Calculation
1/Rtotal = 1/R₁ + 1/R₂
The same force acts through both springs; their deflections add.
Roloff/Matek Gl. (10.2)
Springs in Series Calculator
The same force acts through both springs; their deflections add.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Combined spring rate Rtotal — The spring rate of the whole chain when the springs are connected in series – as a result from 1/R₁+1/R₂(+1/R₃). It is always smaller (softer) than the softest individual spring.
- Spring rate R₁ — The spring rate of the first spring. Source: the spring's datasheet, or the slope of its force-deflection curve.
- Spring rate R₂ — The spring rate of the second spring, in series with the first (both carry the same force; their deflections add).
- Additional spring R₃ — An optional third spring in the same series chain; enter 0 if absent.
Example
10 N/mm and 20 N/mm give 6.67 N/mm.
Assumptions and limits
Linear characteristics, equal force in every spring and no stops.
Understand Springs in Series Calculator
Series spring combination is a focused preliminary calculation based on Roloff/Matek. The calculator rearranges the closed-form relationship for every included quantity and deliberately separates this result from a complete component verification.
What does this quantity describe?
In series, the same force passes through each linear spring while deflections add. The reciprocals of the rates therefore add.
Formula and variables
1/Rtotal = 1/R₁ + 1/R₂
1/Rges = 1/R1 + 1/R2 (+ 1/R3)
| Symbol / input | Meaning |
|---|---|
| Combined spring rate Rtotal | The spring rate of the whole chain when the springs are connected in series – as a result from 1/R₁+1/R₂(+1/R₃). It is always smaller (softer) than the softest individual spring. |
| Spring rate R₁ | The spring rate of the first spring. Source: the spring's datasheet, or the slope of its force-deflection curve. |
| Spring rate R₂ | The spring rate of the second spring, in series with the first (both carry the same force; their deflections add). |
| Additional spring R₃ | An optional third spring in the same series chain; enter 0 if absent. |
Choose the inputs correctly
R1 to R3 are positive individual rates; R3=0 omits the third spring. Rtotal is always below the smallest individual rate.
How to use the calculator
Select the target, enter all remaining quantities for the actual component, and verify the units. Then compare the result with the stated model limits and with the required strength, safety and operating checks.
Worked example
10 and 20 N/mm give 6.67 N/mm.
Understand the result and units
The softer spring dominates; a very stiff second spring changes Rtotal only slightly.
The calculator converts internally to coherent SI units. Length, force, torque, stress and angle may therefore use the offered units; dimensionless factors are entered as decimals.
What is taken from Roloff/Matek
Only the closed-form relationship from Kapitel 10.1.1, Gleichung (10.2) is used. Tabulated data, material limits and detailed design checks are not silently added; they remain explicit inputs or are expressly outside the model.
Typical applications
Series spring combination supports option comparison, plausibility checks and early sizing within its machine-element cluster. Releasing a design requires the additional checks described in the cited chapter.
Assumptions, limits and common mistakes
Valid for linear characteristics, equal force in all springs and operation without stops or preload transitions.
Common mistake: Typical errors are misreading the effective length or force, entering percentages instead of decimals, and treating a preliminary result as a complete verification. In particular: Valid for linear characteristics, equal force in all springs and operation without stops or preload transitions.
Frequently asked questions
Is Series spring combination a complete strength verification?
No. Valid for linear characteristics, equal force in all springs and operation without stops or preload transitions.
Where do the equation and validity limits come from?
Roloff/Matek, Machine Elements, Kapitel 10.1.1, Gleichung (10.2); the local 21st edition was cross-checked against the available 24th edition.
Can I order the calculated value directly as a nominal size?
Only after matching it to available standard or manufacturer series and completing the additional safety, material and operating checks.