Linear Current Density Converter
Convert linear current density between A/m, kA/m, A/cm, mA/mm, and µA/µm. Enter a value and select its original and target units.
Convert Linear Current Density Between Units
Linear Current Density Formula
Where:
- \(K_{\mathrm{from}}\) — value in the original unit
- \(K_{\mathrm{to}}\) — value in the target unit
- \(f_{\mathrm{from}}\) and \(f_{\mathrm{to}}\) — the number of amperes per meter represented by one original or target unit, respectively
Convert the original value to A/m, then divide by the A/m equivalent of the target unit. The conversion factors must represent the units as defined; see the warning below about two factors currently used by this calculator.
Linear Current Density – Calculation Example
Example: convert the default value of 5 A/m to A/cm. Because 1 A/cm equals 100 A/m, divide by 100.
\[5\ \mathrm{A/m}\times\frac{1\ \mathrm{A/cm}}{100\ \mathrm{A/m}}=0.05\ \mathrm{A/cm}\]
Result: 5 A/m = 0.05 A/cm.
How to use the calculator
- Enter a nonnegative number in Current density value. The default is 5.
- Choose the value’s existing unit in From unit.
- Choose the unit you want in To unit.
- Read Converted Linear Current Density, which includes the selected target unit. The displayed number is rounded to eight decimal places.
The default selection converts A/m to A/cm. Before relying on any other selection, read the unit-factor warning in the practical notes: the current calculator code does not convert mA/mm or µA/µm correctly when the other unit differs.
What linear current density means
Linear current density describes electric current per unit length, rather than current alone. For example, if current is distributed uniformly across the width of an idealized conducting sheet, dividing the total current by that width gives a value in A/m. The quantity can also arise when describing an equivalent surface current in electromagnetic models. Its meaning depends on what length is being measured, so the physical setup matters as much as the unit.
A value of 5 A/m means five amperes for each meter of the specified width or length in that model; it does not mean that a particular wire necessarily carries five amperes. You need the relevant dimension and a suitable distribution assumption to infer a total current. If you need to change the units of current itself, use the Electric Current converter.
Linear current density is not the same as current density through a cross-sectional area, which has units of A/m². It also has the same units as magnetic field strength, but sharing units does not make the two quantities interchangeable. In electromagnetic work, other quantities may need separate conversions: use the Magnetic Flux Density converter for magnetic flux density and the Magnetomotive Force converter for magnetomotive force.
Unit factors and practical limitations
For a physically correct conversion, use these A/m equivalents. Each factor is the number of A/m in one unit of the left-hand column.
| Unit | Equivalent in A/m |
|---|---|
| 1 A/m | 1 A/m |
| 1 kA/m | 1,000 A/m |
| 1 A/cm | 100 A/m |
| 1 mA/mm | 1 A/m |
| 1 µA/µm | 1 A/m |
Important: the calculator code currently assigns mA/mm a factor of 1,000 and µA/µm a factor of 1,000,000. Both should have a factor of 1. Consequently, its displayed results are incorrect when converting either of those units to or from a different unit. Conversions between A/m, kA/m, and A/cm use the correct factors. Selecting the same unit for both fields also returns the entered value.
A quick check is that 1 A/m = 1 mA/mm = 1 µA/µm: the current and the length shrink by the same factor in each expression. For example, 5 A/m should convert to 5 mA/mm, not 0.005 mA/mm. Until the calculator’s factors are corrected, use the table and formula above for conversions involving mA/mm or µA/µm.
Unit conversion only changes how a value is expressed; it cannot verify the underlying measurement, the chosen length, or whether a uniform distribution is appropriate. Very small converted values may display as zero because the result is rounded to eight decimal places. Keep more precision in intermediate calculations if a tiny difference matters.
Frequently Asked Questions
How can I convert linear current density by hand?
Convert the current and length units separately, then simplify the ratio. For example, \(12\ \mathrm{mA/mm}\) equals \(12\ \mathrm{A/m}\), because both milli- units contribute a factor of one thousand. Since \(1\ \mathrm{A/cm}=100\ \mathrm{A/m}\), the result is \(0.12\ \mathrm{A/cm}\). For conversions involving mA/mm or µA/µm, use this method rather than the calculator’s current displayed result.
What is a normal or good linear current density?
There is no universal normal value. An appropriate value depends on the conductor or electromagnetic model, its dimensions, the intended current, and any heating or material limits. A unit conversion cannot establish whether a design is safe or a measurement is plausible. Compare your value with specifications for the particular device or model, using the same definition of the measured length.
How do I convert A/m to amperes per inch?
Multiply the numerical value in A/m by \(0.0254\) to express it in A/in, because one inch is \(0.0254\) meters. For example, \(10\ \mathrm{A/m}=0.254\ \mathrm{A/in}\). Conversely, multiply a value in A/in by approximately \(39.3701\) to obtain A/m. A/in is not among this calculator’s selectable units.
Can I find total current from a nonuniform linear current density?
Yes, if you know how the density varies across the relevant width. Integrate it over that width: \(I=\int K(s)\,\mathrm{d}s\), where \(K(s)\) is measured perpendicular to the current flow. Multiplying one density value by the full width is valid only when that value represents the distribution adequately, such as for a uniform sheet.
How is linear current density related to current density in A/m²?
A volume current density in A/m² can yield a sheet current density in A/m when integrated through the sheet’s thickness. If it is uniform through a thickness \(t\), then \(K=Jt\). If it varies, integrate \(J\) through the thickness instead. This relationship requires a defined geometry and current direction; the two quantities cannot be interchanged by changing units alone.
Can linear current density be negative?
Yes, a negative value can indicate current flowing opposite to a chosen positive direction. The magnitude is then its absolute value. This calculator accepts only nonnegative inputs, so it converts magnitudes rather than preserving a directional sign. If direction matters in your calculation, record the sign separately and apply it after converting the units.
Does converting an AC linear current density change whether it is RMS or peak?
No. Changing between units such as A/m and A/cm preserves whether the original value is RMS, peak, or instantaneous. Those descriptions refer to different ways of specifying a time-varying current, not different length units. Label the convention alongside the converted value; for a sinusoid, converting between RMS and peak also requires a separate factor of \(\sqrt{2}\).