Encyclopedia Magnetica™

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This section is an interactive calculator	Stan Zurek, Calculator of Helmholtz coil inductance - simplified, Encyclopedia Magnetica, https://www.e-magnetica.pl/doku.php/calculator/helmholtz_coil_inductance_simple, {accessed: 2025-03-13}
	See more: Calculators of inductance.

An approximate value of the inductance of a Helmholtz coil can be estimated with this following equation.

Approximate inductance of Helmholtz coil (two halves connected in series)
$L \approx 2 · π· \left( \frac{4}{5} \right)^{3/2} · μ_0 · r · N_{half}^2$	(H)
where: $N_{half}$ - number of turns in each half-coil (unitless), $r$ - radius of the coils (m) measured to the centre of the bunch of wires, $μ_0$ - permeability of vacuum (H/m)
source: Yuan Jiang, Qing Li, Vacuum Circuit Breaker for Aviation Variable Frequency Power System, Theory and Application of Arc in Electrical Apparatus, Springer Nature, 2021, ISBN 9789813347816

Note: The equation ignores the size/diameter of the wire bunches in each coil and therefore gives only an approximate value.