Solenoid Inductance
Calculates the inductance of a single-layer solenoid (helical) coil from its number of turns, diameter, and length. Wheeler's current-sheet formula is used for the practical result — it corrects for the coil's finite length, unlike the idealised long-solenoid formula, which is also shown for comparison. Optionally enter a wire diameter (or pick an AWG gauge) to apply the round-wire (Rosa) correction, and tick close-wound to derive the coil length from the turns and wire gauge. Enter a relative permeability for a cored coil, and an optional frequency to get the reactance.
Equations & Parameters ▸
\(L_{\text{Wheeler}} = \mu_r\dfrac{D^2 N^2}{18D + 40\ell}\ \mu\text{H}\ \ (D,\ell\text{ in inches}) \qquad L_{\text{ideal}} = \dfrac{\mu_0\mu_r N^2 A}{\ell},\ \ A=\tfrac{\pi D^2}{4}\)
\(L_{\text{Rosa}} = L_{\text{Wheeler}} - \mu_0\mu_r N\,a\,(k_s + k_m),\quad k_s = \tfrac{5}{4}-\ln\!\dfrac{2p}{d},\quad k_m \approx \big(\ln 2\pi-\tfrac{3}{2}\big)-\dfrac{0.3308}{N},\quad p=\dfrac{\ell}{N}\)
\(L_{\text{Rosa}} = L_{\text{Wheeler}} - \mu_0\mu_r N\,a\,(k_s + k_m),\quad k_s = \tfrac{5}{4}-\ln\!\dfrac{2p}{d},\quad k_m \approx \big(\ln 2\pi-\tfrac{3}{2}\big)-\dfrac{0.3308}{N},\quad p=\dfrac{\ell}{N}\)
| N | Number of turns. |
| D | Coil diameter (mm), to the centre of the winding. |
| ℓ | Coil (winding) length (mm). In close-wound mode it is derived as ℓ = N·d. |
| d | Bare wire diameter (mm), optional. Sets the winding pitch p = ℓ/N and drives the round-wire (Rosa) correction. Pick an AWG gauge to fill it automatically. |
| µr | Relative permeability of the core (1 for air). |
| ks, km | Rosa's round-wire self- and mutual-inductance corrections. The current-sheet formula assumes an ideal conducting cylinder; real round wire gives slightly less inductance. ks depends on the pitch-to-wire-diameter ratio; km uses Knight's approximation to Rosa's data and depends only on N. |
| L | Inductance. Wheeler is most accurate for real single-layer coils; the round-wire (Rosa) value refines it using the wire gauge; the ideal formula overestimates when the coil is short. |
References: H. A. Wheeler, "Simple inductance formulas for radio coils," Proc. IRE, vol. 16, no. 10, 1928. · E. B. Rosa, "Calculation of the self-inductance of single-layer coils," Bull. Bureau of Standards, vol. 2, no. 2, 1906. · D. W. Knight, "Solenoid inductance calculation," 2016 (round-wire corrections).
Inputs
Number of turns
mm
To centre of windingmm
Winding lengthmm
For round-wire corr.Turns touching — set ℓ = N·d
Needs wire dia.1 = air core
MHz
For reactanceResults
Inductance
Wheeler (single-layer)—
+ round-wire (Rosa)—
Ideal (long-coil)—
At frequency
Reactance, XL—
Diagram