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A winding's wire must be thick enough to carry its RMS current without overheating, and thin enough to fit the available window. The design target is a current density J (amps per mm² of copper) that keeps resistive heating manageable: A = Irms/J. From that cross-sectional area you can look up the nearest standard AWG (or SWG/metric) wire size. Once the wire is chosen, its resistance and the resulting copper loss can be estimated from the total wire length (turns × mean length per turn).
| Quantity | Formula |
|---|---|
| Required copper area | A = Irms / J |
| Wire diameter (round) | d = √(4A/π) |
| Total wire length | L = N × MLT |
| Winding resistance | R = ρ × L / A |
| Copper loss | Pcu = Irms² × R |
Copper resistivity ρ is about 1.72×10⁻⁸ Ω·m at 20 °C and rises roughly 0.4%/°C, which this calculator accounts for. Typical current densities range from about 2–3 A/mm² for large, natural-convection transformers to 5–8 A/mm² for small, well-cooled high-frequency windings.
Winding wire is normally sized from current density, in amperes per square millimetre of conductor cross-section. Typical practice is 3–5 A/mm2 for transformers with natural convection cooling, so a 10 A winding needs roughly 2–3.3 mm2 of copper — about AWG 13 to AWG 12.
Lower density means cooler running and better efficiency but a larger, heavier, more expensive transformer. Higher density is acceptable where cooling is forced or the duty is intermittent. There is no universal right answer; the figure is a thermal decision, not an electrical one.
At high frequency, current crowds into the outer surface of a conductor and the centre carries almost nothing. The depth at which current density has fallen to 1/e is the skin depth, and for copper it is:
| Frequency | Skin depth | Max useful diameter |
|---|---|---|
| 50 Hz | 9.23 mm | ~18.4 mm |
| 20 kHz | 0.46 mm | ~0.92 mm |
| 100 kHz | 0.21 mm | ~0.41 mm |
| 500 kHz | 0.09 mm | ~0.18 mm |
At 50 Hz skin effect is irrelevant for any practical winding wire. At 100 kHz it dominates: a conductor thicker than about 0.4 mm gains almost no extra usable copper, because the added metal sits in the dead centre where no current flows. Using heavier wire in the hope of lowering resistance simply adds cost and winding volume.
The standard solution is to divide the conductor into many strands each thinner than a skin depth. Litz wire goes further by transposing the strands so each one spends equal time at the outside and the inside of the bundle, which also addresses the proximity effect — the related crowding caused by the magnetic fields of neighbouring turns. Above roughly 50 kHz, proximity effect in a multi-layer winding is often a larger loss term than skin effect alone.
Divide the RMS winding current by your target current density: A = Irms/J. This gives the required copper cross-sectional area, which you then match to the nearest standard AWG, SWG or metric wire gauge.
Typical values are 2–3 A/mm² for large, naturally-cooled transformers, and 4–8 A/mm² for small, well-ventilated or forced-air-cooled windings. Higher density means thinner wire but more heating.
For round wire, d = √(4A/π). A 0.5 mm² area corresponds to about 0.80 mm bare copper diameter, before adding enamel insulation thickness.
R = ρ×L/A, where ρ is copper resistivity (about 1.72×10⁻⁸ Ω·m at 20 °C), L is the total wire length (turns × mean length per turn), and A is the cross-sectional area.
It is the average length of wire used for one turn around the core, depending on the core's window dimensions and bobbin shape. It is usually taken from the core/bobbin datasheet or measured on an existing sample winding.
Yes. Copper resistance rises about 0.39–0.40% per °C above 20 °C, so a winding running hot has noticeably higher resistance (and copper loss) than at room temperature.
Copper loss is the I²R heating in the winding. It directly determines the winding's temperature rise, so keeping it within budget (via wire size and current density) is essential to avoid insulation damage.
At high frequency, skin and proximity effects make current crowd toward the wire surface, so several thinner, insulated strands (litz wire) in parallel can carry the same current with less effective resistance than one thick wire.
Compare your calculated area (in mm² or circular mils) to a standard AWG table and pick the nearest gauge with equal or greater area. Common transformer wires range from about AWG 40 (very fine) to AWG 10 (heavy).
Yes. The bare conductor area sets the resistance and current capacity, but the insulated (enamelled) outer diameter is what determines how many turns fit in the core window — always check the insulated OD in the wire's data sheet.
Either choose a larger core (more window area, see the Core Selection calculator), increase the allowed current density, or split the winding into parallel strands to fit the available space.
It is a good DC-resistance estimate for lower frequencies. At high switching frequencies, skin and proximity effects raise the AC resistance above this DC value, so add margin or use an AC-resistance correction for SMPS designs.
Typically 3–5 A/mm² with natural convection. Lower values run cooler and more efficiently at the cost of size and weight; higher values are acceptable with forced cooling or intermittent duty.
About 2–3.3 mm² depending on the current density chosen, which corresponds roughly to AWG 13 to AWG 12.
The tendency of alternating current to crowd toward the surface of a conductor as frequency rises, leaving the centre carrying almost nothing. It increases the effective resistance above the DC value.
About 9.2 mm at 50 Hz, 0.46 mm at 20 kHz, 0.21 mm at 100 kHz and 0.09 mm at 500 kHz. Conductors thicker than roughly twice the skin depth gain little useful cross-section.
It divides the conductor into many strands thinner than a skin depth and transposes them so each spends equal time at the inside and outside of the bundle. This addresses both skin effect and the proximity effect from neighbouring turns.
Current redistribution caused by the magnetic fields of adjacent conductors rather than by a conductor's own field. In multi-layer high-frequency windings it is often a larger source of loss than skin effect on its own.
Core Selection (Area Product) • Turns (Faraday's Law) • Wire Gauge / Ampacity • All Calculators