The spring constant calculator solves Hooke's Law (F=kx) for any variable and calculates elastic potential energy (PE=½kx²). A third mode determines the spring constant from an oscillating mass and its period. Distinct from the simple-harmonic-motion-calculator which focuses on oscillation frequencies — this tool focuses on spring forces and stored energy.
Result
Spring Visualization
Spring stretches proportional to displacement
How to Use the Spring Constant Calculator
Hooke's Law (F = -kx) is one of the most fundamental equations in classical mechanics. It describes how springs, rubber bands, guitar strings, and many other elastic materials respond to force. This calculator has three modes: direct Hooke's Law, elastic potential energy, and finding k from oscillation period.
Mode 1: Hooke's Law (F = -kx)
Select what you want to solve for — force F, spring constant k, or displacement x. For example: a spring with k=200 N/m compressed by x=0.1 m exerts F = 200 × 0.1 = 20 N. The negative sign in F = -kx means the force opposes the displacement — when you push down, the spring pushes back up.
Mode 2: Elastic Potential Energy (PE = ½kx²)
Compressed or stretched springs store energy. With k=200 N/m and x=0.1 m, PE = ½ × 200 × 0.1² = 1 J. This energy converts to kinetic energy when the spring releases. A spring with 10 J stored can launch a 1 kg mass to √(2 × 10 / 1) = 4.47 m/s.
Mode 3: Spring Constant from Period
If you observe a mass oscillating on a spring, you can determine k without measuring force directly. From T = 2π√(m/k), rearranging gives k = (2π/T)² × m. A 0.2 kg mass oscillating with period 0.628 s has k = (2π/0.628)² × 0.2 = 100 × 0.2 = 20 N/m — useful for lab measurements.
FAQ
What is Hooke's Law?
Hooke's Law states that the force exerted by a spring is proportional to its displacement from equilibrium: F = -kx. The negative sign means the spring force opposes the displacement (it's a restoring force). The spring constant k (N/m) measures stiffness — a larger k means a stiffer spring that resists deformation more strongly.
What does the spring constant k represent?
The spring constant k (measured in N/m or lb/in) is the stiffness of the spring. k = 1 N/m means 1 newton of force stretches the spring 1 meter. A car suspension spring might have k ≈ 20,000–30,000 N/m. A stiff metal spring in a pen click mechanism might have k ≈ 50–200 N/m.
What is elastic potential energy?
Elastic potential energy (PE = ½kx²) is the energy stored in a compressed or stretched spring. At maximum displacement, all energy is potential. At equilibrium (x=0), all energy has converted to kinetic energy. The total energy in a spring-mass system is conserved: KE + PE = constant = ½kA², where A is the amplitude.
How do I find the spring constant from the oscillation period?
For a mass m attached to a spring oscillating with period T, k = (2π/T)² × m. For example, if a 0.5 kg mass oscillates with period 0.2 s, then k = (2π/0.2)² × 0.5 = (31.4)² × 0.5 ≈ 493 N/m. This is derived from the SHM period formula T = 2π√(m/k).
Is this tool free?
Yes, completely free with no signup required. All calculations run locally in your browser.
What is the difference between this calculator and the simple harmonic motion calculator?
This tool focuses on Hooke's Law (F=kx), elastic potential energy, and finding k from spring properties. The simple-harmonic-motion-calculator focuses on oscillation period, frequency, and angular frequency of the resulting motion. Both are useful together — find k here, then use the SHM calculator for oscillation properties.