Compression spring calculator to find
spring parameters with the knowledge of design type (dimensional or rate based), wire diameter,
spring diameter, free height, number of active/total coils, spring rate,
end type and material. Material selection can be done from listed spring steels including music wire, stainless steel wire, chrome vanadium, etc.
Calculation results generated by the calculator are spring rate, spring solid height, torsional shear stress at solid height,
factor of safety at solid height, buckling check, outer diameter expansion, loaddeflection curve, stress–deflection curve,
spring index.
This calculator can be used to design statically loaded compression springs. For compression springs
which work under a cyclic loading, first use this calculator for sizing
according to static loading and then
visit the "Critical Frequency of Coil Springs" and
"Stress analysis of Coil (Helical) Compression Spring for Fatigue Loading" calculators to check the compression spring
design against cyclic loading.
Note 1 : ^{x} Spring material properties are from Ref2 except "User defined"
selection.
Note 2 : ^{+} Equals maximum allowable torsional stress in static
applications. See "Supplements" for reference values.
Note 3 : * Ends supported by flat surfaces must be squared and ground [Ref2] .
RESULTS 
DIMENSIONAL PARAMETERS 
Parameter 
Value 
Number of active coils [N_{a}] 


 
Number of total coils [N_{t}] 


Spring index [C*] 


Spring rate [k] 



Spring wire diameter [d] 



Spring outer diameter [OD] 


Spring mean diameter [D] 


Spring inner diameter [ID] 


Outer diameter at solid length [OD_{at solid}***] 


Spring free length (height) [L_{f}] 


Spring solid height [L_{s}] 


Maximum deflection (L_{f} to L_{s}) [Δx] 


Pitch at free length [p**] 


SPRING MATERIAL & STRESS RELEATED PARAMETERS 
Parameter 
Value 
Load at solid height [F_{s}] 



Shear stress at solid height [τ_{s}] 



Ultimate tensile strength of material [S_{ut}] 


Allowable torsional strength [S_{all}] 


Factor of safety at solid height against shear stress [fos_{s}
(S_{all} / τ_{s })^{#}] 


 
Modulus of rigidity [G] 



Elastic modulus [E] 


Material ASTM No. 


SPRING STABILITY (BUCKLING) 
Parameter 
Value 
Stability condition (includes n_{b}) 


Factor of safety against buckling [fos_{b}^{+}] 


 
Note 1 : * The preferred index range is 4 to 12 according to [Ref1] .
Compression springs with high indexes tangle and may require individual
packaging, especially if the ends are not squared. Compression springs with
indexes lower than 4 are difficult to form [Ref1] .
Note 2 : ** According to no yielding assumption and L_{f} length shall be same after loading.
Note 3 : *** Does not include the effect if the spring ends are allowed to unwind.
Note 4 : ^{+} Shall be larger than the design factor for buckling (n_{b}
≤ fos_{b} )
Note 5 : ^{#} Shall be larger than the design factor at solid height (n_{s} ≤
fos_{s} )
Force vs Deflection
Shear Stress vs Deflection
Note 1 : The load deflection curve for helical compression springs is
essentially a straight line up to the elastic limit, provided that the amount of
active material is constant. The initial spring rate and the rate as the spring
approaches solid often deviate from the average calculated rate. When it is
necessary to specify the rate, it should be specified between two test heights
which lie within 15 to 85 % of the full deflection range. [From Ref1]