Spring Force Calculator Formula
Understand the math behind the spring force calculator. Each variable explained with a worked example.
Formulas Used
Spring Force
force = spring_k * displacementStored Elastic Energy
energy = 0.5 * spring_k * pow(displacement, 2) / 1000Variables
| Variable | Description | Default |
|---|---|---|
spring_k | Spring Constant (k)(N/mm) | 5 |
displacement | Displacement (x)(mm) | 20 |
How It Works
Hooke's Law for Springs
A spring produces a restoring force proportional to its displacement from equilibrium.
Formulas
F = k x (Hooke's law)
U = 0.5 k x^2 (elastic potential energy)
where k is the spring constant, x is the displacement, F is the resulting force, and U is the stored energy. This holds as long as the spring remains in its linear elastic range.
Worked Example
A spring with k = 5 N/mm compressed by 20 mm.
- 01F = 5 x 20 = 100 N
- 02U = 0.5 x 5 x 20^2 = 0.5 x 5 x 400 = 1000 N-mm = 1.0 J
Frequently Asked Questions
When does Hooke's law stop being valid?
Hooke's law is valid only in the linear elastic range. When a spring is compressed beyond its solid length or stretched past its elastic limit, the force-displacement relationship becomes nonlinear and the spring may take a permanent set.
What is the difference between compression and extension springs?
Compression springs resist pushing forces and get shorter. Extension springs resist pulling forces and get longer. Both follow F = kx in the elastic range, but extension springs have an initial tension that must be overcome before they start to extend.
How do I calculate spring energy in practical units?
Energy in joules = F x / 2 = k x^2 / 2, where force is in newtons and displacement in metres. If k is in N/mm and x in mm, divide the result by 1000 to get joules.
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