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Coil Resistance Calculator: DC and RF (Skin Effect)

What it works out

The resistance of a coil's wire twice: at DC, corrected for temperature, and at radio frequency, where the current flows only in a thin layer under the surface of the wire. The difference can be tenfold: a metre of 1 mm copper wire at 7 MHz has ten times the resistance an ohmmeter shows on the bench.

d 1 mmR₌
d — wire diameter, δ — skin depth. Red marks the part of the cross-section that carries the current
Result

💡 What the numbers mean

R~ is worked out for a single straight wire. In a coil the neighbouring turns also push the current to one side (the proximity effect), so the real RF resistance of a close-wound coil is noticeably higher and the Q lower than shown.

Once δ is much smaller than the diameter, a thicker wire helps less than it does at DC: R~ falls in proportion to the diameter, not to its square. Spacing the turns reduces the proximity effect, and Litz wire only pays off up to a few megahertz.

📐 The formulas​

Wire length from the turns — along the axis of the wire, i.e. over the mean turn diameter:

l = N · π · (D + d)

DC resistance with temperature correction:

ρ(t) = ρ₂₀ · (1 + α · (t − 20))
R₌   = ρ(t) · l / S,      S = π·d²/4
Metalρ₂₀, Ω·mα, 1/°C
Copper (IACS standard)1.724·10⁻⁸0.00393
Aluminium2.65·10⁻⁸0.00403

Skin depth — the depth at which the current density falls by e ≈ 2.7:

δ = √( ρ / (π · f · μ₀) ),     μ₀ = 4π·10⁻⁷ H/m

For copper that is 66 µm at 1 MHz, 25 µm at 7 MHz and 12 µm at 30 MHz.

Resistance at frequency f. The current flows in a ring δ thick, so the cross-section is replaced by the area of that ring:

R~ = ρ · l / (π · δ · (d − δ)),    if δ < d/2
R~ = R₌,                           if δ ≥ d/2

Q — an upper bound, from the wire resistance alone:

Q = 2π · f · L / R~

Symbols:​

  • N — number of turns, D — former diameter [mm]
  • l — wire length [m], d — bare wire diameter [mm]
  • t — wire temperature [°C]
  • f — frequency [MHz], L — inductance [µH]
  • δ — skin depth [µm]
  • R₌, R~ — resistance at DC and at frequency f [Ω]

Sources: the resistivity of copper is the International Annealed Copper Standard (IACS); the skin-depth formula and the ring model follow F. E. Terman, Radio Engineers' Handbook (1943), section on the resistance of conductors at high frequencies.

Limits of the calculator:
  • The proximity effect is not included. R~ is for a single straight wire. In a coil the field of the neighbouring turns crowds the current further, and the real RF resistance of a close-wound coil can be several times higher (R. G. Medhurst, Wireless Engineer, 1947). The Q shown is therefore a limit the coil will not reach.
  • Losses in the former, insulation and screen are not included either.
  • Non-magnetic metals only. For steel the skin-depth formula without magnetic permeability gives the wrong δ, so steel is not in the list.
  • The ring model is accurate while δ is well below the wire radius; in the transition region (δ close to d/2) the error is up to a few per cent.
  • Wire length from the turns excludes the leads — add them if they are long.

🎯 Practical use​

  • Resistance of a relay, solenoid or supply choke winding at DC, remembering that hot copper at +75 °C has 22 % more resistance.
  • Heating of a choke in a feedline or power supply: I²·R.
  • HF tank and tuner coils: how much the resistance grows at the working frequency and what Q to expect at best.
  • Magnetic loops and antenna loading coils, where wire resistance eats straight into efficiency.
Practical tips:
  1. On HF a thicker wire helps less than it seems: once δ is much smaller than the diameter, R~ falls in proportion to the diameter, not the cross-section. Going from 1 mm to 2 mm cuts R₌ by four but R~ only by two.
  2. Spacing the turns reduces the proximity effect: a pitch of about two wire diameters noticeably raises the Q of an air-wound coil.
  3. Litz wire only pays off up to roughly a few megahertz; above that its strands become "thick" relative to δ themselves.
  4. To turn an AWG gauge into a diameter — AWG converter; for the inductance of the coil — single-layer coil.

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

How to cite this calculator
UR3PKI. «Coil Resistance Calculator: DC and RF (Skin Effect)». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/coil_resistance/ (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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