Single layer coils

L = NR2 / (6R + 9X)

where

L = Inductance in microHenries
N = Number of rotations in winding
R = Radius of wire form
X = Length of wire form

This formula is for air core coils only and is accurate within 10%.

Multiple layer coils

L = 0.8NR2 / (6R + 9X + 10D)

where the above variables are used and

D = Depth of windings in wire form

This formula is also for air core coils and is accurate within 30%.