Electromagnetic Densities Converter
Convert linear, surface and volume charge or current density between SI and CGS units — single page covering all five common electromagnetic-density quantities.
Written by Rahman · Last reviewed
Quick answer
This page covers five related quantities that spread charge or current over length, area or volume: linear, surface and volume charge density, plus linear and surface current density. Their SI units are C/m, C/m², C/m³, A/m and A/m² respectively, and each converts independently — so choose the quantity from the dropdown first.
Electric charge per unit length.
| Coulomb per metre (C/m) | 1 |
| Coulomb per centimetre (C/cm) | 0.01 |
| Coulomb per inch (C/in) | 0.0254 |
| Abcoulomb per metre (abC/m) | 0.1 |
About the Electromagnetic Densities Converter
Electromagnetic densities describe how electric charge or current is spread out across a length, area or volume. This unified page covers all five common density quantities used in electromagnetism: linear, surface and volume charge density, plus linear and surface current density.
Use the quantity selector at the top to switch between the five forms. Each is its own independent linear conversion with its own units, but they all share the same underlying concept: "amount of charge or current per unit of geometric extent".
Five quantities, and which one you need
This page consolidates quantities that look similar and are not interchangeable. Three describe charge distributed over a geometry, and two describe current. The unit tells you which: what appears after "per" is the dimension the quantity is spread across.
Linear charge density is coulombs per metre, used for charged wires and line charges. Surface charge density is coulombs per square metre, used for plates and conductor surfaces. Volume charge density is coulombs per cubic metre, used where charge fills a region. Linear current density is amperes per metre, and surface current density is amperes per square metre — the figure that governs how much current a conductor cross-section can carry.
- Selecting the wrong family produces a number with the wrong dimensions, which no amount of arithmetic will fix.
- Surface current density is the practical one in electrical engineering, since conductor sizing and current-carrying capacity depend on it.
- Abcoulomb units belong to the older CGS electromagnetic system and appear in historical texts; one abcoulomb is ten coulombs.
Watch the squared and cubed prefixes
Converting these units repeats a trap from the area and volume converters. Where the denominator is squared or cubed, the prefix is raised to the same power — so the factor between coulombs per square metre and coulombs per square centimetre is 10,000, not 100.
For volume densities it is a million: a coulomb per cubic centimetre is a million coulombs per cubic metre. Doing these conversions by moving the decimal point the way you would for a linear unit gives an answer wrong by two or three orders of magnitude.
- Per-metre to per-centimetre is a factor of 100; per-square-metre is 10,000; per-cubic-metre is 1,000,000.
- Inch-based versions carry the same squaring, which is why the factors are awkward numbers rather than round ones.
- Converting through the SI base unit rather than chaining prefix conversions avoids the error entirely.
Frequently Asked Questions
Why are these grouped together?
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They are all "density" measures in electromagnetism — quantity (charge or current) divided by a geometric extent (length, area or volume). Grouping them on one page reflects how textbooks and engineers think about them and reduces clutter for a niche topic.
What is the SI unit for each?
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Linear charge density: coulomb per metre (C/m). Surface charge density: coulomb per square metre (C/m²). Volume charge density: coulomb per cubic metre (C/m³). Linear current density: ampere per metre (A/m). Surface current density: ampere per square metre (A/m²).
When do I use each?
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Use linear forms for one-dimensional objects (wires, rods), surface forms for two-dimensional ones (plates, sheets, capacitors), and volume forms when charge is spread throughout a three-dimensional region (semiconductors, plasmas).
How does the SI to CGS conversion work?
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The abcoulomb (abC) is the CGS-emu unit of charge. 1 abC = 10 C, so charge-density CGS units carry that factor. The converter applies it automatically.