Spring Constant Calculator

Calculate spring constant (k) using Hooke's Law or from oscillation period. Essential for physics, mechanical engineering, and understanding elastic systems.

**Method 1: Hooke's Law** F = kx Where: • F = Applied force (N) • k = Spring constant (N/m) • x = Displacement from equilibrium (m) Rearranged: k = F/x **Method 2: Simple Harmonic Motion** T = 2π√(m/k) Where: • T = Period of oscillation (s) • m = Attached mass (kg) • k = Spring constant (N/m) Rearranged: k = 4π²m/T²
**Example 1 (Hooke's Law):** A spring stretches 5 cm when a 10 N force is applied. • Force = 10 N • Displacement = 0.05 m • k = 10 / 0.05 = 200 N/m **Example 2 (Oscillation):** A 0.5 kg mass oscillates on a spring with period 0.8 s. • Mass = 0.5 kg • Period = 0.8 s • k = 4π²(0.5) / (0.8)² = 30.84 N/m **Example 3 (Stiff Spring):** A force of 500 N compresses a spring by 2 cm. • Force = 500 N • Displacement = 0.02 m • k = 500 / 0.02 = 25,000 N/m (very stiff spring)

What is Hooke's Law?

Hooke's Law states that the force needed to extend or compress a spring is proportional to the displacement: F = kx, where k is the spring constant, F is force, and x is displacement from equilibrium.

What is the spring constant?

The spring constant (k) measures a spring's stiffness. Higher k means a stiffer spring. Units are N/m (newtons per meter) or lbf/in (pounds-force per inch).

How do I calculate spring constant from period?

For a mass-spring system, the period T = 2π√(m/k). Rearranging: k = 4π²m/T². This method works when you know the oscillation period and attached mass.

What is the elastic limit?

The elastic limit is the maximum stress a material can withstand while still returning to its original shape. Beyond this point, permanent deformation occurs and Hooke's Law no longer applies.

Can I use this for compression springs?

Yes! Hooke's Law applies to both extension and compression springs. The spring constant remains the same whether the spring is stretched or compressed within its elastic limit.

What factors affect spring constant?

Spring constant depends on material properties (shear modulus), wire diameter, coil diameter, and number of active coils. Stiffer materials, thicker wire, smaller coil diameter, or fewer coils increase k.

How accurate is Hooke's Law?

Hooke's Law is very accurate for small deformations within the elastic limit. For large deformations or non-linear springs, more complex models are needed.

What are typical spring constant values?

Values vary widely: car suspension springs ~20-80 kN/m, door springs ~100-500 N/m, pen springs ~10-50 N/m, and precision springs in instruments can be <1 N/m.

Can springs have different constants for extension vs compression?

Ideally no, but in practice some springs (especially long or non-ideal ones) may show slightly different behavior in extension vs compression due to buckling or geometric effects.

How do series and parallel springs combine?

Springs in series: 1/k_total = 1/k₁ + 1/k₂ (softer). Springs in parallel: k_total = k₁ + k₂ (stiffer). This is opposite to resistors in electrical circuits.

What is potential energy in a spring?

Elastic potential energy stored in a spring is PE = ½kx², where k is spring constant and x is displacement. This energy is released when the spring returns to equilibrium.

How do I measure spring constant experimentally?

Hang known masses on the spring, measure displacement for each mass, plot force (F=mg) vs displacement, and find the slope. The slope is the spring constant k.