## Wheeler Formulas for Inductance

These formulas, developed by Wheeler at the (then) NBS, give approximate
inductances for various coil configurations. They are primarily based on empirical
measurements, and are accurate to a few percent.

#### Single layer air core solenoid

`L (uH) = r^2 * n^2 / (9 * r + 10 * l)`

where

`r = coil radius in inches`

l = coil length in inches

n = number of turns

#### Multi layer air core solenoid

`L {uH} = 31.6 * N^2 * r1^2 / (6*r1 + 9*L + 10*(r2-r1))`

L{uH} = Inductance in microHenries

N^2 = Total Number of turns on coil Squared

r1 = Radius of the inside of the coil {meters}

r2 = Radius of the outside of the coil {meters}

L = Length of the coil {meters}

Note the similarity to the formula for the single layer

air core coil. Hope this helps everyone.

`L (uH) = 0.8 * a^2 * n^2 / (6*a + 9*b + 10*c )`

where

`a = average radius of windings`

b = length of the coil

c = difference between the outer and inner radii of the coil.

all dimensions in inches.

It states that it is accurate to 1% when the terms in the denominator are

about equal. This is also an equation by Wheeler. It applies as long as the

coil has a rectangular cross section.

#### Flat "pancake" coil

`L (uH) = r^2 * n^2 / (8 * r + 11 * w)`

where

`r = radius to center of windings in inches`

w = width of windings (in inches)

n = number of turns

### References

The original Wheeler papers:

- Harold A. Wheeler, "Formulas for the Skin Effect,"
*Proceedings of the
I.R.E.*, September 1942, pp. 412-424
- Harold A. Wheeler, "Simple Inductance Formulas for Radio Coils,"
*Proceedings
of the I.R.E.*, October 1928, pp. 1398-1400.

An enormous compendium of inductance references compiled by Dr. Marc Thompson.

Copyright 2001, Jim Lux / wheeler.htm / 10 Jan 2001 / Back
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