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Series and Parallel Spring Forces Calculator

Spring Engineering and Design

Series and Parallel Spring Rate Formula and Calculator

When more than one spring is being used in a design, they are either in series, meaning one after another, or in parallel, meaning side by side, or a combination of both. These two arrangements are shown for three springs in Fig. 1, combined in series in (a) and combined in parallel in (b).

Series and parallel springs

Using the spring rate (k) of each spring, an equivalent spring rate (k_eq) can be determined depending on whether the springs are in series or parallel. For the three springs in series in Fig. 1 (a), the equivalent spring rate (keq) is given by Eq. 1 as

Eq 1

k_eq = 1 / [ 1 / ( 1 / k₁ + 1 / k₂ + 1 / k₃ ) ]

For the three springs in parallel in Fig. 1(b), the equivalent spring rate (k_eq) is given

Eq. 2
k_eq = k₁ + k₂ + k₃

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Source:

Mark's Calculations for Machine Design
Thomas H. Brown, Jr.
Faculty Associate
Institute for Transportation Research and Education
NC State University
Raleigh, North Carolina