Linear Current Density Converter
Print pageAll Equivalents Reference Table
| Unit | Equivalent Value |
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Linear Current Density (also known as Surface Current Density, Lineic Electric Current Concentration, or Sheet Current Flow Rate, symbolized by K or Js) measures the quantity of electric current flowing per unit spatial width across a conductor sheet, PCB busbar trace, or solenoid coil winding (K = dI ÷ dw = I ÷ W, where dI or I is electric current in amperes and dw or W is spatial sheet width in meters or centimeters). In electromagnetics and electrical machine design, linear current density K on a thin sheet or solenoid winding directly determines the tangential magnetic field intensity H (H = K = n · I, where n is turn density in turns/meter). Across MRI superconducting magnet design, electric motor armature stator winding, transformer busbar heat dissipation, RF microstrip shielding, induction heating coils, and planetary magnetosphere modeling, linear current density is categorized across three major engineering unit families: International System of Units (SI metric fundamental: Ampere per Meter / A/m, Ampere per Centimeter / A/cm), CGS Electromagnetic System metrics (Oersted / Oe, Gilbert per Centimeter / Gi/cm, Abampere per Meter / abA/m, Abampere per Centimeter / abA/cm), and Imperial Electrical standards (Ampere per Inch / A/in, Abampere per Inch / abA/in).
Our free online Linear Current Density Converter provides instant, high-precision conversions across all SI metric, CGS magnetic field intensity, and imperial sheet current units:
- Ampere per Centimeter to A/m [Motor Winding Standard]: Multiply A/cm by
100.0(1 A/cm = 100.0 A/m = 10.0 abA/m ⇒ 1 A/m = 0.01 A/cm). - Ampere per Inch to A/m & A/cm [Imperial Electrical Standard]: Multiply A/in by
39.37007874(1 A/in = 39.3701 A/m = 0.393701 A/cm = 3.93701 abA/m ⇒ 1 A/m = 0.0254 A/in). - Oersted (Oe) to A/m & A/cm [CGS Magnetic Field Unit]: Multiply Oe by
79.57747151(1 Oe = 1 Gilbert/cm = 79.5775 A/m = 0.795775 A/cm ⇒ 1 A/m = 0.01256637 Oe). - Abampere per Meter to A/m [CGS Electromagnetic Standard]: Multiply abA/m by
10.0(1 abA/m = 10.0 A/m = 0.10 A/cm = 0.125664 Oe). - Abampere per Centimeter to A/m & Oe [High-Density CGS Metric]: Multiply abA/cm by
1,000.0(1 abA/cm = 1,000.0 A/m = 10.0 A/cm = 12.56637 Oe). - Kiloampere per Meter (kA/m) to A/m & Oersteds:
1 kA/m = 1,000.0 A/m = 10.0 A/cm = 12.56637 Oe = 25.40 A/in.
Master Linear Current Density Conversion Table
The table below displays exact mathematical conversion relationships, SI Ampere per Meter (A/m) multipliers, and Oersted (Oe) equivalents relative to 1 Ampere per Meter (1 A/m = 0.01 A/cm = 0.01256637 Oe):
| Linear Current Density Unit Name | Symbol | Exact Value in A/m | A/cm, A/in & Oersted (Oe) Equivalent | Domain & Technical Application Standard |
|---|---|---|---|---|
| 1 Ampere per Meter (Base SI Unit) | A/m |
1.0 A/m (Base SI Unit) |
0.01 A/cm (0.0254 A/in / 0.0125664 Oe / 0.10 abA/m) |
SI Fundamental Base Unit of Surface Current Density & H-Field |
| 1 Ampere per Centimeter | A/cm |
100.0 A/m |
1.0 A/cm (2.54 A/in / 1.256637 Oe / 10.0 abA/m) |
Electric Motor Stator & Transformer Winding Loading Metric |
| 1 Ampere per Inch | A/in |
39.3700787 A/m |
0.393701 A/cm (1.0 A/in / 0.49474 Oe / 3.93701 abA/m) |
US Electrical Engineering PCB Copper Busbar Width Standard |
| 1 Oersted (Gilbert/cm) | Oe, Gi/cm |
79.5774715 A/m |
0.795775 A/cm (2.02129 A/in / 1.0 Oe / 7.95775 abA/m) | CGS Magnetic Field Intensity (H-Field) Standard Unit |
| 1 Abampere per Meter | abA/m |
10.0 A/m |
0.10 A/cm (0.254 A/in / 0.125664 Oe / 1.0 abA/m) | CGS Electromagnetic System Lineic Current Unit |
| 1 Abampere per Centimeter | abA/cm |
1,000.0 A/m |
10.0 A/cm (25.4 A/in / 12.56637 Oe / 100.0 abA/m) | High-Power Industrial Electromagnet Solenoid Winding |
Step-by-Step Air-Core Solenoid Magnetic Field & Surface Current Calculation Example
To calculate the magnetic field intensity (H) and magnetic flux density (B) produced inside an air-core cylindrical solenoid wound with a turn density of 1,200 turns per meter (n = 1,200 turns/m = 12 turns/cm) carrying a current of 2.5 Amperes (I = 2.5 A) into Amperes per Meter (A/m), Amperes per Centimeter (A/cm), and Oersteds (Oe) (given free space permeability μ0 = 4π × 10-7 T·m/A):
Step 1 (Linear Surface Current Calculation): K = H = n · I = 1,200 turns/m × 2.5 A = 3,000 Amperes per Meter (3,000 A/m)
Step 2 (Unit Conversions): K = 3,000 A/m ÷ 100 = 30.0 A/cm = 76.20 A/in = 300.0 abA/m
Step 3 (Oersted Conversion): HOe = 3,000 A/m ÷ 79.5774715 = 37.6991 Oersteds (37.70 Oe)
Step 4 (Magnetic Flux Density B Calculation): B = μ0 · H = (4π × 10-7) × 3,000 = 0.0037699 Tesla (3.77 Millitesla mT or 37.7 Gauss)
Thus, the 1,200 turns/m solenoid carries a linear surface current density of 3,000 A/m (30.0 A/cm), establishing an internal magnetic field intensity of 37.70 Oersteds (3.77 mT flux density).
