Wire Resistance Calculator (DC and AC)
DC resistance is the easy part. This calculator also gives the AC resistance of an isolated round wire from the exact Kelvin-function solution, so you can see where skin effect starts to matter for your conductor size and frequency.
Choosing something to solve for makes DC resistance an editable target and computes the chosen input from it.
Formula
| A | cross-sectional area (m^2) |
| rho20 | resistivity at 20 degC (ohm m) |
| alpha | linear temperature coefficient of resistivity (1/K) |
| L | conductor length (m) |
| delta | skin depth (m) |
| ber, bei | Kelvin functions of order zero |
What this model assumes, and where it stops
Assumptions
- Round, solid, homogeneous conductor of constant cross-section.
- A single isolated straight conductor with no return path nearby.
- Sinusoidal current at one frequency; the current given is RMS.
- Resistivity varies linearly with temperature over the range of interest.
- The conductor is isothermal at the temperature entered - no self-heating loop is solved.
Limitations
- Proximity effect is not included. Put a return conductor or an adjacent turn nearby and the real AC resistance rises above this figure, often by a large factor.
- The Kelvin solution assumes a straight conductor. Bending it into a coil changes the internal current distribution.
- Above xi = 20 the code switches to the asymptotic form, which agrees with the exact series to about 0.01% - far inside the model uncertainty, but it is a seam.
- The linear tempco is a fit near 20 degC. For copper above roughly 200 degC, or for alloys, use a measured curve.
- Stranded and litz constructions are not modelled: strand transposition, bundle-level proximity effect and the fill factor all matter, and none appear here.
When you need a 3D field solution instead
Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:
- Any winding where conductors sit within a few diameters of each other, which is essentially every transformer and inductor.
- Litz wire, where the point is to control proximity effect that this model does not represent.
- Busbars and rectangular conductors, where corner current crowding sets the hot spot.
- Conductors passing near a gapped core, where fringing flux drives large local eddy currents.
- Cases where you need the temperature and the resistance solved together, because each depends on the other.
Common questions
How much does AC resistance rise above DC resistance?
It depends entirely on the conductor diameter measured in skin depths. Below about d/delta = 1 the rise is negligible. At d/delta = 4 an isolated round wire is around 1.6 times its DC resistance, and the ratio grows roughly linearly with diameter after that. This page solves the exact Kelvin-function result rather than an approximation.
Why does my winding measure a higher AC resistance than this calculator predicts?
Almost certainly proximity effect. This model is for a single isolated straight conductor. Put conductors next to each other, as in any real winding, and the field from the neighbours drives additional circulating currents that this figure does not include - often the larger of the two effects.
How does temperature change wire resistance?
Copper resistivity rises about 0.393% per kelvin near 20 degC. A winding running at 100 degC therefore has roughly 31% more DC resistance than at 20 degC, which is why bench measurements on a cold part flatter the design.
References
- Kelvin function solution - Ramo, Whinnery & Van Duzer, Fields and Waves, section 4.16
- AWG definition - ASTM B258, geometric progression d = 0.127 mm x 92^((36-n)/39)