Compression Spring Formulas: A Guide to Spring Design

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compression

COMPRESSION

extension

EXTENSION

torsion

TORSION

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Input results shown will be +/- 10% from middle value.
Hint: The closer your min and max inputs are, the more accurate your results will be!

Wire Diameter

Wire Diameter

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Outer Diameter

Outer Diameter

Inner Diameter

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Free Length

Free Length

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Total Coils

Total Coils

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Material Type

Material Type

spring-wire-diameter

End Types

Wind Direction

Wind Direction

Wire Diameter

Wire Diameter

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Min Max - IN
Outer Diameter

Outer Diameter

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Min Max - IN
Length Inside Hooks

Length Inside
Hooks

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Material Type

Material Type

Hook Types

Hook Types

Wire Diameter

Wire Diameter

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Min Max - IN

Outer Diameter

Outer Diameter

Inner Diameter

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Min Max - IN
Leg Length 1

Leg Length 1

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>
Min Max - IN
Leg Length 2

Leg Length 2

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Min Max - IN
Free Position

Free Position or Leg Position in degrees

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Min Max -  
Total Coils

Total Coils

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Material Type

Material Type

Wind Direction

Wind Direction

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Introduction

Compression spring formulas are fundamental algorithms that engineers use to compute various parameters for compression springs. These formulas, honed through extensive research by the Acxess Spring team, are the backbone of our reliable spring design tool, Spring Creator. With these formulas, you can effortlessly determine your compression spring's, spring constant (k), working loads, wire length, and even measurements such as the wire length needed for producing one to a thousand springs or the total weight of one to a thousand springs. Spring Creator is a comprehensive spring design tool that enables you to generate a live 3D blueprint of your compression spring design at the click of a button, which can be emailed to yourself or a colleague for technical use. Produce custom spring 3D CAD files in seconds, no more drawing by hand.

Calculating Solid Height For Compression Springs with closed and squared ends:

To calculate solid height for a compression spring with closed and squared ends: (Lsolid), add one (1) to your total coils (N) and then multiply the result by the wire diameter (d).

Example: You have 9 total coils then add 1. 9+1=10
Wire Diameter: 0.040

10 x 0.040=0.400 Solid Height for closed and squared ends (with no grind).

Calculating Solid Height For Compression Springs with closed and ground ends:

In cases where your spring has ground ends, you only need to multiply the wire diameter by the total coils to get your solid height. Spring Manufacturers only grind half a wire diameter off each spring end which means they grind off a total of (1) one wire diameter from the spring's free length

Example: You have 9 total coils.
Wire Diameter: 0.040

10 x 0.040=0.400 Solid Height for closed and squared ends (with grind).

Solid Height Diagram

a spring at free length next to a spring at solid height and text explaining how to calculate solid height along with the solid height formula

Calculating Spring Diameter:

Determining your compression spring's diameters is straightforward. To calculate for the inner diameter (D inner), multiply the wire diameter (d) by two and subtract the result from the outer diameter (D outer). To calculate the outer diameter, perform the opposite operation; multiply the wire diameter by two and then add the result to the inner diameter. To calculate for the mean diameter (D) is the average of these two values, calculated by either subtracting one wire diameter from the outer diameter or adding one wire diameter to the inner diameter gives you mean diameter.

Inner Diameter = Outer Diameter – 2 (Wire Diameter)
D inner = D outer – 2d

Outer Diameter = Inner Diameter + 2 (Wire Diameter)
D outer = D inner + 2d

Mean Diameter = Outer Diameter – Wire Diameter
D = D outer – d
OR
Mean Diameter = Inner Diameter + Wire Diameter
D = D inner + d


Spring Index Formula

The spring index of your compression spring influences the tightness of your springs diameter and the manufacturing complexity to see if your spring can be manufactured. To calculate the spring index, divide the mean diameter (D) by the wire diameter (d).

Index = Mean Diameter ÷ Wire Diameter
I = D ÷ d

Large and Small Index

Different sized coils, each with a different wire thickness; visually explaining the difference between a tight spring index and a loose one

Calculating Wire Length:

Determining the length of your compression spring's wire helps estimate the material needed for manufacturing the springs. Calculate the wire length of one coil (cL) by multiplying the mean diameter by π (approximately 3.14). To find the total compression spring wire length (tL), multiply the coil wire length (cL) by the total number of coils (N).

Coil Wire Length = Mean Diameter x Pi
cL =

Total Wire Length = Coil Wire Length x Total Coils
tL = cL x N

Wire Length Calculation Example

visual explanation of the coil spring wire length formula showing each dimension and symbol

Load and Travel Formulas:

The load and travel compression spring formulas provided here are essential for calculating your working loads. These formulas are invaluable for determining whether a spring meets your required load and travel distance. To calculate the distance traveled (T), divide the load (L) by the spring rate (k). To find the load (L), multiply the travel (T) by the spring rate (k).

Travel = Load ÷ Rate
T = L ÷ k

Load = Travel x Rate
L = Tk

Working Loads and Deflection Diagram

compression spring load formula example

Explore Spring Creator 5.0 and all these compression spring formulas will streamline your spring design and manufacturing process. Achieve greater precision and efficiency in your engineering endeavors. Discover the power of these formulas and the convenience of Spring Creator today.

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