Surface Charge Density Converter
Convert surface charge density, the electric charge carried per unit of area, between coulomb per square meter, coulomb per square centimeter, coulomb per square 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.
Surface charge density is charge per area (C/m²). It is not linear charge density (C/m), not volume charge density (C/m³) and not total charge (C).
Surface Charge Density Formula
Surface charge density is charge divided by area: σ = Q ÷ A, in C/m². Every unit is a fixed multiple of C/m². Result = value × (source factor ÷ target factor). Area scales with the square of length, so 1 cm² = 10⁻⁴ m² and 1 C/cm² = 10,000 C/m². Exact building blocks: 1 in² = 0.00064516 m² and 1 abcoulomb = 10 C.
What Is Surface Charge Density?
Surface charge density, usually written σ (sigma), is the amount of electric charge spread over a surface, per unit of area. It is the natural description of the charge on a capacitor plate, on the surface of a conductor, on a charged membrane or on a sheet of insulating film. Its SI unit is the coulomb per square meter (C/m²).
If a plate of 0.02 m² carries 40 nC of charge spread evenly, its surface charge density is 40 nC ÷ 0.02 m² = 2 µC/m². The total charge on a surface is the density times the area, Q = σ × A. For a large flat sheet, the electric field next to the surface follows directly from σ: it is σ ÷ (2ε₀) for an isolated sheet, and σ ÷ ε₀ just outside the surface of a conductor.
The units here pair a charge unit (the coulomb or the abcoulomb of the CGS electromagnetic system) with an area unit (square meter, square centimeter or square inch). Area scales with the square of length, so changing the area unit changes the number faster than a length unit would: 1 C/cm² is 10,000 times 1 C/m², and 1 C/in² is about 1,550 times 1 C/m².
Do not confuse it with other quantities. Linear charge density is charge per length (Linear Charge Density Converter), volume charge density is charge per volume (Volume Charge Density Converter) and total charge is in coulombs (Charge Converter). Surface charge density is also not surface current density, which is current per area.
Supported Units
This converter supports the following 6 surface charge density units. The last column gives the value of each unit in the base unit, C/m².
| Unit | Symbol | Value in C/m² |
|---|---|---|
| Coulomb per square meter | C/m² | 1 |
| Coulomb per square centimeter | C/cm² | 10,000 |
| Coulomb per square inch | C/in² | 1,550.0031 |
| Abcoulomb per square meter | abC/m² | 10 |
| Abcoulomb per square centimeter | abC/cm² | 100,000 |
| Abcoulomb per square inch | abC/in² | 15,500.031 |
How to Use the Surface Charge Density Converter
- Type the surface 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/m²): 1 C/cm² = 10,000 C/m² and 1 C/m² = 1 C/m².
- Divide the source size by the target size to get the conversion factor: 10,000 ÷ 1 = 10,000, so 1 C/cm² = 10,000 C/m².
- Multiply by your value: 0.002 C/cm² × 10,000 = 20 C/m².
Charge density can be positive or negative, so a minus sign is accepted. Zero is also valid.
Common Surface Charge Density Conversions
- Per square centimeter to per square meter: 0.002 C/cm² equals 20 C/m².
- Per square inch to per square meter: 3 C/in² equals 4,650.0093 C/m².
- CGS to SI: 5 abC/cm² equals 500,000 C/m².
- Square inch to square centimeter: 1 C/in² equals 0.15500031 C/cm².
- Same charge, different area: 1 abC/m² equals 0.0001 abC/cm².
- Small value: 0.0001 C/m² equals 6.4516e-8 C/in².
C/m² to Other Surface Charge Density Units
Quick reference for frequently used values
| C/m² | C/cm² | C/in² | abC/m² |
|---|---|---|---|
| 0.001 | 1e-7 | 6.4516e-7 | 0.0001 |
| 0.01 | 1e-6 | 6.4516e-6 | 0.001 |
| 0.1 | 1e-5 | 6.4516e-5 | 0.01 |
| 1 | 0.0001 | 0.00064516 | 0.1 |
| 5 | 0.0005 | 0.0032258 | 0.5 |
| 10 | 0.001 | 0.0064516 | 1 |
| 100 | 0.01 | 0.064516 | 10 |
Where and Why This Conversion Is Used
- Capacitors: charge per unit plate area sets the field and the stored energy in a parallel-plate capacitor.
- Conductors and shielding: the surface charge on a conductor determines the field just outside it.
- Electrochemistry and colloids: the charge on an electrode or a particle surface, and the electrical double layer.
- Electrets, films and printers: charge held on photoconductor drums and polymer films.
- Reading older literature: CGS texts give surface charge in abcoulombs per square centimeter.
Limitations
- The value describes a uniform distribution over a surface. It gives the total charge only when the area is known.
- Only per-area units are offered here. Prefixed versions such as µC/m² are not in the supported list, so enter the value in C/m² using scientific notation, for example 2e-6.
Important Differences Between Related Electrical Measurements
- Surface charge density, C/m² is charge per area. Total charge, C is the density multiplied by the area: 2 µC/m² over 0.02 m² is 40 nC.
- Surface vs linear vs volume density: C/m², C/m and C/m³ spread charge over a surface, along a line and through a volume. They have different dimensions and cannot be converted into each other without a geometry.
- Surface charge density vs surface current density: the first is coulombs per square meter, the second is amperes per square meter. One is an amount per area, the other a rate per area.
- Surface charge density vs electric field: the density is the source. The field it produces, in V/m, depends on the geometry and the surrounding material.
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.