Surface Current Density Converter
Convert surface current density, the electric current flowing through a unit of cross-sectional area, between ampere per square meter, square centimeter, square inch, square mil, circular mil and abampere per square centimeter. Pick two units, enter a value and read the result instantly.
Select two units to see the conversion factor.
Surface current density is current per area (A/m²), the usual “current density” J. It is not electric current (A), not linear current density (A/m) and not surface charge density (C/m²).
Surface Current Density Formula
Surface current density is current divided by the cross-sectional area it flows through: J = I ÷ A, in A/m². Every unit is a fixed multiple of A/m². Result = value × (source factor ÷ target factor). Area scales with the square of length, so 1 A/cm² = 10,000 A/m². Exact building blocks: 1 in² = 0.00064516 m², 1 mil = 0.0000254 m, 1 square mil = 6.4516 × 10⁻¹⁰ m², 1 circular mil = (π/4) square mil and 1 abampere = 10 A.
What Is Surface Current Density?
Surface current density, written J and usually just called current density, is the electric current that passes through each unit of cross-sectional area of a conductor. Its SI unit is the ampere per square meter (A/m²). It tells you how concentrated the current is, which matters far more than the total current when you ask whether a wire will overheat, a track will fail from electromigration or a contact will burn.
A 10 A current through a conductor of 2.5 mm² cross-section gives J = 10 A ÷ 2.5 × 10⁻⁶ m² = 4 × 10⁶ A/m², which is 4 A/mm². Copper in ordinary building wiring is typically run at about 1 to 10 A/mm², that is 10⁶ to 10⁷ A/m²; thin on-chip interconnects are limited to around 10¹⁰ A/m² by electromigration.
Wire sizes in the US are often given in circular mils, the area of a circle one mil (a thousandth of an inch) in diameter, about 5.07 × 10⁻¹⁰ m². A classic rule of thumb allows roughly 500 circular mils of copper per ampere, that is 0.002 A per circular mil, which is about 3.95 × 10⁶ A/m² or 3.95 A/mm². The ampere per square mil is larger by a factor of 4/π, since a circle of diameter one mil has only π/4 of the area of a one-mil square.
Do not confuse it with other quantities. Current density per area (A/m²) is different from linear current density per width (A/m) (Linear Current Density Converter), from the total current (Current Converter) and from surface charge density (C/m²) (Surface Charge Density Converter).
Supported Units
This converter supports the following 6 surface current density units. The last column gives the value of each unit in the base unit, A/m².
| Unit | Symbol | Value in A/m² |
|---|---|---|
| Ampere per square meter | A/m² | 1 |
| Ampere per square centimeter | A/cm² | 10,000 |
| Ampere per square inch | A/in² | 1,550.0031 |
| Ampere per square mil | A/mil² | 1,550,003,100 |
| Ampere per circular mil | A/cmil | 1,973,525,241 |
| Abampere per square centimeter | abA/cm² | 100,000 |
How to Use the Surface Current Density Converter
- Type the surface current density in the value box. Decimals and scientific notation such as 0.0025 or 2.5e-3 are accepted.
- Choose the From unit and the To unit.
- The result appears instantly, or press Convert Now. Very large or very small results are shown in scientific notation.
- Use Swap Units to reverse the conversion, Copy Result to copy the answer, open Show this value in all units for a full list, and Clear to start again.
Step-by-step by hand
- Find the size of each unit in the common base unit (A/m²): 1 A/cmil = 1,973,525,241 A/m² and 1 A/m² = 1 A/m².
- Divide the source size by the target size to get the conversion factor: 1,973,525,241 ÷ 1 = 1,973,525,241, so 1 A/cmil = 1,973,525,241 A/m².
- Multiply by your value: 0.002 A/cmil × 1,973,525,241 = 3,947,050.483 A/m².
Current density can be positive or negative (a sign shows direction), so a minus sign is accepted. Zero is also valid.
Common Surface Current Density Conversions
- Rule of thumb for copper: 0.002 A per circular mil (500 cmil per ampere) equals 3,947,050.483 A/m².
- Per square centimeter: 400 A/cm² equals 4,000,000 A/m².
- Per square inch: 1,000 A/in² equals 1,550,003.1 A/m² and 155.00031 A/cm².
- Circular mil to square mil: 1 A/cmil equals 1.273239545 A/mil².
- CGS to SI: 3 abA/cm² equals 300,000 A/m².
- A/mm² as a check: 4 × 10⁶ A/m² is 4 A/mm², and 1 A/mm² equals 100 A/cm².
A/m² to Other Surface Current Density Units
Quick reference for frequently used values
| A/m² | A/cm² | A/in² | A/cmil |
|---|---|---|---|
| 1 | 0.0001 | 0.00064516 | 5.067074791e-10 |
| 100 | 0.01 | 0.064516 | 5.067074791e-8 |
| 10,000 | 1 | 6.4516 | 5.067074791e-6 |
| 100,000 | 10 | 64.516 | 5.067074791e-5 |
| 1,000,000 | 100 | 645.16 | 0.0005067074791 |
| 4,000,000 | 400 | 2,580.64 | 0.002026829916 |
| 10,000,000 | 1,000 | 6,451.6 | 0.005067074791 |
Where and Why This Conversion Is Used
- Wire and cable sizing: comparing ampacity rules given in A/mm², A/in² and circular mils per ampere.
- Electrochemistry: electroplating, batteries and fuel cells specify current per electrode area, often in A/cm² or mA/cm².
- Semiconductors and interconnects: electromigration limits are quoted as current density.
- Superconductors and plasma physics: critical current density is a defining property of a material.
- Reading older literature: US wire tables use circular mils, CGS texts use abampere per square centimeter.
Limitations
- The value assumes the current is spread evenly over the cross-section. Real conductors crowd current toward the surface at high frequency (the skin effect).
- Ampacity depends on insulation, temperature and cooling as well as current density, so a density alone is not a safe rating.
- Only the listed per-area units are offered. For A/mm² enter the value in A/m² using 1e6 per A/mm².
Important Differences Between Related Electrical Measurements
- Surface current density, A/m² is current per area of cross-section. Current, A is the total: 4 A/mm² through 2.5 mm² is 10 A.
- Surface vs linear current density: A/m² applies when current crosses an area. A/m applies to a thin sheet, per unit width. Multiplying a surface density by the sheet thickness gives a linear density.
- Surface current density vs surface charge density: amperes per square meter is a flow rate through an area. Coulombs per square meter is an amount of charge on an area. Charge density times drift speed gives current density.
- Current density vs electric field: in a conductor they are linked by Ohm’s law in point form, J = σ × E, where σ is the electrical conductivity.
Each converter on this site changes units within one quantity only, and none of them mixes quantities. The related tools are: Charge, Current, Linear Charge Density, Surface Charge Density, Volume Charge Density, Linear Current Density, Surface Current Density, Electric Field Strength, Electric Potential, Electric Resistance, Electric Resistivity, Electric Conductance, Electric Conductivity, Electrostatic Capacitance and Inductance.