Linear Current Density Converter
Convert linear current density, the electric current carried per unit of length across a current sheet, between ampere per meter, ampere per centimeter, ampere per inch, the abampere units, oersted and gilbert per centimeter. Pick two units, enter a value and read the result instantly.
Select two units to see the conversion factor.
Linear current density is current per length (A/m). It is not electric current (A), not surface current density (A/m²) and not linear charge density (C/m).
Linear Current Density Formula
Linear current density is current divided by the width it flows across: K = I ÷ w, in A/m. Every unit is a fixed multiple of A/m. Result = value × (source factor ÷ target factor). Because length is in the denominator, “per centimeter” is 100 times larger than “per meter”. Exact building blocks: 1 in = 0.0254 m, 1 abampere = 10 A, 1 gilbert = 10/(4π) A and so 1 oersted = 1 gilbert per centimeter = 1000/(4π) A/m.
What Is Linear Current Density?
Linear current density, often written K and also called sheet current density or surface current per unit width, is the amount of electric current flowing across a unit length of a very thin conducting layer. It is the right quantity when a current runs in a sheet whose thickness is negligible: a printed-circuit trace, a superconducting film, a thin metal coating, a solenoid winding treated as a continuous sheet or an idealised current sheet in electromagnetism. Its SI unit is the ampere per meter (A/m).
If a 2 cm wide copper trace carries 3 A uniformly across its width, its linear current density is 3 A ÷ 0.02 m = 150 A/m. In a long solenoid of n turns per meter carrying current I, the winding behaves like a sheet with K = n × I, and the magnetic field inside is μ₀ × K.
The list also includes the oersted and the gilbert per centimeter. Both are CGS units that have the same dimension as A/m, and the converter treats them as equal to each other: 1 Oe = 1 Gi/cm = 1000/(4π) A/m, about 79.58 A/m. The oersted is better known as a unit of magnetic field strength H; the two ideas are linked because the jump in H across a current sheet equals the sheet’s K. For field-strength work use the Magnetic Field Strength Converter.
Do not confuse it with other quantities. It is not the current itself (Current Converter), not surface current density in A/m² where the current crosses an area (Surface Current Density Converter) and not linear charge density in C/m (Linear Charge Density Converter).
Supported Units
This converter supports the following 8 linear current density units. The last column gives the value of each unit in the base unit, A/m. The oersted and the gilbert per centimeter are the same size.
| Unit | Symbol | Value in A/m |
|---|---|---|
| Ampere per meter | A/m | 1 |
| Ampere per centimeter | A/cm | 100 |
| Ampere per inch | A/in | 39.37007874 |
| Abampere per meter | abA/m | 10 |
| Abampere per centimeter | abA/cm | 1,000 |
| Abampere per inch | abA/in | 393.7007874 |
| Oersted | Oe | 79.57747155 |
| Gilbert per centimeter | Gi/cm | 79.57747155 |
How to Use the Linear Current Density Converter
- Type the linear 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/m): 1 A/cm = 100 A/m and 1 A/m = 1 A/m.
- Divide the source size by the target size to get the conversion factor: 100 ÷ 1 = 100, so 1 A/cm = 100 A/m.
- Multiply by your value: 12 A/cm × 100 = 1,200 A/m.
Current density can be positive or negative (a sign shows direction), so a minus sign is accepted. Zero is also valid.
Common Linear Current Density Conversions
- Per centimeter to per meter: 12 A/cm equals 1,200 A/m.
- Per inch to per meter: 3 A/in equals 118.1102362 A/m.
- CGS to SI: 5 abA/cm equals 5,000 A/m.
- Oersted: 1 Oe equals 79.57747155 A/m and 0.7957747155 A/cm.
- Oersted and gilbert per centimeter: 100 Oe equals 100 Gi/cm.
- Inch to centimeter: 1 A/in equals 0.3937007874 A/cm.
A/m to Other Linear Current Density Units
Quick reference for frequently used values
| A/m | A/cm | A/in | Oersted (Oe) |
|---|---|---|---|
| 1 | 0.01 | 0.0254 | 0.01256637061 |
| 10 | 0.1 | 0.254 | 0.1256637061 |
| 50 | 0.5 | 1.27 | 0.6283185307 |
| 100 | 1 | 2.54 | 1.256637061 |
| 500 | 5 | 12.7 | 6.283185307 |
| 1,000 | 10 | 25.4 | 12.56637061 |
| 10,000 | 100 | 254 | 125.6637061 |
Where and Why This Conversion Is Used
- Printed-circuit and thin-film design: current per width of a trace or a film.
- Superconductors: the critical sheet current of a thin superconducting layer.
- Electromagnetics: current sheets, solenoids and surface-current boundary conditions.
- Magnetics: reading oersted or ampere-turns-per-meter data next to sheet-current data, since they share a dimension.
Limitations
- The value assumes the current is spread evenly across the width. It gives the total current only when the width is known.
- Only per-length units are offered here. Prefixed versions such as mA/m are not in the supported list, so enter the value in A/m using scientific notation, for example 5e-3.
Important Differences Between Related Electrical Measurements
- Linear current density, A/m is current per width of a sheet. Current, A is the total: 150 A/m across a 2 cm trace is 3 A.
- Linear vs surface current density: A/m describes current in a thin sheet, per unit width. A/m² describes current through a cross-section, per unit area. Multiply a surface density by the sheet thickness to get a linear density.
- Linear current density vs linear charge density: amperes per meter is a flow rate of charge across a width. Coulombs per meter is an amount of charge along a length. Charge density times speed gives current density.
- Linear current density vs magnetic field strength: both are measured in A/m, but one is a source (current in a sheet) and the other a field. The oersted and the gilbert per centimeter are listed here because they have the same dimension.
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.