Extension Spring Calculator to find shear and tensile stresses on ordinary helical extension springs with full twisted end for static loading case. Calculations are done with the knowledge of extension spring wire diameter, spring diameter and maximum working load. Calculation results generated by the calculator are shear and tensile stress at extension spring end, shear stress at spring body, factor of safety values for the points where the stress values are calculated.

The points where maximum stresses occurred on extension spring twisted end are shown in the following figure. At point A, maximum tensile stress is occurred due to bending moment and axial force. At point B, maximum torsion stress is occurred. In addition to these points, high shear stresses are occured at the body of the extension spring.

Mechanical springs - Extension spring terminology Mechanical springs - Extension spring terminology
Location of Maximum Bending and Torsion Stresses in Twisted Loops
Mechanical springs - Extension spring terminology
Extension Spring Design with Twisted End

For the extension springs which works under static loading, first define the design parameters with the " Dimensional Design of Extension Spring " calculator. Then use this calculator to check spring against yielding.

Extension Spring Calculator for Static Loading:

Parameter Value
Wire diameter [d]
Radius-1 [R1]
Radius-2 [R2]
Maximum working load [Fmax]
Parameter Value
Material selectionx
Material tensile strength [Sut]
Allowable torsional strength of the spring body  (% of Sut)+ %
Allowable torsional strength of the spring end  (% of Sut)+ %
Allowable bending strength of the spring end  (% of Sut)+ %
Design factor for static loading [ns]o ---

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

Note 2 : +  See supplements for reference values.

Note 3 : o  The design factor value that used for all of the points of interest ( Tensile stress at point-A, shear stress at point-B and shear stress at spring body).

Parameter Value
Maximum working load [Fmax] ---
Shear stress at point B for maximum working load [τB] ---
Allowable torsional strength at point B [Sall_B] ---
Safety factor at point B [fosB] + --- ---
Tensile stress at point A for maximum working load [σA] ---
Allowable tensile strength at point A [SA] ---
Safety factor at point A [fosA] + --- ---
Shear stress at spring body for maximum working load [τsb] ---
Allowable torsional strength for spring body [Ssb] ---
Safety factor at spring body [fossb] + --- ---
Ultimate tensile strength of material [Sut] ---
Material ASTM No. ---

Note 1 : + Green color means, fos ≥ ns, red color means fos ≤ ns


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.

Design factor (nd):  The ratio of failure stress to allowable stress. The design factor is what the item is required to withstand .The design factor is defined for an application (generally provided in advance and often set by regulatory code or policy) and is not an actual calculation.

Factor of Safety (Safety Factor): The ratio of failure stress to actual/expected stress. The difference between the factor of safety (safety factor) and design factor is: The factor of safety gives the safety margin of designed part against failure. The design factor gives the requirement value for the design. Safety factor shall be greater than or equal to design factor.

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.

Static/Quasistatic Loading: Following loading cases are defined as Static/Quasistatic loading:

  • A constant loading
  • A cycling loading with torsional shear stress range up to 10 % of fatigue strength (or endurance strength)
  • A cycling loading with torsional shear stress range more than 10 % of fatigue strength (or endurance strength) up to 104 cycles

  • Supplements:

    Link Usage
    Spring Steels for Coil Springs List of spring steel materials given in the calculator.
    Formulas For Extension Spring Static Design List of formulas used in the calculator.
    Allowable Stresses for Extension Springs Supplemantary tables about the material strength properties of helical extension springs.


    • Courtesy of Associated Spring (1987)., Design Handbook
    • Budynas.R , Nisbett.K . (2014) . Shigley's Mechanical Engineering Design . 10th edition.  McGraw-Hill