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Springs in Series and Parallel Calculator

Find the equivalent spring constant of up to three springs wired in series or in parallel.

Equivalent spring constant
500 N/m
Springs used (nonzero values)
2

How it works

Springs wired in parallel all stretch or compress by the same amount, so each one adds its own restoring force to the total — their stiffnesses simply add: k_total = k1 + k2 + k3. Springs wired in series instead share the same force but divide up the total displacement between them, so it's their compliances (1/k) that add: 1/k_total = 1/k1 + 1/k2 + 1/k3 — the exact opposite rule from resistors, since force here plays the role voltage plays in a circuit.

Leaving Spring 3 at 0 treats it as not present — in parallel that adds nothing to the sum automatically, and in series it's explicitly skipped rather than treated as a literal zero-stiffness spring, so the same three-field form works for either a two- or three-spring combination.

FAQ

Why is the series combination weaker than any single spring, when parallel is the opposite?

In series, every spring stretches under the full applied force, so the combination always ends up softer (lower k) than its weakest member — the same reason a long bungee cord stretches more than a short one. In parallel, each spring only has to carry a share of the total load for the same displacement, so stacking more springs side by side always makes the combination stiffer, never softer.

How is this different from the resistors in series/parallel calculator?

The math is structurally the same three-field combination, but the combination rules are swapped: resistors add directly in series and by reciprocals in parallel, while springs add directly in parallel and by reciprocals in series — because current splits across parallel resistor branches the same way displacement splits across series springs.

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