Tension/ Extension spring design calculator 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. Results generated by the calculator are tension spring height,  number of body coils,  spring body length, spring rate, spring initial preload range, spring index.

Tension spring calculator is valid for ordinary extension springs with twisted end where hook/loop mean diameter is same with spring mean diameter ( R1=D/2). Shape of an ordinary extension coil spring is given in the figure.

Mechanical springs - Extension spring terminology

Extension Spring Design with Twisted End

Extension spring 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.

Extension Spring Calculator:

Known parameters in addition to wire diameter

Parameter Value
Wire diameter [d]
Free length inside hooks [Lo]
Initial Preload [Fi]
Spring Rate [k]
Number of body coils [Nb] ---
Parameter Value
Material selectionx
Elastic modulus [E]
Poisson's ratio [v] ---

Note 1 : x Extension spring material properties are from Ref-2 except "User defined" selection.

Parameter Value
Number of active coils [Na] --- ---
Number of body coils [Nb] ---
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 [Lo] ---
Spring body length [Lb] ---
Parameter Value
Preferred initial preload range [Fi] Min Max
--- ---
Modulus of rigidity [G] ---
Elastic modulus [E] ---
Material ASTM No. ---  


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.


Link Usage
Spring Steels for Coil Springs List of spring steel materials given in the calculator.

List of Equations:

Parameter Formula
Spring outer diameter [OD] OD=D+d
Spring inner diameter [ID] ID=D-d
Spring index [C] C=D/d
Spring rate [k] k=d4G/(8D3Na)
Number of active coils [Na*] Na=Nb+G/E
Extension spring free length [Lf*] Lf=(2C-1+Nb)d
Initial tension stress range [τi] $${ \tau }_{ i }=\frac { 33500 }{ exp(0.105C) } \pm 1000(4-\frac { C-3 }{ 6.5 } )$$

Note 1 :* Equation is valid for ordinary extension spring with twisted loop where hook/loop mean diameter is same with spring mean diameter ( r1=D/2)

List of Parameters
Symbol Definition
Na Number of active coils
Nb Number of body coils
d Wire diameter
Lf Spring free length