The Standard Resonance Equation: MHz = 1000/(SQRT(L*C)*6.2832)
Therefore: pF or uH = 1,000,000/(39.4786 *(MHz)^2 *uH or pF)

Standard impedance equations using MHz, uH, and pF

XL = MHz * uH * 6.2832 and -XC = 1,000,000/(pF * MHz * 6.2832)

Standard (ideal) Inductance Equation: uH = N^2 * d^2/(18*d + 40*length)

Where: N = Number of turns (loops) of wire, d = form diameter PLUS wire diameter,
and length is the length of the coil

Diameters and lengths are in inches

Inductance in the Metric System and Loops

The constants change, and the radius if the coil (loop) is used.
This actually simplifies the equation to r^2 N^2 / 24* (r + l).
Here, the measurements are in centimeters, and DO NOT include the wire diameter
in the coil diameter determination.

LOOPS are coils with a length much shorter than the diameter.
A good rule of thumb is the diameter is greater than 6x the length.
The metric system handles this easily as above by reducing the 24* (r + l)
in the denominator to 23* (r + l). This adjustment works well with coil diameters
in excess of 7" (17.5 cm).

Ideal inductance of a ferrite rod core inductor

uH= Ue*K*N^2*r^2 / (25.33*lr)

Where ALL measurements are in centimeters (cm).

NOTE that this answer is for low (audio) frequencies, application to the AM-BCB or HF-SW bands will increase the apparent inductance due to capacitive effects of the coil and the antenna-ground system among several factors. It is prudent to 'design low'.

Ue is the stated Effective Permeability of the rod, generally based upon the length to diameter ratio. NOTE that this may vary between manufacturers, as there are differences in production methods, materials, and recipe that allow similar general properties, yet have unique Ue. Variance noted for a ferrite rod with a 6 to 1 length to diameter ratio can be Ue = 20 to 25. CHART on next page.

K is the correction factor when lc is less than lr. K ~= n^(1/n^0.43) WHERE n = lr/lc

This formula is accurate when n is between 2 and 4. CHART on next page illustrates 1/n: corresponding values are 0.25 to 0.50. Error occurs at each endpoint but is +/- 1%. The optimum mix of K (maximizing inductance) and the figure of merit Q apparently occurs at n = 3. At n = 3 K = 1.984

N Capital N is the Number of turns or loops of wire around the ferrite rod.

lr is the length of the rod, and lc is the length of the coil winding.

r is the radius of the ferrite rod

25.33 is a consolidation of constants Uo = 4pi*10E-7 nH/cm, 10000 (Maxwells/Gauss), and pi (from the cross-sectional area formula A=r^2*pi). The result is 0.0394784 which is then inverted (1/x) and placed in the denominator as 25.33 ~= 1/0.0394784

The expanded formula can be entered into a scientific calculator as:

r^2 * N^2 * Ue * (n^(1/n^0.43)) / (25.33 * lr)

Many thanks go out to Ben Tongue and Dan McGillis for illuminating this rather tricky subject. The one or two tweaks and/or simple errors fixed make this a good starting point for construction. I'd been racking my brain over differing results using same construction.

Formula for Skin Effect Depth

This fomula closely approximates the depth of penetration a signal at radio frequency "f" has in a solid copper wire loop (coil). Note that a smaller diameter wire is favored, in spite of having a higher electrical (DC) resistance.

The figure of 1.68 E-8 is the resistivity for copper. The Reletive Permeability (Ur) is also a factor, but for air-coils using copper wire this value is considered to be unity (1.00). In this formula Ur has been set to 1, and ignored. The factor of 503292 is an approximation of 1/(SQRT[pi * 4 * pi * 10E-7]). You may recognize 4pi*10E-7 as being Uo, the permeability of free space used in the ferrite inductor formula above. The value of "f" is in Hz. The final answer is in millimeters (mm).

503292 * SQRT(1.68E-8 / f*Ur) = mm depth