Linear Charge Density Converter
Convert linear charge density, the electric charge carried per unit of length, between coulomb per meter, coulomb per centimeter, coulomb per inch and the matching abcoulomb units. Pick two units, enter a value and read the result instantly.
Select two units to see the conversion factor.
Linear charge density is charge per length (C/m). It is not total charge (C), not surface charge density (C/m²) and not volume charge density (C/m³).
Linear Charge Density Formula
Linear charge density is charge divided by length: λ = Q ÷ L, in C/m. Every unit is a fixed multiple of C/m. Result = value × (source factor ÷ target factor). Because length is in the denominator, a unit that is “per centimeter” is 100 times larger than the same charge “per meter”. Exact building blocks: 1 m = 100 cm, 1 in = 0.0254 m and 1 abcoulomb = 10 C.
What Is Linear Charge Density?
Linear charge density, usually written λ (lambda), is the amount of electric charge spread along a line, per unit of length. It is the natural description of a charged wire, a thin rod, a charged filament or the beam of charged particles in an accelerator, where the length matters far more than the thickness. Its SI unit is the coulomb per meter (C/m).
If a uniformly charged rod 0.5 m long carries a total charge of 2 µC, its linear charge density is 2 µC ÷ 0.5 m = 4 µC/m. Going the other way, the total charge on a line is the density times the length: Q = λ × L. The field around a long, straight line of charge is found from λ alone with Gauss’s law, and falls off in proportion to 1 ÷ r with distance r.
The units here pair a charge unit (the coulomb or the abcoulomb of the CGS electromagnetic system) with a length unit (meter, centimeter or inch). Changing the length unit scales the value in the opposite direction from what many people expect: 1 C/cm is more charge density than 1 C/m, since the same coulomb is packed into a hundredth of the length.
Do not confuse it with other quantities. Total charge is in coulombs, surface charge density is charge per area (Surface Charge Density Converter) and volume charge density is charge per volume (Volume Charge Density Converter). Linear charge density is also different from linear current density, which is current per length (Linear Current Density Converter).
Supported Units
This converter supports the following 6 linear charge density units. The last column gives the value of each unit in the base unit, C/m.
| Unit | Symbol | Value in C/m |
|---|---|---|
| Coulomb per meter | C/m | 1 |
| Coulomb per centimeter | C/cm | 100 |
| Coulomb per inch | C/in | 39.37007874 |
| Abcoulomb per meter | abC/m | 10 |
| Abcoulomb per centimeter | abC/cm | 1,000 |
| Abcoulomb per inch | abC/in | 393.7007874 |
How to Use the Linear Charge Density Converter
- Type the linear charge 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 (C/m): 1 abC/cm = 1,000 C/m and 1 C/m = 1 C/m.
- Divide the source size by the target size to get the conversion factor: 1,000 ÷ 1 = 1,000, so 1 abC/cm = 1,000 C/m.
- Multiply by your value: 5 abC/cm × 1,000 = 5,000 C/m.
Charge density can be positive or negative, so a minus sign is accepted. Zero is also valid.
Common Linear Charge Density Conversions
- Per centimeter to per meter: 2 C/cm equals 200 C/m.
- Per inch to per meter: 3 C/in equals 118.1102362 C/m.
- CGS to SI: 5 abC/cm equals 5,000 C/m.
- Same charge, different length: 1 abC/m equals 0.01 abC/cm and 0.0254 abC/in.
- Inch to centimeter: 1 C/in equals 0.3937007874 C/cm.
- Small value: 0.0005 C/m equals 1.27e-5 C/in.
C/m to Other Linear Charge Density Units
Quick reference for frequently used values
| C/m | C/cm | C/in | abC/m |
|---|---|---|---|
| 0.001 | 1e-5 | 2.54e-5 | 0.0001 |
| 0.01 | 0.0001 | 0.000254 | 0.001 |
| 0.1 | 0.001 | 0.00254 | 0.01 |
| 1 | 0.01 | 0.0254 | 0.1 |
| 5 | 0.05 | 0.127 | 0.5 |
| 10 | 0.1 | 0.254 | 1 |
| 100 | 1 | 2.54 | 10 |
Where and Why This Conversion Is Used
- Electrostatics teaching: line-charge problems solved with Gauss’s law, where the result depends on λ.
- High-voltage engineering: estimating the field around charged conductors and corona onset on lines and cables.
- Particle beams: the charge per meter of a bunched beam in an accelerator.
- Electrospinning and printing: charge carried along a fibre or a jet.
- Reading older literature: CGS texts give line charge in abcoulombs per centimeter.
Limitations
- The value describes a uniform distribution along a line. It does not give the total charge unless the length is known.
- Only per-length units are offered here. Metric prefixed versions such as µC/m are not in the supported list, so enter the value in C/m using scientific notation, for example 2e-6.
Important Differences Between Related Electrical Measurements
- Linear charge density, C/m is charge per length. Total charge, C is the density multiplied by the length: a density of 4 µC/m over 0.5 m is 2 µC.
- Linear vs surface vs volume density: C/m, C/m² and C/m³ describe charge spread along a line, over a surface and through a volume. They have different dimensions and can never be converted into each other without a geometry.
- Charge density vs current density: linear charge density is coulombs per meter. Linear current density is amperes per meter. Multiplying a charge density by its drift speed gives a current.
- Charge density vs electric field: the density is the source, and the field in V/m is the result it produces around the line.
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.