...under perpetual construction.

Most of the formulas for the inductance of a coil are valid for the *current sheet* approximation, where the current flows in an indefinitely thin surface around the coil diameter. This is the same as assuming the coil wound with an indefinitely thin tape with negligible separation between turns. If the separation between turns is not small, a correction factor should be applied. Moreover, at high frequencies the current crowds towards the inside of the coil so the effective radius where the current flows become smaller. Sometimes it is suggested to use the internal radius of the coil instead of the wire mean radius in the calculations, in order to compensate for this effect. However the difference between the low- and high-frequency inductances is usually not large `[1]`.

To compute accurately the inductance of any kind of coil (or also of more complicated conducting structures) one has to use an electromagnetic simulator.

Regarding current sheet inductance formulas for single-layer coils, one of the most widely known is the one by Wheeler `[2]`, which states (after converting to metric units):

L = (dwhere^{2}n^{2}) / (l + 0.45d) [μH]

The above formula is accurate within 1 % for

Some useful formulas, applicable for any diameter to length ratio, are presented in

The

References:

[1] |
F.E. Terman, "Radio Engineers' Handbook," London, McGraw-Hill, 1st ed., Sep. 1950. |

[2] |
H.A. Wheeler, "Simple Inductance Formulas for Radio Coils," Proc. I.R.E., vol. 16, pp. 1398-1400, Oct. 1928. |

[3] |
H. Nagaoka, "The Inductance Coefficients of Solenoids," J. Coll. Sci., vol. 27, pp. 18-33, 1909. |

[4] |
H.A. Wheeler, "Inductance Formulas for Circular and Square Coils," Proc. IEEE, vol. 70, no. 12, pp. 1449-1450, Dec. 1982. |

[5] |
R. Lundin, "A Handbook Formula for the Inductance of a Single-Layer Circular Coil," Proc. IEEE, vol. 73, no. 9, pp. 1428-1429, Sep. 1985. |

[6] |
F. Langford-Smith (ed.), "The Radiotron Designer's Handbook," 4th edition, Australia, Wireless Press, 1952. |