Real-World Electromagnetic Coil & Motor Winding Benchmarks
Below is a comparative reference chart showing linear current density values (K) across PCB traces, electric motors, MRI magnets, and Earth’s geomagnetic field:
| Physical System / Electromagnet Winding | Linear Current Density in A/m | A/cm & Oersted (Oe) Equivalent | Electromagnetic & Motor Engineering Context |
|---|---|---|---|
| Earth’s Geomagnetic Surface Field Intensity (H) | 31.83 A/m (0.0318 kA/m) | 0.3183 A/cm (0.40 Oersteds Oe ≈ 50 μT) | Natural planetary magnetic field intensity baseline |
| Printed Circuit Board High-Current Copper Busbar Trace | 500.0 – 2,000.0 A/m | 5.0 – 20.0 A/cm (6.28 – 25.13 Oe) | PCB heavy copper power trace linear current loading |
| Precision Air-Core Solenoid Winding (1,000 turns/m at 2A) | 2,000.0 A/m (2.0 kA/m) | 20.0 A/cm (25.13 Oersteds Oe) | Standard lab calibration solenoid internal H-field |
| Industrial Heavy Electric Motor Stator Armature Sheet | 10,000.0 – 50,000.0 A/m (10 – 50 kA/m) | 100.0 – 500.0 A/cm (125.7 – 628.3 Oe) | AC induction / synchronous motor stator current loading |
| Superconducting Hospital MRI Solenoid Magnet (1.5 Tesla) | 1,193,662.0 A/m (1.1937 MA/m) | 11,936.6 A/cm (15,000.0 Oersteds Oe) | Ultra-high field liquid helium cooled MRI coil winding density |
History & Physics: 1820 Ampère’s Circuital Law vs 1930 IEC CGS Oersted
1820 André-Marie Ampère & Circuital Boundary Jump (ΔH = K)
In 1820, French physicist André-Marie Ampère formulated Ampère’s Circuital Law (∮ H · dl = Ienclosed). Applying this law across a current-carrying surface sheet proves that linear surface current density K creates a discontinuous tangential magnetic field jump across the surface: ΔH = Hside1 - Hside2 = K. This exact identity forms the mathematical boundary condition for all electromagnetic field solvers.
1930 IEC Standardization of the CGS Oersted Unit
In 1930, the International Electrotechnical Commission (IEC) officially adopted the Oersted (Oe) as the CGS unit of magnetic field strength H (where 1 Oe = (1,000 ÷ 4π) A/m ≈ 79.5774715 A/m), honoring Danish physicist Hans Christian Oersted, who discovered in 1820 that electric currents deflect magnetic compass needles.
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Frequently Asked Questions (FAQ)
How do you convert Ampere per Centimeter (A/cm) to Ampere per Meter (A/m)?
To convert A/cm to SI A/m, multiply A/cm by 100. For example, 25 A/cm × 100 = 2,500.0 A/m.
How do you convert Oersteds (Oe) to Ampere per Meter (A/m)?
To convert Oersteds to SI A/m, multiply Oe by 79.5774715 (approx. 79.577). For example, 100 Oe × 79.577 = 7,957.75 A/m.
What is the relationship between Linear Current Density (K) and Magnetic Field Intensity (H)?
Inside a tightly wound long solenoid or thin current sheet, linear surface current density (K in A/m) is 100% numerically equal to the internal magnetic field strength (H in A/m): H = K = n · I.
What is 1 Gilbert per Centimeter (Gi/cm) equal to?
1 Gilbert per Centimeter (Gi/cm) is 100% mathematically identical to 1 Oersted (1 Oe), equaling exactly 79.5774715 Amperes per Meter (79.577 A/m).