Compression Spring Calculations

Definition of Compression Spring Calculation:

The process of computing shear modulus of a spring wire, youngs modulus of spring wire, poission's ratio for spring wire along with a springs wire diameter, outer diameter and number of active coils to obtain a compression spring calculation.

Here is an easier and faster way to calculate your compression spring calculations by using our free online spring calculator; which provides you with a full spring analysis of your spring. Just enter a few of your compression spring's dimensions, and you'll have all the information you need to make sure your spring will function correctly in your application.

Basic Compression Spring Calculation Formulas:

Sometimes, you might only have a couple of your compression spring's dimensions but in order to calculate other things such as rate and travel, you'll need to know a bit more. Here you will see a couple examples of different scenarios where a certain spring dimension is needed.

To Calculate Wire Diameter:

If you only have your Outer Diameter (OD) and Inner Diameter (ID) but need Wire Diameter (WD), you must subtract your Inner Diameter (ID) from your Outer DIameter (OD) and then divide the result by two as shown in the formula below:

a coil with lines and arrows signaling where the wire diameter is

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

To Calculate Outer Diameter from Inner Diameter:

Multiply your Wire Diameter by two and then add it to your Inner Diameter; as shown in the formula below.

Compression Spring Outer Diameter

2 * Wire Diameter + Inner Diameter = Outer Diameter
2WD + ID = OD

To Calculate Inner Diameter from Outer Diameter:

Multiply your wire diameter by two and then subtract the result from your Outer Diameter; as shown in the following formula.

a coil with lines and arrows signaling where the inner diameter is

Outer Diameter - 2 * Wire Diameter = Inner Diameter
OD - 2WD = ID

To Calculate Mean Diameter:

This specific dimension is calculated by taking one wire diameter and subtracting it from your compression spring's outer diameter or adding it to the inner diameter as shown below.

Mean Diameter

Outer Diameter - Wire Diameter = Mean Diameter
OD - WD = MD

Inner Diameter + Wire Diameter = Mean Diameter
ID + WD = MD

To Calculate Your Spring's Index:

This spring calculation is needed to make sure that the spring you require is manufacturable. You must divide your mean diameter by your wire diameter to do so as displayed in the following spring index formula.

Spring Index

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

Advanced Compression Spring Calculations

The next step to designing your spring is making sure that the dimensions you already have, give you a spring rate that will work with the loads you plan to apply to your compression spring as well as travel. Here we will show you how to get to these compression spring calculations.

To Calculate Compression Spring Constant K / Rate:

Calculating your compression spring's rate is no easy task since you have to keep many things in mind. We have provided the formula below in order to obtain a compression spring calculation.

k = Gd^4 / [8^3D na]
G = E / 2(1 + V)
d = D outer - d

If Spring constant is 1 LBF/inch
it takes 1 lb of force to travel
1 LBF/INCH=1LB of force per 1 inch of travel distance

Meaning of Variables in Above Formulas
G = Shear modulus of material
d = Spring wire diameter
D = Outer diameter of spring
na = number of active coils
E = Young's modulus of material
V = Poisson's ratio of material

How to Calculate Your Compression Spring's Load:

Multiply your spring's Rate (R) by the distance you expect your spring to travel (DT) as shown below.

Rate * Distance Traveled = Load
R * DT = L

How to Calculate Your Compression Spring's Distance Traveled:

Divide the Load (L) you will be applying to your spring by your spring's Rate (R) as shown in the following formula:

Load ÷ Rate = Distance Traveled
L ÷ R = DT

How to Calculate Your Compressions Spring's Rate From Load and Travel:

In case that you aren't able to calculate your spring's rate with the formula previously provided but you know how much load you plan to apply on your spring in order for it to travel a certain distance, you must divide the load by the distance your spring will travel as displayed on the formula below.

Load ÷ Distance Traveled = Rate
L ÷ DT = R