + 1/k₂. Example: two 100 N/m springs in series: 1/k_total = 1/100 + 1/100 = 1/50. k_total = 50 N/m (less stiff). Conservation of energy considerations: in vibration isolation (washing machine drum, car suspension), parallel springs provide higher load capacity but le