Spring Combination Calculator (Series and Parallel)
Combined stiffness of two or three springs in parallel and in series, and the deflection each arrangement gives under a load.
Results
Combined stiffness in parallel
30.000
N/mm
Combined stiffness in series
6.667
N/mm
Deflection under the load, in parallel
3.333
mm
Deflection under the load, in series
15.000
mm
What this tool does
Springs sharing a load side by side (parallel) add their stiffnesses — the combination is stiffer than any one. Springs end to end (series) add their compliances, 1/k: the combination is softer than the softest spring, and the softest one does most of the stretching. It is the reverse of resistors, and the same as capacitors. The result assumes ideal linear springs on a common line with negligible mass and no binding; for parallel springs the load shares out in proportion to stiffness.
Formula
parallel: k = k₁ + k₂ + k₃ · series: 1/k = 1/k₁ + 1/k₂ + 1/k₃ · deflection = F ÷ k
Variables
| Symbol | Meaning | Unit |
|---|---|---|
k1 | Stiffness of spring 1 | N/mm |
k2 | Stiffness of spring 2 | N/mm |
k3 | Stiffness of spring 3 (0 for none) | N/mm |
f | Force | N |
KP | Combined stiffness in parallel | N/mm |
KS | Combined stiffness in series | N/mm |
XP | Deflection under the load, in parallel | mm |
XS | Deflection under the load, in series | mm |
Worked example
- Stiffness of spring 110 N/mm
- Stiffness of spring 220 N/mm
- Stiffness of spring 3 (0 for none)0 N/mm
- Force100 N
- Combined stiffness in parallel30.000 N/mm
- Combined stiffness in series6.667 N/mm
- Deflection under the load, in parallel3.333 mm
- Deflection under the load, in series15.000 mm
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.