This linear current density converter changes current per unit width between amperes per meter, amperes per centimeter, amperes per inch and abamperes per centimeter. Formula: 1 A/cm = 100 A/m; 1 A/in = 1/0.0254 A/m. The SI unit is A/m. 1 A/cm is exactly 100 A/m, 1 A/in is about 39.3701 A/m, and 1 abA/cm is 1,000 A/m because an abampere is 10 A.
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How to use the linear current density converter
- Enter the value, for example 25 A/cm from a motor design sheet.
- In the linear current density converter, choose its unit and the target unit, such as A/cm to A/m.
- Read the linear current density converter result: 25 A/cm = 2,500 A/m.
For A/m to A/cm, divide by 100; for A/in to A/m, multiply by 39.3701.
What is linear current density?
Linear current density is current per unit width of a conducting sheet or edge, in amperes per meter (A/m). It is used in electromagnetics and motor design.
Conversion formula
The linear current density converter stores every unit as a multiple of the base unit, the ampere per meter (A/m). 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 meter.
Common linear current density conversions
| From | To | 1 unit equals |
|---|---|---|
| ampere per meter (A/m) | ampere per centimeter (A/cm) | 0.01 A/cm |
| ampere per centimeter (A/cm) | ampere per meter (A/m) | 100 A/m |
Linear current density converter worked example
Convert 25 amperes per meter to amperes per centimeter:
- Factor of A/m = 1 A/m
- Factor of A/cm = 100 A/m
- 25 × 1 ÷ 100 = 0.25 A/cm
Linear current density unit reference
| Unit | Symbol | Group | Equals (A/m) |
|---|---|---|---|
| Ampere per Meter | A/m | SI | 1 |
| Ampere per Centimeter | A/cm | SI | 100 |
| Ampere per Inch | A/in | US/Imperial | 39.37007874 |
| Abampere per Centimeter | abA/cm | CGS-EMU | 1,000 |
Reverse factors for each linear current density unit
The reference table gives each unit in ampere per meters. To go the other way, divide by that factor; the list below does the division for you.
- Ampere per Centimeter (A/cm), SI: 1 A/cm = 100 A/m, so 1 A/m = 0.01 A/cm.
- Ampere per Inch (A/in), US/Imperial: 1 A/in = 39.37008 A/m, so 1 A/m = 0.0254 A/in.
- Abampere per Centimeter (abA/cm), CGS-EMU: 1 abA/cm = 1,000 A/m, so 1 A/m = 0.001 abA/cm.
Solenoids and current sheets
A long solenoid with n turns per meter carrying current I acts like a current sheet with K = n × I, in A/m. Inside it, B = μ₀ n I, with μ₀ ≈ 1.25663706127 × 10⁻⁶ N/A² (CODATA):
| Turns per meter | Current (A) | K = nI (A/m) | B inside (mT) |
|---|---|---|---|
| 500 | 1 | 500 | 0.6283 |
| 1,000 | 1 | 1,000 | 1.2566 |
| 1,000 | 2 | 2,000 | 2.5133 |
| 2,000 | 5 | 10,000 | 12.5664 |
An infinite flat sheet carrying K produces B = μ₀ K ÷ 2 on each side, half the solenoid value.
Same unit as magnetic field strength
Magnetic field strength H is also measured in A/m, and that is no coincidence: at a current sheet, the jump in H across the sheet equals K. In motor design, the total current per meter of air-gap circumference is called the electric loading and is quoted in A/m or A/cm. Convert the resulting flux density with the magnetic flux density converter and total current with the electric current converter.
Electric loading in machines
Motor and generator designers use linear current density under the name electric loading: the total current in the slots divided by the air-gap circumference. It is quoted in A/m, A/cm or A/in. A value of 20 kA/m becomes 200 A/cm or about 508 A/in in the linear current density converter.
The same idea applies to flat conductors and current sheets. A copper tape 25 mm wide carrying 50 A has a linear current density of 2,000 A/m. Divide by the thickness as well and you get the ordinary current density in A/m², which is a different quantity used for heating checks.
Electric loading and magnetic loading together set the torque a machine can produce for its size, which is why designers compare these numbers across frames.
Related converters and calculators
Related electrical tools:
- Electric current converter: A and mA
- Current density converter: A/m²
- Magnetic flux density converter: tesla and gauss
- Linear charge density converter: C/m
- Length converter: m, ft, in
Sources
NIST CODATA: Vacuum magnetic permeability; NIST Special Publication 811, Appendix B.
Questions about this calculator
What is the SI unit of linear current density?
Ampere per meter (A/m).
How do I convert A/m to A/cm?
Divide by 100. For example, 3,000 A/m = 30 A/cm.
How do I convert A/in to A/m?
Multiply by 39.3701. For example, 10 A/in ≈ 393.7 A/m.
What is an abampere per centimeter?
The CGS unit: 1 abA/cm = 10 A per 0.01 m = 1,000 A/m.
What is K in a solenoid?
K = n × I; 1,000 turns per meter carrying 2 A gives 2,000 A/m.
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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