Convert surface charge density between coulomb/m², coulomb/cm² and microcoulomb units.
Electricity • 5 units
All 5 units on the Surface Charge Density Converter are defined against the Coulomb/meter² (C/m²), so each result is one conversion factor away from a single reference rather than the end of a chain of roundings.
The conversion this page is most often opened for is ready before you type anything: 1 C/m² = 1,000,000 µC/m². Change either side and every row in the table recalculates with it.
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Because the length unit is squared, the steps in this table are larger than they look: one coulomb per square centimetre is ten thousand coulombs per square metre, and one coulomb per square inch is about 1,550. Applying the factor once rather than twice is the characteristic error here, and it produces a result that is wrong by exactly the square root of the intended factor — close enough to be plausible and far enough to matter.
A capacitor makes the quantity tangible. Charge sits on the plates rather than passing through the dielectric, so a 1 µF capacitor charged to 10 V holds 10 µC, and spreading that over a square metre of plate gives 10 µC/m². The field the insulator has to survive follows directly from the charge density and the permittivity between the plates, which is why extra capacitance is bought with plate area rather than by raising the voltage: more area stores more charge at the same field.
There is also a natural ceiling to how much charge a free surface in air can hold. Air breaks down at roughly 3 MV/m, and the surface charge density corresponding to that field is about 26.6 µC/m² — so a charged sheet of plastic or a moving web cannot accumulate much beyond that before the surrounding air ionises and carries the excess away. This is why static control in industry is specified through surface resistivity in ohms per square and charge-decay time rather than by targeting a charge density directly: the density largely takes care of its own upper bound, and the useful control is how quickly it drains.
Quick reference — 1 Coulomb/meter² (C/m²) is equal to:
| Millicoulomb/meter² | mC/m² | 1,000 |
| Microcoulomb/meter² | µC/m² | 1,000,000 |
| Coulomb/centimeter² | C/cm² | 0.0001 |
| Coulomb/inch² | C/in² | 0.00064516 |
Surface charge density describes charge spread over an area — coulombs per square metre — and it is the quantity that governs behaviour at boundaries. On a conductor in electrostatic equilibrium all excess charge migrates to the surface, so surface density is what determines the external field: it is exactly σ/ε₀ just outside a conductor. That relationship explains why charge concentrates at sharp points, where a small radius forces a high surface density, and why lightning rods are pointed rather than blunt. It is also the density that matters in capacitor plates, electrophotography and electrostatic discharge, where the concern is always what happens at an interface rather than inside a volume.
σ = Q ÷ AField just outside a conductor: E = σ ÷ ε₀1 C/m² = 10⁻⁴ C/cm² = 10⁶ µC/m²ε₀ = 8.854 × 10⁻¹² F/mwhere:
Assumptions: Assumes charge is uniformly distributed, which holds for a flat plate and fails at edges and points, where density rises sharply. On a real conductor the distribution is set by geometry, not by choice.
Find the surface charge density on a capacitor plate and the field it produces.
Resultσ = 5.0 × 10⁻⁵ C/m² (50 µC/m²)
The breakdown check is the practical point of computing σ rather than total charge: dielectric failure depends on field strength at the surface, which depends on charge per unit area, not on how much charge the device holds in total.
Surface charge density is charge per unit area, in coulombs per square metre. The conversions are steeper than they first appear because the length unit is squared: coulombs per square centimetre are ten thousand times larger than coulombs per square metre, and coulombs per square inch about 1,550 times larger. A factor applied once instead of twice is the standard error in this family.
The quantity is what makes a capacitor work. Charge accumulates on the plates rather than through the dielectric, so it is the charge per unit area, together with the permittivity of the material between, that sets the field the insulator has to withstand. Increasing plate area at fixed voltage stores more charge without raising that field, which is why capacitance is bought with area rather than with voltage rating.
It also explains why sharp edges are dangerous. Charge on a conductor distributes itself unevenly, concentrating where the surface curves most tightly, so a point carries a far higher surface charge density than a flat face at the same potential. The field just outside the surface rises with it, which is why corona discharge starts at edges and pins, why high-voltage hardware is built with generous radii, and why a lightning conductor is pointed rather than blunt.