Electricity converters
Surface Current Density Converter
Convert current density units: A/m², A/mm², A/cm² and A/in².
Result
1000000 A/m²
1 A/mm² = 1000000 A/m²
All units for this value
| Unit | Symbol | Value |
|---|---|---|
| Ampere per square meter | A/m² | 1000000 |
| Ampere per square centimeter | A/cm² | 100 |
| Ampere per square millimeter | A/mm² | 1 |
| Kiloampere per square meter | kA/m² | 1000 |
| Milliampere per square meter | mA/m² | 1000000000 |
| Ampere per square inch | A/in² | 645.16 |
| Ampere per circular mil | A/cmil | 0.000506707 |
| Abampere per square meter | abA/m² | 100000 |
| Abampere per square centimeter | abA/cm² | 10 |
About this calculator
Surface current density measures how much electric current passes through each unit of cross-sectional area, a figure engineers use to check whether a conductor is being pushed beyond a safe current-carrying capacity. This converter switches between SI units such as ampere per square meter, the US ampere per square inch and ampere per circular mil, and the CGS abampere-based units.
How it works in plain English
Because surface current density is a current divided by an area, the converter anchors every unit to ampere per square meter and rescales your entered value through that shared base. Metric multiples like kiloampere per square meter follow ordinary factor-of-1000 steps, while ampere per square centimeter and ampere per square millimeter scale by the square of the length ratio, giving factors of 10,000 and 1,000,000 respectively.
Ampere per square inch converts through the square of the standard inch (0.0254 meters), giving roughly 1550 A/m² per A/in². Ampere per circular mil is a specialized US wire-sizing unit based on the circular mil area of 5.067074790974977e-10 square meters, commonly seen on cable ampacity tables. The CGS abampere-based units again carry the abampere's factor of 10 on top of the area scaling.
Choose the from and to units, enter a value, and the result updates immediately, with a full table showing the same current density across every supported unit at once. A precision selector adjusts the number of decimal places shown, and a swap button flips the two chosen units in one click.
The formula
- value_in_target = value_in_source × (source factor to A/m²) ÷ (target factor to A/m²)
- 1 A/in² = 1 ÷ 6.4516e-4 = 1550.0031 A/m²
- 1 A/cmil = 1 ÷ 5.067074790974977e-10 A/m²
- 1 abA/cm² = 100,000 A/m²
Worked example
Suppose a cable ampacity table lists a conductor rated at 800 A/cmil and an electrician wants that in A/m² to compare against a metric design standard. Dividing by the circular-mil area factor: 800 ÷ 5.067074790974977e-10 ≈ 1.579 × 10¹² A/m².
Entering 800 into the A/cmil field with A/m² selected as the target returns roughly 1.579 × 10¹² A/m². The unit table also shows this same value as about 157,900 A/cm² and 1019.1 A/in², all derived from that single entry with no additional conversion steps required. Checking the kiloampere-per-square-meter row, which reads about 1,579,000,000 kA/m², confirms the result is consistent no matter which unit in the table is used as a cross-check.
Surface current density unit factors
| Unit | Value in A/m² |
|---|---|
| 1 ampere per square meter (A/m²) | 1 |
| 1 ampere per square centimeter (A/cm²) | 10,000 |
| 1 ampere per square millimeter (A/mm²) | 1,000,000 |
| 1 ampere per square inch (A/in²) | 1,550.0031 |
| 1 ampere per circular mil (A/cmil) | ≈1.9739 × 10⁹ |
| 1 abampere per square meter (abA/m²) | 10 |
Standard unit definitions
Frequently asked questions
What is surface current density used for?
It's used to describe how densely current is packed into a conductor's cross-section, which relates directly to heating: a higher current density in the same material generally means more resistive heating per unit volume. Cable and busbar ampacity ratings are often expressed or checked against maximum allowable current density figures.
Why does ampere per circular mil use such an unusual area unit?
The circular mil is a traditional US wire-sizing unit equal to the area of a circle one mil (0.001 inch) in diameter, and it remains common on American Wire Gauge tables and cable ampacity charts. This converter includes it so figures from those tables can be compared directly against metric A/m² or A/mm² values.
How does surface current density differ from linear current density?
Surface current density is current divided by a cross-sectional area, describing how densely current fills a conductor's interior, while linear current density is current divided by a width or length along a surface, describing how current spreads across a sheet or edge. They apply to different physical situations and use different units.
Can I convert A/mm² figures from a European cable standard into A/cmil?
Yes. Select ampere per square millimeter as the from unit and ampere per circular mil as the target, then enter the rated value. The converter routes the calculation through the shared A/m² anchor automatically, applying both the metric and circular-mil area factors without any manual lookup.
Is a higher surface current density always unsafe?
Not necessarily on its own, since safe current density depends on the conductor material, insulation, cooling, and duty cycle. This converter only performs the unit conversion; comparing a converted figure against a specific material's rated ampacity or design standard is a separate step outside what the conversion itself provides.
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