Spring Calculator

An ideal spring exerts a restoring force proportional to its displacement from equilibrium. Hooke's law expresses that relationship as F = −kx, where k is the spring constant and x is displacement. The minus sign indicates that force points opposite the displacement. This calculator reports force magnitude, so the displayed value follows kx while the physical direction remains toward equilibrium. The spring constant measures stiffness in newtons per meter. A larger value requires more force for the same extension or compression. Elastic potential energy equals one half kx squared, representing the work stored while deforming the spring from equilibrium. Energy is never negative in this ideal model because displacement is squared, although the signed force reverses when displacement changes direction. Adding a mass creates a simple harmonic oscillator when damping, friction, gravity shifts, and spring mass can be neglected. Its period is T = 2π√(m/k), and frequency is the reciprocal of period. A stiffer spring oscillates faster, while a larger attached mass oscillates more slowly. Amplitude does not change the ideal oscillator's period, even though it changes maximum force and stored energy. For k = 200 N/m, displacement 0.1 m, and mass 2 kg, the spring force magnitude is 20 N and elastic energy is 1 J. The corresponding ideal period is approximately 0.63 s and frequency is 1.59 Hz. Those values describe small oscillations around equilibrium. In a vertical setup, gravity shifts the equilibrium position but does not change the ideal small-oscillation frequency for a linear spring. Real springs depart from the model. Coils have mass, materials have elastic limits, attachments add compliance, and air resistance or friction dissipates energy. Large deformation can make stiffness nonlinear. Closely wound extension springs may also have initial tension, while compression springs can buckle if poorly guided. Never assume the linear result remains safe beyond the manufacturer's rated travel, load, fatigue life, or solid height. Use the calculator for physics study, initial mechanism sizing, vibration estimates, and consistency checks between force, energy, and frequency. Measure displacement from the loaded equilibrium appropriate to the problem and use the effective moving mass, which may include a fraction of spring mass and attached hardware. For machinery, suspension, launching devices, or safety-critical designs, account for preload, damping, resonance, tolerances, fatigue, impact factors, and boundary conditions with validated engineering methods.