Electricity converters
Linear Charge Density Converter
Convert linear charge density units: charge carried per unit length.
Result
0.01 C/cm
1 C/m = 0.01 C/cm
All units for this value
| Unit | Symbol | Value |
|---|---|---|
| Coulomb per meter | C/m | 1 |
| Coulomb per centimeter | C/cm | 0.01 |
| Coulomb per millimeter | C/mm | 0.001 |
| Microcoulomb per meter | µC/m | 1000000 |
| Nanocoulomb per meter | nC/m | 1000000000 |
| Coulomb per inch | C/in | 0.0254 |
| Coulomb per foot | C/ft | 0.3048 |
| Abcoulomb per meter | abC/m | 0.1 |
| Abcoulomb per centimeter | abC/cm | 0.001 |
| Abcoulomb per inch | abC/in | 0.00254 |
About this calculator
Linear charge density describes how much electric charge is distributed along each unit of length, a quantity used when modeling charged wires, rods, or beams. This converter switches between the SI unit coulomb per meter and its metric variants, US units based on inches and feet, and CGS units built from the abcoulomb.
How it works in plain English
Linear charge density combines a charge unit with a length unit, so the converter anchors every entry to coulombs per meter and rescales through that shared base. Metric variants such as coulomb per centimeter and coulomb per millimeter follow simple factor-of-100 and factor-of-1000 relationships, since those are the corresponding relationships between the length units themselves.
The microcoulomb and nanocoulomb per meter units apply the same small-scale prefixes used for charge itself, useful when describing thin charged filaments or laboratory wires that carry comparatively small amounts of charge. The US-customary units convert the inch (0.0254 m) and foot (0.3048 m) into their reciprocal form, since a smaller length unit means more of that unit fits into a meter, giving a larger coulomb-per-inch or coulomb-per-foot factor. The CGS abcoulomb-based units multiply the abcoulomb's factor of 10 coulombs by the same length reciprocals.
Choose your from and to units, enter a value, and the converted linear charge density displays immediately, with a table showing that same quantity across every supported unit. A precision selector controls how many decimal places appear, and a swap button reverses the two chosen units in one click.
The formula
- value_in_target = value_in_source × (source factor to C/m) ÷ (target factor to C/m)
- 1 C/cm = 100 C/m
- 1 C/in = 1 ÷ 0.0254 ≈ 39.3701 C/m
- 1 abC/m = 10 C/m
Worked example
Suppose a charged rod carries a uniform linear charge density of 5 microcoulombs per meter, and an engineer needs that figure in coulombs per centimeter for a formula written in centimeter-based units. Converting first to coulombs per meter gives 5 × 10⁻⁶ C/m, then dividing by the coulomb-per-centimeter factor of 100 gives 5 × 10⁻⁸ C/cm.
Entering 5 into the microcoulomb-per-meter field with coulomb-per-centimeter selected as the target returns 5 × 10⁻⁸ C/cm right away. The accompanying unit table also lists this same density as roughly 1.27 × 10⁻⁷ C/in and 5 × 10⁻⁷ abC/m, all generated from that one entered value.
Linear charge density unit reference values
| Unit | Value in C/m |
|---|---|
| 1 coulomb per centimeter (C/cm) | 100 |
| 1 coulomb per millimeter (C/mm) | 1,000 |
| 1 coulomb per inch (C/in) | ≈39.3701 |
| 1 coulomb per foot (C/ft) | ≈3.2808 |
| 1 abcoulomb per meter (abC/m) | 10 |
| 1 abcoulomb per centimeter (abC/cm) | 1,000 |
Standard SI, US customary, and CGS unit definitions
Frequently asked questions
What kind of situations use linear charge density?
Linear charge density is common when modeling charge spread along a one-dimensional object, such as a straight wire, a charged fiber, or a beam of particles. Physics problems involving the electric field around a long charged rod typically express the rod's charge this way rather than as a single total charge value.
Why do smaller length units give larger conversion factors?
Because more small units fit into a meter than large ones, describing the same physical charge distribution in coulombs per inch requires a bigger number than describing it in coulombs per meter. This converter applies the reciprocal of the length conversion automatically so the physical quantity stays consistent across units.
How does linear charge density relate to total charge?
Multiplying a uniform linear charge density by the total length of the charged object gives its total charge in coulombs. This converter handles only the density itself, so the length of the object needs to be tracked separately when working out a total.
What's the difference between abcoulomb per meter and coulomb per meter?
The abcoulomb is a CGS electromagnetic unit equal to exactly 10 coulombs, so one abcoulomb per meter corresponds to 10 coulombs per meter. This converter applies that factor directly, so switching between the two systems doesn't require looking up the abcoulomb definition separately.
Can I convert a US engineering figure in coulombs per foot into metric units?
Yes. Select coulomb per foot as the from unit and coulomb per meter, centimeter, or millimeter as the target, then enter the value. The converter applies the exact foot-to-meter factor automatically, avoiding the need to convert the length unit by hand first.
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