This is for steel springs such as fork or shock springs, other metal compositions have a different spring coefficients
The spring rate rises when shortening a spring due to the reduced number of coils. Where considering shortening a spring estimate the number of coils to remain in the spring and use that to estimate the new spring rate.
There is often discussion of front spring rates with confusion over the rates required with different fork types.
An example of the difference in spring rate between piston rod forks and cartridge forks is below.
The increased reliance on damping in cartridge forks can be seen in the graphs
A pdf with total weight and rider weight graphs in metric and imperial
Dont forget to tale into account any linkages and leverage when comparing springs between models.