Coil Spring Calculations and Definition


Wire wound spirally in order to form coils one on top of the other to make up a coil spring.

Coil springs can be either compression, torsion, extension, or conical springs because all of these springs are made up of helically wound coils of wire. There are many calculations these coil springs have in common when it comes to their physical dimensions but when it comes to spring rate, it can get a little tricky. Especially since conical tapered springs don’t eject a constant force.

Calculations and Formulas

The coil spring calculations that are similar for all springs are the ones shown below. For conical springs, you may do these calculations as well but keep in mind that you might have to do some calculations twice because one of the ends is bigger than the other, therefore the diameters change.

Inner Diameter:

Outer Diameter - 2(Wire Diameter) = Inner Diameter
OD - 2WD = ID

outer diameter minus two wire diameters equals inner diameter

Outer Diameter:

Inner Diameter + 2(Wire Diameter) = Outer Diameter
ID + 2WD = OD

inner diameter plus two wire diameters equals outer diameter

Wire Diameter:

Outer Diameter - Inner Diameter = Wire Diameter
OD - ID = WD

outer diameter minus inner diameter equals two wire diameters

Mean Diameter:

Inner Diameter + Wire Diameter = Mean Diameter
ID + WD = MD
Outer Diameter - Wire Diameter = Mean Diameter
OD - WD = MD

inner diameter plus wire diameter equals mean diameter and outer diameter minus wire diameter equals mean diameter

Spring Index:

Mean Diameter ÷ Wire Diameter = Index
MD ÷ WD = I

mean diameter divided by wire diameter equals spring index

Total Coils:

Body Length ÷ Wire Diameter - 1 = TC
BL ÷ WD - 1 = TC

solid height divided by wire diameter minus one equals total coils


Rate * Distance Traveled = Load
R(DT) = L

distance traveled divided spring rate equals load

Distance Traveled:

Load ÷ Rate = Distance Traveled
L ÷ R = DT

load divided by spring rate equals distance traveled


Load ÷ Distance Traveled = Rate
L ÷ DT = R

load divided by distance traveled equals spring rate