Convert electric charge per unit length between metre-, centimetre-, and millimetre-based units, with full supported-unit equivalents and SI base-value context. Use it to test different inputs quickly, compare outcomes, and understand the main factors behind the result before moving on to related tools or deeper guidance.
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Convert electric charge per unit length between metre-, centimetre-, and millimetre-based units without doing the SI prefix shifts by hand.
This is useful when a formula uses the line-charge symbol λ = Q / L and you need to reconcile a value reported in one length scale with another.
Unit guidance
C/m is the base SI expression for charge per unit length and is the clearest reference when you want the raw metre-based quantity.
Add a value to convert Provide a linear charge density value and choose the source and target units to see the converted result and full equivalence table.
Linear charge density converter: convert C/m, µC/m, C/cm, C/mm, and related units
A linear charge density converter helps you move between different ways of expressing electric charge per unit length without manually shifting both the charge prefix and the length scale. This page converts common metre-, centimetre-, and millimetre-based line-charge units, then shows the same quantity across every supported unit so you can compare scales cleanly.
What linear charge density means
Linear charge density describes how much electric charge is distributed along a one-dimensional length. It is usually written with the symbol lambda, λ, and is defined as charge divided by length. In electrostatics problems, it often appears when a charged wire, rod, or ideal line of charge is treated as a continuous distribution rather than as a collection of separate point charges.
The base SI-style way to express it is coulombs per metre, written as `C/m`. But depending on the magnitude of the charge and the physical length scale, the same quantity may be easier to read as microcoulombs per metre, coulombs per centimetre, or microcoulombs per millimetre. A converter is useful because changing the charge prefix and the denominator length at the same time is easy to misread under pressure.
λ = Q / L
Linear charge density equals total charge divided by the length over which that charge is distributed.
1 C/cm = 100 C/m
A centimetre is one hundredth of a metre, so per-centimetre values are one hundred times larger than the corresponding per-metre values.
1 C/mm = 1000 C/m
A millimetre is one thousandth of a metre, so per-millimetre values are one thousand times larger than the equivalent per-metre value.
How the conversion works
The safest way to convert a line-charge value is to translate the source into one consistent base unit first, then translate that base quantity into the target unit. This page uses coulombs per metre as the internal reference point. Every supported unit has a known relationship to that base unit.
For example, converting from `µC/cm` to `C/m` requires two shifts at once: one for the micro prefix and one for the centimetre denominator. Instead of doing both in your head, convert the source into coulombs per metre first, then divide or multiply into the target scale. The calculator also lists every supported equivalent so you can spot-check the order of magnitude immediately.
Worked example: 2 µC/cm
Suppose a charged line is reported as `2 µC/cm`. One microcoulomb is `10^-6` coulombs, and one centimetre is `0.01` metres. That means `2 µC/cm` is `2 × 10^-6 C / 0.01 m`, which simplifies to `2 × 10^-4 C/m`, or `0.0002 C/m`.
That same quantity can also be written as `0.2 mC/m`, `200 µC/m`, or `0.2 µC/mm`. Seeing all of those equivalents side by side is often the fastest way to confirm you shifted the denominator correctly and did not accidentally reverse the length conversion.
When to prefer metre, centimetre, or millimetre units
Use metre-based units when you want the clearest SI reference point or when the rest of the problem is written in metres. Use centimetre- or millimetre-based units when the physical geometry is short enough that metre-based values would force awkward decimals or very small prefixes.
The best reporting unit is usually the one that keeps the number readable without hiding the real scale. For example, a very small metre-based value may be easier to compare as `µC/m`, while a short-geometry setup may be easier to discuss as `µC/cm` or `mC/mm`. The converter is there to help you compare those presentations, not to imply that one unit is always universally better.
Frequently asked questions
What is the formula for linear charge density?
The standard formula is `λ = Q / L`, where `Q` is charge and `L` is length. The result tells you how much charge is distributed per unit length.
Why does C/cm look much larger than C/m?
Because one centimetre is shorter than one metre. If the same total charge is spread over one centimetre instead of one metre, the per-unit-length number becomes larger. Numerically, `1 C/cm` equals `100 C/m`.
How do I convert µC/cm to C/m?
Convert the microcoulomb prefix into coulombs and the centimetre denominator into metres. Since `1 µC = 10^-6 C` and `1 cm = 0.01 m`, `1 µC/cm = 10^-4 C/m`.
Is linear charge density the same as surface or volume charge density?
No. Linear charge density is charge per unit length, surface charge density is charge per unit area, and volume charge density is charge per unit volume. They describe different dimensional distributions of charge.
