This current density unit converter changes current per unit area between amperes per square meter, amperes per square centimeter and amperes per square inch. Formula: 1 A/cm² = 10000 A/m²; 1 A/mm² = 1000000 A/m². The SI unit is A/m². 1 A/cm² is exactly 10,000 A/m², 1 A/in² is about 1,550.0031 A/m², and 1 A/mm² is 1,000,000 A/m², or 100 A/cm².
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How to use the current density unit converter
- Enter the value, for example 6 A/mm² entered as 600 A/cm².
- In the current density unit converter, choose its unit and the target unit, such as A/cm² to A/m².
- Read the current density unit converter result: 600 A/cm² = 6,000,000 A/m².
For A/mm² to A/cm², multiply by 100. For A/cm² to A/m², multiply by 10,000. For A/m² to mA/cm², divide by 10: 1 A/m² = 0.1 mA/cm².
What is current density?
Current density is electric current per unit cross-sectional area, in amperes per square meter (A/m²). It is used to size wires, busbars and PCB traces and in electroplating.
Conversion formula
The current density unit converter stores every unit as a multiple of the base unit, the ampere per square meter (A/m²). To convert:
value in target unit = value × (factor of source unit ÷ factor of target unit)
where each factor is the size of the unit in amperes per square meter.
Common current density conversions
| From | To | 1 unit equals |
|---|---|---|
| ampere per square meter (A/m²) | ampere per square centimeter (A/cm²) | 0.0001 A/cm² |
| ampere per square centimeter (A/cm²) | ampere per square meter (A/m²) | 10,000 A/m² |
Current density unit converter worked example
Convert 25 amperes per square meter to amperes per square centimeter:
- Factor of A/m² = 1 A/m²
- Factor of A/cm² = 10,000 A/m²
- 25 × 1 ÷ 10,000 = 0.0025 A/cm²
Current density unit reference
| Unit | Symbol | Group | Equals (A/m²) |
|---|---|---|---|
| Ampere per Square Meter | A/m² | SI | 1 |
| Ampere per Square Centimeter | A/cm² | SI | 10,000 |
| Ampere per Square Inch | A/in² | US/Imperial | 1,550.0031 |
Reverse factors for each current density unit
The reference table gives each unit in ampere per square meters. To go the other way, divide by that factor; the list below does the division for you.
- Ampere per Square Centimeter (A/cm²), SI: 1 A/cm² = 10,000 A/m², so 1 A/m² = 0.0001 A/cm².
- Ampere per Square Inch (A/in²), US/Imperial: 1 A/in² = 1,550.003 A/m², so 1 A/m² = 0.00064516 A/in².
Current density in household wire
AWG diameters follow d = 0.127 mm × 92^((36 − n)/39). At common US breaker pairings the copper carries these densities:
| Wire | Area (mm²) | Current | Density (A/mm²) | Density (A/cm²) |
|---|---|---|---|---|
| 14 AWG | 2.081 | 15 A | 7.21 | 721 |
| 12 AWG | 3.309 | 20 A | 6.04 | 604 |
| 10 AWG | 5.261 | 30 A | 5.7 | 570 |
The breaker size per gauge here is the usual pairing; it is shown for scale, not as a design rule. Check the electrical code and conductor insulation rating before sizing wire. Use the voltage drop calculator for long runs.
Electroplating and battery current density
Plating baths are specified in A/dm²: 1 A/dm² = 100 A/m² = 10 mA/cm². In batteries and fuel cells, mA/cm² of electrode area is common: 1 mA/cm² = 10 A/m². The total current is density times area, so a 2 dm² part at 3 A/dm² needs 6 A. Convert the total with the electric current converter and area with the area converter.
Circular mils per amp
US electrical practice often states current density inversely, as circular mils per amp. One square millimeter is about 1,973.5 circular mils, so current density in A/mm² is 1,973.5 divided by the cmil/A figure. A rule of 500 cmil/A is about 3.95 A/mm²; 700 cmil/A is about 2.8 A/mm².
The current density unit converter works in A/m², A/mm², A/cm² and A/in². To use a cmil/A rule with it, convert to A/mm² first with the division above.
These are rules of thumb for heating. Real limits depend on insulation class, ambient temperature, bundling and how long the current flows, so treat them as starting points.
A quick example: a 2.5 mm² conductor carrying 16 A runs at 6.4 A/mm², which is about 308 cmil/A. That is common for short runs of building wire, while transformer and motor windings, which are packed tightly and run for hours, are usually designed for lower densities. PCB traces are judged by temperature rise instead, using charts from IPC-2152.
Related converters and calculators
Related electrical tools:
- Electric current converter: A and mA
- Linear current density converter: A/m
- Voltage drop calculator: wire runs
- Area converter: m² and ft²
- Electrical resistivity converter: Ω·m and Ω·cm
Sources
NIST Special Publication 811, Appendix B; BIPM: SI Brochure.
Questions about this calculator
What is the SI unit of current density?
Ampere per square meter (A/m²).
How do I convert A/mm² to A/cm²?
Multiply by 100. For example, 4 A/mm² = 400 A/cm².
How do I convert A/cm² to A/m²?
Multiply by 10,000. For example, 0.5 A/cm² = 5,000 A/m².
How do I convert A/m² to mA/cm²?
Divide by 10. For example, 250 A/m² = 25 mA/cm².
What is 1 A/dm² in A/m²?
100 A/m², since 1 dm² = 0.01 m².
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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