Rectangular Loop Inductance Calculator

Width (W)

Enter width of the loop (outer dimensions)

Height (H)

Enter height of the loop (outer dimensions)

Conductor diameter (d)

Wire / conductor diameter (use same scale as W/H)

Relative permeability (μr)

Use μr ≈ 1 for air

Result

Inductance (L_rec):

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Formula (rectangular loop)

\( L_{rec} \;=\; \frac{\mu_0 \mu_r}{\pi} \Big[ -2(W+H) \;+\; 2\sqrt{H^2+W^2} \;-\; H\ln\!\left(\frac{H+\sqrt{H^2+W^2}}{W}\right) \;-\; W\ln\!\left(\frac{W+\sqrt{H^2+W^2}}{H}\right) \;+\; H\ln\!\left(\frac{4H}{d}\right) \;+\; W\ln\!\left(\frac{4W}{d}\right) \Big] \)

Where: \(W,H,d\) in meters, \( \mu_0 = 4\pi\times10^{-7}\, \mathrm{H/m}\), and \(\mu_r\) is relative permeability.

Rectangular Loop Inductance Calculator

Result

Formula (rectangular loop)

Quick Information

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