Spring Constant Calculator

Calculate spring constant using Hooke's law (F = kx)

Spring Constant

Hooke's Law: F = kx

Formula
k = F / x

What Is the Spring Constant?

The spring constant (k) is a measure of a spring's stiffness — how much force is required to stretch or compress it by a given distance. A high spring constant means the spring is stiff and requires a lot of force to deform, while a low constant indicates a softer, more flexible spring.

Defined by Hooke's Law, the spring constant is fundamental to mechanical engineering, physics, and everyday products from car suspensions to ballpoint pens. It determines how a spring-mass system oscillates and how energy is stored as elastic potential energy.

How to Use the Spring Constant Calculator

  1. Enter the force applied to the spring in Newtons (N).
  2. Enter the displacement (extension or compression) in meters.
  3. Click Calculate to get the spring constant k in N/m.
  4. Use the result to compare stiffness or design spring-loaded mechanisms.

Formula & Explanation

k = F / x k = spring constant (N/m) F = applied force (N) x = displacement (m)

Hooke's Law states that force is proportional to displacement within the elastic limit. Exceeding this limit causes permanent deformation.

Worked Examples

Measuring a Coil Spring

A 50 N force stretches a spring 0.1 m. k = 50 / 0.1 = 500 N/m. This is a moderately stiff spring suitable for small mechanical assemblies.

Automotive Suspension

A car spring compresses 0.05 m under a 2000 N load. k = 2000 / 0.05 = 40,000 N/m. Heavy-duty springs like this absorb road shocks effectively.

Precision Scale Spring

A lab scale spring deflects 2 mm (0.002 m) under a 0.5 N weight. k = 0.5 / 0.002 = 250 N/m. Low k values suit sensitive measurement instruments.

Frequently Asked Questions

What units is spring constant measured in?▾
The SI unit is Newtons per meter (N/m), also written as kg/s². It tells you how many Newtons of force are needed to stretch or compress the spring by one meter.
Does spring constant change with temperature?▾
Yes, spring stiffness decreases slightly at higher temperatures as the material's elastic modulus changes. For precision applications, temperature-rated springs are used.
What is elastic potential energy?▾
Elastic potential energy stored in a spring is PE = ½kx². A spring with k = 500 N/m compressed by 0.1 m stores ½ × 500 × 0.01 = 2.5 joules.
How do springs in series and parallel differ?▾
Springs in series: 1/k_total = 1/k1 + 1/k2 (softer combined). Springs in parallel: k_total = k1 + k2 (stiffer combined). Parallel arrangements are used in heavy-load applications.
What is Hooke's Law limit?▾
Hooke's Law only applies within the elastic limit. Beyond this point the spring deforms permanently and the linear relationship between force and displacement no longer holds.