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Dimensions and calculation

Springs in series and parallel

The arrangement of multiple springs changes equivalent rate and the load carried by each element.

Three platen arrangements: one spring, two springs in series, and two in parallel.
Educational illustration generated for this guide.
Ideal springs in parallel and in series k₁k₂ k₁k₂ k = k₁ + k₂1/k = 1/k₁ + 1/k₂
Ideal linear models: equal travel in parallel; equal force in series.

Ideal case

For ideal linear springs with the same deflection in parallel, rates add: k total = k1 + k2. In series, each carries the same force and compliances add: 1/k total = 1/k1 + 1/k2.

Arrangement limits

Actual load sharing depends on supports, alignment, tolerances, preload, contact between parts, and changing rate. If a spring reaches solid height or loses contact, the equivalent model no longer describes the assembly.

Worked example

With k1=4 and k2=6 N/mm, parallel rate is 10 N/mm. In series, rate is 2.4 N/mm; at F=12 N, deflections are 3 and 2 mm, 5 mm total. Two parallel springs compressed 2 mm ideally carry 20 N.