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Rectangular loop inductance calculator

When you need this

A loop antenna, a coupling turn, the loop of a magnetic antenna — anything that is one rectangular turn of wire.

Rectangular loop: width a, height b, wire diameter dw
a — loop width, b — loop height, dw — wire diameter
Loop width a (m)
Loop height b (m)
Wire diameter dw (mm)
Permeability of the wire material μ
Result
Inductance L
The same in nanohenries

📐 Formulas​

A rectangle of four straight segments: the self-inductance of every side plus the mutual inductance of the opposite pairs with a minus sign. Collected together:

diag = √(a² + b²)
r₀   = dw / 2

L [µH] = 0.4·μ · [ −2(a + b) + 2·diag
                     − b·ln((b + diag)/a) − a·ln((a + diag)/b)
                     + b·ln(2b/r₀) + a·ln(2a/r₀) ]

All lengths are in metres. The factor 0.4 is μ₀/π · 10⁶, i.e. the conversion to microhenries.

Notation:​

  • a — loop width [m]
  • b — loop height [m]
  • dw — wire diameter [mm]
  • μ — relative permeability of the wire material
  • L — inductance [µH]
Limits of the calculator:
  • This is a lumped-element model: the perimeter of the loop must be much smaller than the wavelength, in practice below λ/10
  • A longer loop already behaves as a transmission line, not as an inductance
  • The wire is round and solid; the skin effect is not taken into account
  • The wire must not be too thick relative to the sides of the loop

🎯 Where it is used​

  • Receiving loop antennas for long and medium waves.
  • Coupling turns in tuned circuits and filters.
  • Estimating the stray inductance of a ground loop or a supply loop on the board.
Practical notes:
  1. For reference: copper has μ = 0.999994, aluminium 1.000022, steel around 100. For non-magnetic materials leave it at one.
  2. A square loop of 1 × 1 m in 1 mm wire gives 5.46 µH. That is a handy benchmark for checking you have not slipped an order of magnitude.
  3. Thicker wire lowers the inductance — and raises the Q of the loop at the same time. For a receiving antenna that is a double win.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Rectangular loop inductance calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/rect_loop (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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