Spring & SHM Calculator
Solve Hooke's law F = k·x for the spring constant, force, or displacement given the other two, and compute simple harmonic motion for a mass on a spring: the period T = 2π·√(m/k), frequency, angular frequency ω = √(k/m), elastic potential energy U = ½·k·x², and the maximum velocity and acceleration for a given amplitude. Units for force (N, kN, lbf), spring constant (N/m, N/cm, lbf/in), displacement (m, cm, mm, in), and mass (kg, g, lb). Pairs with the Newton's Second Law and Projectile Motion calculators. Everything runs locally in your browser.
Hooke's law F = k·x: a spring exerts a restoring force proportional to its displacement from equilibrium (k is the stiffness in N/m). The elastic potential energy stored is U = ½·k·x². A mass m on an ideal spring (massless, no friction) oscillates in simple harmonic motion with angular frequency ω = √(k/m), period T = 2π·√(m/k), and frequency f = 1/T. For an amplitude A the maximum speed is v_max = A·ω and the maximum acceleration is a_max = A·ω². Everything runs locally — nothing leaves your browser.