The "unit of springiness" is known as the Spring rate. This is expressed as the force required to compress, or extend, the spring by a set unit of length, such a Pound per Inch, in old money., as as above.
Spring design is quite an art, and can be very frustrating. You design a spring to give the desired rate, and to fit into the space available, but then when you check the stress, it is excessive. So back to the drawing board! When you get the stress within limits, the wire size is likely to be such that the spring is coil bound before reaching the required travel!
You recalculate and everything is now fine, except for the spring rate! And so it goes on, until eventually, if you are lucky, all falls within limits. If not, think about changing the coil diameter or the space into which the spring needs to fit?
Howard