EXTENSION SPRING DIMENSIONAL DESIGN CALCULATOR
Tension/ Extension spring design calculator has been developed to calculate
dimensional parameters of ordinary coil extension springs with the knowledge of different parameter sets such as extension spring
rate & spring free length, extension spring diameter & free length, extension spring preload & spring rate, extension spring
diameter & spring rate. Calculation results generated by the calculator are
tension spring height, number of body coils, spring body length, spring
rate, spring initial preload range, spring index.
This calculator is valid for ordinary extension springs with twisted end where hook/loop mean
diameter is same with spring mean diameter ( R_{1}=D/2). Shape of an ordinary
extension coil spring is given in the figure.

Extension Spring Design with Twisted End 
This calculator can be used for dimensional sizing of the
tension springs. For the stress
calculations of the extension springs, visit "Extension Spring Design for Static
Loading" and "Extension Spring Design for Fatigue Loading" calculators.
The formulas and parameters used in the calculator are given in "List of Equations " section of this page.
Note: This calculator was
developed by mainly using Shigley's Mechanical Engineering Design book. For
further information on subject , this reference source can be used.
Calculator:
Note 1 : ^{x} Extension spring material properties are from Ref2 except "User
defined" selection.
RESULTS 
DIMENSIONAL PARAMETERS 
Parameter 
Symbol 
Value 
Unit 
Number of active coils 
N_{a} 


 
Number of body coils 
N_{b} 


Spring index 
C 


Spring rate 
k 



Wire diameter 
d 



Spring outer diameter 
OD 


Spring mean diameter 
D 


Spring inner diameter 
ID 


Free length inside hooks 
L_{o} 


Spring body length 
L_{b} 


SPRING MATERIAL & STRESS RELEATED PARAMETERS 
Parameter 
Symbol 
Value 
Unit 
Preferred initial preload range 
F_{i} 
Min 
Max 





Modulus of rigidity 
G 



Elastic modulus 
E 


Material ASTM No. 



Definitions:
Extension spring: Extension /
tension springs
are coil springs which work under tensile loading. In order to carry and transfer tensile loads, extension springs require special ends in the form of hooks or loops. These special ends are generally produced by using the last coil of the spring or a separate component like screwed inserts. Generally, extension springs are connected to other component via these ends. If there is a motion to extend extension spring, it exerts force to component to move it back.
Extension springs are usually
coiled with an initial tension which keeps the extension spring coils closed. Due to initial tension incorporated into spring, spring can’t be extended theoretically until a force that is greater than initial tension. In practice, extension springs extends slightly with smaller forces than initial tension due to deflection of end loops.
Tension springs are generally used to return back the component to its default position by providing return force.
Spring rate: A parameter which shows relation between applied force and deflection. In other words, reaction force per unit deflection or spring resistance to length change.
Spring index: The ratio of spring
mean diameter to coil diameter.
Supplements:
List of Equations:
Parameter 
Symbol 
Formula 
Spring outer diameter 
OD 

Spring inner diameter 
ID 

Spring index 
C 

Spring rate 
k 

Number of active coils 
N_{a}^{*} 

Extension spring free length 
L_{f}^{*} 

Initial tension stress range 
τ_{i} 

Note 1 :^{*} Equation is valid for ordinary extension spring with
twisted loop where hook/loop mean diameter is same with spring mean diameter ( r_{1}=D/2)
List of Parameters 
Symbol 
Definition 
N_{a} 
Number of active coils 
N_{b} 
Number of body coils 
d 
Wire diameter 
L_{f} 
Spring free length 
Reference: