Convert current density between A/m², A/cm², A/mm² and A/in².
Electricity • 6 units
All 6 units on the Surface Current Density Converter are defined against the Ampere/meter² (A/m²), so each result is one conversion factor away from a single reference rather than the end of a chain of roundings.
The conversion this page is most often opened for is ready before you type anything: 1 A/mm² = 1,000,000 A/m². Change either side and every row in the table recalculates with it.
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The SI unit is unusably small for engineering work: 1 A/mm² is 1,000,000 A/m², which is why conductor design is universally discussed per square millimetre or per square inch and almost never in the base unit. Reading a value from this table, the practical rows are the ones with the small numbers, and a figure in the millions of A/m² is an ordinary current density rather than an extraordinary one.
The working limits are set by cooling rather than by the metal. Insulated copper windings relying on natural convection are typically designed somewhere around 3–6 A/mm² continuous, rising above 10 with forced cooling or a short duty cycle, while heavy busbars sit lower because their surface area grows more slowly than their cross-section. Copper itself tolerates far more; it is the insulation system that fails first, which is why the same conductor carries very different ratings in free air, in a conduit and buried in a slot.
Short-duration limits scale differently again, and the difference is counter-intuitive. A wire's fusing current rises roughly with the 1.5 power of its diameter while its area rises with the square, so doubling the diameter multiplies cross-section by four but fusing current by only about 2.83. The current density a conductor survives therefore falls as conductors get larger, and a thin wire briefly tolerates a density that would destroy a thick one — the reason fuse elements are thin, and the reason a fusing calculation cannot be scaled from a rating table by area alone.
Quick reference — 1 Ampere/millimeter² (A/mm²) is equal to:
| Ampere/meter² | A/m² | 1,000,000 |
| Ampere/centimeter² | A/cm² | 100 |
| Ampere/inch² | A/in² | 645.160042 |
| Kiloampere/meter² | kA/m² | 1,000 |
| Milliampere/meter² | mA/m² | 1,000,000,000 |
6 units of surface current density, each a fixed multiple of the A/m². The table spans 1,000,000,000:1, from mA/m² (0.001 A/m²) to A/mm² (1000000 A/m²). Conversion is one multiplication into the base unit and one division out of it, with no lookup table and no approximation.
value_to = value_from × (factor_from ÷ factor_to)1 A/m² = 1 A/m²1 A/cm² = 10000 A/m²1 A/mm² = 1000000 A/m²1 A/in² = 1550 A/m²1 kA/m² = 1000 A/m²1 mA/m² = 0.001 A/m²where:
Assumptions: Factors are exact definitions. Full double precision is carried internally and rounding is applied only for display.
Result25 A/mm² = 25000000 A/m²
Surface current density is current per unit cross-sectional area, in amperes per square metre (A/m²). It is the quantity that actually determines whether a conductor overheats, because heating depends on current concentration rather than on current alone.
This is why wire gauge tables exist. Circuit-board designers work in amperes per square millimetre and rules of thumb about track width; power engineers work in amperes per square inch of busbar. The skin effect complicates matters at high frequency by pushing current into a thin outer layer, so the effective area shrinks and the real current density rises well above what the conductor's full cross-section would suggest.