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,

where G is the material shear modulus, n_{a} 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 n_{t} 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:

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 L_{a} can also be used to form an expression for the deflection,

The maximum shear stress t_{max} 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,
