Surface Charge Density Converter

How to use the calculator

1. Enter a nonnegative number in Surface charge density. The default is 0.000001.
2. Choose the unit of that number in From unit. The default is C/m².
3. Choose the unit you need in To unit. The default is µC/m².
4. Read Converted Surface Charge Density. The unit appears alongside the converted number.

You can select the same unit in both menus to leave the value unchanged. If your source gives a value in scientific notation, you can enter it that way—for example, 1e-6 for 0.000001—if your browser accepts that notation in the number field.

What surface charge density means

Surface charge density describes how much electric charge is associated with a unit area of a surface. Its SI unit is coulombs per square meter (C/m²). For charge spread uniformly over an area, the density is the total charge divided by that area: \(\sigma=Q/A\). If the charge varies across the surface, the density at a particular point describes the charge per unit area near that point. Converting units does not determine how the charge is distributed.

The quantity is useful when describing charged plates, conductor surfaces, insulating films, and interfaces in electrostatic models. For example, 1 µC/m² and 0.000001 C/m² describe the same density. The larger-looking number in µC/m² does not mean that more charge is present; a microcoulomb is one millionth of a coulomb. Keeping units consistent matters when combining a density with an area or using it in an electric-field calculation.

Surface charge density is not the same as electric current, which measures charge flowing per unit time. If you need to change current units, use the Electric Current converter. Likewise, Linear Current Density concerns current per unit length, not stored charge per unit area; its units cannot be converted directly to C/m².

Supported units and conversion factors

Each factor below gives the number of C/m² in one unit. The calculator multiplies by the factor for From unit and divides by the factor for To unit.

• C/m²: 1 C/m²; the SI unit.
• µC/m²: \(10^{-6}\) C/m² per µC/m².
• nC/m²: \(10^{-9}\) C/m² per nC/m².
• pC/m²: \(10^{-12}\) C/m² per pC/m².
• esu/cm²: approximately \(3.33564\times10^{-5}\) C/m² per esu/cm². Here, esu denotes a statcoulomb, a unit from the CGS electrostatic system.

The area unit remains square meters for the first four choices. In esu/cm², both the charge unit and the area unit differ, so replacing only the charge prefix would give an incorrect conversion. This converter does not offer nC/cm² or other per-square-centimeter units.

Assumptions and practical limits

The Surface charge density field has a minimum of zero. Physical surface charge density can be negative, but this calculator is set up for nonnegative inputs, so it cannot directly convert a signed negative value. To convert the magnitude of a negative density, enter its positive magnitude and retain the negative sign when reporting the result separately. Zero converts to zero in every supported unit.

The esu/cm² factor used by the calculator is rounded to 3.33564 × 10⁻⁵ C/m². Conversions involving esu/cm² are therefore approximate. The calculator also rounds its displayed numerical result to ten decimal places. A very small nonzero result—for example, 1 pC/m² converted to C/m²—may consequently display as zero. If that happens, keep the value in a smaller unit or calculate with scientific notation when the small magnitude matters.

A unit conversion alone does not tell you the total charge on a surface. For a uniform density, multiply the density in C/m² by the area in m² to obtain charge in coulombs. For a nonuniform density, the charge must instead be summed over the surface. Check the area units and whether the supplied density represents the whole surface or only a local region before using the converted value.