The elasticity of the spring is obtained by design. You should design the spring first, or buy a standard spring. In short, you should know the stiffness of the spring, and then design how much compression the spring should have according to the compression required by your design. Then elasticity = stiffness × compression.

If you simply want to know how big the elasticity is, then you should know how much water pressure your dynamic and static rings bear under actual working conditions (generally calculated by the water depth of 5m). Your elastic force should be designed to be one level higher than the water pressure, otherwise your dynamic and static rings will not be able to complete the mechanical seal and will leak water.