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For the springs in this discussion, Hooke's Law is typically assumed to hold,
 We can expand the spring constant k as a function of the material properties of the spring. Doing so and solving for the spring displacement gives,
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where G is the material shear modulus, na is the number of active coils, and D and d are defined in the drawing. The number of active coils is equal to the total number of coils nt minus the number of end coils n* that do not help carry the load,
 The value for n* depends on the ends of the spring. See the following illustration for different n* values:
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Geometrical Factors
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The spring index, C, can be used to express the deflection,
 The useful range for C is about 4 to 12, with an optimum value of approximately 9. The wire diameter, d, should conform to a standard size if at all possible. The active wire length La can also be used to form an expression for the deflection,
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Shear Stress in the Spring
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The maximum shear stress tmax in a helical spring occurs on the inner face of the spring coils and is equal to,
 where W is the Wahl Correction Factor which accounts for shear stress resulting from spring curvature,
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