Spring Force Calculator Formula

Understand the math behind the spring force calculator. Each variable explained with a worked example.

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Formulas Used

Spring Force

force = spring_k * displacement

Stored Elastic Energy

energy = 0.5 * spring_k * pow(displacement, 2) / 1000

Variables

VariableDescriptionDefault
spring_kSpring Constant (k)(N/mm)5
displacementDisplacement (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.

spring_k = 5displacement = 20
  1. 01F = 5 x 20 = 100 N
  2. 02U = 0.5 x 5 x 20^2 = 0.5 x 5 x 400 = 1000 N-mm = 1.0 J

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