How this calculator works
An ideal spring develops a restoring force proportional to its extension or compression. The minus sign is directional: a stretched spring pulls inward and a compressed spring pushes outward. Stored elastic energy is positive for either direction. The relaxed-length option calculates signed extension before applying the same relation. Beyond the elastic linear range, a constant stiffness is no longer a good model.
Formula
Fspring = -kx; x = Lfinal-Lrelaxed; k = -Fspring/x; U = kx²/2.
Worked example
A 100 N/m spring extended 0.1 m exerts -10 N and stores 0.5 J. Shortening a 200 N/m spring from 0.5 to 0.4 m gives a +20 N restoring force.
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Frequently asked questions
Why is the force negative?
For positive extension, the spring pulls back in the negative direction. The external holding force has the opposite sign.
Does stiffness have units of newtons?
Stiffness is newtons per metre. It describes force change per metre of displacement.
Can I model a permanently deformed spring?
No. Hooke's law assumes reversible elastic behaviour in a linear range.