Spring rate for a helical compression spring obeying Hooke's Law:

k= F/y = (d^4)(G)/8(D^3)Na

Where:

k is the spring rate
F is the applied force
y is the deflection
d is the wire diameter
D is the mean coil diameter
G is the shear modulus of the material, which should be about 11.7 million psi for steel
Na is the effective number of coils. Depending on the end treatments this will be between the actual number of coils and the number of coils minus two. I'm guessing you'll most likely be dealing with plain ground ends, so Na will be the actual number of coils minus one.

Source: My old machine design textbook, Machine Design, An Integrated Approach, Robert Norton.

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