This surface charge density converter changes charge per unit area between coulombs per square meter, per square centimeter and per square inch, and abcoulombs per square centimeter. Formula: 1 C/cm² = 10000 C/m²; 1 µC/cm² = 0.01 C/m². The SI unit is C/m². 1 C/cm² is exactly 10,000 C/m², and 1 µC/cm² equals 0.01 C/m², a unit common in ferroelectrics and electrochemistry.
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How to use the surface charge density converter
- Enter the value, for example 0.02 C/m².
- In the surface charge density converter, choose its unit and the target unit, such as C/m² to C/cm².
- Read the surface charge density converter result: 0.02 C/m² = 0.000002 C/cm² = 2 µC/cm².
For C/m² to µC/cm², multiply by 100; for µC/cm² to C/m², divide by 100. For C/in² to C/m², multiply by 1,550.0031.
What is surface charge density?
Surface charge density is electric charge per unit area, in coulombs per square meter (C/m²). It is used for capacitor plates, membranes and electrostatics.
Conversion formula
The surface charge density converter stores every unit as a multiple of the base unit, the coulomb per square meter (C/m²). To convert:
value in target unit = value × (factor of source unit ÷ factor of target unit)
where each factor is the size of the unit in coulombs per square meter.
Common surface charge density conversions
| From | To | 1 unit equals |
|---|---|---|
| coulomb per square meter (C/m²) | coulomb per square centimeter (C/cm²) | 0.0001 C/cm² |
| coulomb per square centimeter (C/cm²) | coulomb per square meter (C/m²) | 10,000 C/m² |
Surface charge density converter worked example
Convert 25 coulombs per square meter to coulombs per square centimeter:
- Factor of C/m² = 1 C/m²
- Factor of C/cm² = 10,000 C/m²
- 25 × 1 ÷ 10,000 = 0.0025 C/cm²
Surface charge density unit reference
| Unit | Symbol | Group | Equals (C/m²) |
|---|---|---|---|
| Coulomb per Square Meter | C/m² | SI | 1 |
| Coulomb per Square Centimeter | C/cm² | SI | 10,000 |
| Coulomb per Square Inch | C/in² | US/Imperial | 1,550.0031 |
| Abcoulomb per Square Centimeter | abC/cm² | CGS-EMU | 100,000 |
Reverse factors for each surface charge density unit
The reference table gives each unit in coulomb per square meters. To go the other way, divide by that factor; the list below does the division for you.
- Coulomb per Square Centimeter (C/cm²), SI: 1 C/cm² = 10,000 C/m², so 1 C/m² = 0.0001 C/cm².
- Coulomb per Square Inch (C/in²), US/Imperial: 1 C/in² = 1,550.003 C/m², so 1 C/m² = 0.00064516 C/in².
- Abcoulomb per Square Centimeter (abC/cm²), CGS-EMU: 1 abC/cm² = 100,000 C/m², so 1 C/m² = 1 × 10−5 abC/cm².
Field at a charged plate
Just outside a charged conductor, the field is E = σ ÷ ε₀, with ε₀ ≈ 8.8541878188 × 10⁻¹² F/m. Between the plates of an ideal parallel-plate capacitor the field takes the same value. For an isolated thin sheet it is half that, σ ÷ (2ε₀):
| σ (µC/cm²) | σ (C/m²) | E = σ/ε₀ (V/m) |
|---|---|---|
| 0.001 | 0.00001 | 1.13 × 10⁶ |
| 0.01 | 0.0001 | 1.13 × 10⁷ |
| 0.1 | 0.001 | 1.13 × 10⁸ |
Air breaks down at roughly 3 × 10⁶ V/m, so a conductor in air cannot hold much more than about 26.6 µC/m² before sparking.
Surface charge on a capacitor
For a parallel-plate capacitor, σ = Q ÷ A = ε V ÷ d. A 1 cm² air capacitor with a 1 mm gap at 100 V has σ ≈ 8.85 × 10⁻⁷ C/m² and holds Q ≈ 8.85 × 10⁻¹¹ C. Convert the total charge with the electric charge converter and capacitance with the capacitance converter.
The limit set by air
A charged surface in air cannot hold an unlimited charge. The field just outside a conductor is σ ÷ ε₀, and dry air breaks down at roughly 3 MV/m. Setting σ = ε₀ × 3 × 10⁶ V/m gives about 26.6 µC/m². The surface charge density converter shows that as about 2.66 nC/cm². Beyond that, sparks or corona discharge carry charge away.
This is a useful sanity check for static electricity problems. If your calculation gives a charge density many times higher on an object in open air, something in the units is off. Sharp points reach breakdown sooner because the field concentrates there, which is how lightning rods and ionizers work.
Humidity lowers the charge a surface can keep, since moist air and surface films leak it away.
Related converters and calculators
Related electrical tools:
- Linear charge density converter: C/m
- Volume charge density converter: C/m³
- Electric charge converter: C and mAh
- Electric field strength converter: V/m
- Capacitance converter: F, µF, pF
Sources
NIST CODATA: Vacuum electric permittivity; NIST Special Publication 811, Appendix B.
Questions about this calculator
What is the SI unit of surface charge density?
Coulomb per square meter (C/m²).
How do I convert C/m² to µC/cm²?
Multiply by 100. For example, 0.05 C/m² = 5 µC/cm².
How do I convert µC/cm² to C/m²?
Divide by 100. For example, 30 µC/cm² = 0.3 C/m².
How do I convert C/cm² to C/m²?
Multiply by 10,000.
What field does a charged plate produce?
E = σ ÷ ε₀ just outside a conductor; σ ÷ 2ε₀ for an isolated thin sheet.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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