Convert volume charge density between coulomb/m³, coulomb/cm³ and microcoulomb units.
Electricity • 5 units
All 5 units on the Volume Charge Density Converter are defined against the Coulomb/meter³ (C/m³), 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/m³ = 1,000,000 µC/m³. Change either side and every row in the table recalculates with it.
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The length unit here is cubed, so the steps are steeper again than for surface density: a coulomb per cubic centimetre is a million coulombs per cubic metre, and a coulomb per cubic inch is about 61,024. Prefix mistakes in this family tend to be obvious because the results become absurd; exponent mistakes tend not to be, which is the more dangerous of the two.
Semiconductor work is where the quantity takes realistic values. A silicon region doped to 10¹⁶ carriers per cubic centimetre carries roughly 1,600 C/m³ of fixed charge once the elementary charge is applied, and it is that space charge, confined to the depletion region of a junction, that sets the region's width and therefore the diode's junction capacitance. A varactor tuning a radio is that relationship being used deliberately: change the reverse bias, change the depletion width, change the capacitance.
Inside a conductor at equilibrium the volume charge density is zero, because mobile charge redistributes itself to the surface, which is why electrostatics problems about metals reduce to surface quantities. Plasmas are the interesting exception in the other direction: electron and ion densities are individually enormous while the net charge density stays close to zero over any distance larger than the Debye length. In both cases the quantity is calculated from theory far more often than it is measured, because Gauss's law relates it directly to the field it produces.
Quick reference — 1 Coulomb/meter³ (C/m³) is equal to:
| Millicoulomb/meter³ | mC/m³ | 1,000 |
| Microcoulomb/meter³ | µC/m³ | 1,000,000 |
| Coulomb/centimeter³ | C/cm³ | 0.000001 |
| Coulomb/inch³ | C/in³ | 0.0000163871 |
Volume charge density measures charge distributed throughout a three-dimensional region — coulombs per cubic metre — and it applies where charge genuinely permeates a material rather than sitting on its skin. That is the situation inside semiconductors, plasmas, electrolytes and dielectrics under polarisation. It is the source term in Gauss's law in differential form, which is why it appears throughout device physics: the depletion region of a p-n junction is described by the fixed dopant charge density left behind when carriers withdraw, and that density sets the junction's width and built-in field.
ρ = Q ÷ VGauss's law (differential): ∇ · E = ρ ÷ ε₀1 C/m³ = 10⁻⁶ C/cm³ = 10⁶ µC/m³Relation to surface density on a thin sheet: σ = ρ × thicknesswhere:
Assumptions: Assumes uniform distribution through the volume. In semiconductors the density varies with position and the local form ρ(x) is used instead. Note that a conductor in equilibrium has zero internal volume charge density — all of it moves to the surface.
Compute volume charge density, then convert it to the equivalent surface density on a thin slab.
Resultρ = 5.0 × 10⁻⁵ C/m³ (50 µC/m³)
The slab conversion shows how the two densities relate: multiplying a volume density by a thickness yields a surface density. Confusing the two is a dimensional error of one power of length, which is large — for the 2 mm slab above, the numbers differ by a factor of 500.
Volume charge density is charge per unit volume, in coulombs per cubic metre, and the conversions cube the length unit rather than squaring it. Coulombs per cubic centimetre are a million times larger than coulombs per cubic metre, and coulombs per cubic inch about 61,024 times larger — steep enough that a misplaced prefix is usually obvious, and a misapplied exponent usually is not.
The quantity matters most where charge genuinely occupies a region rather than sitting on a surface. Inside a conductor at equilibrium it is zero, because mobile charge migrates to the boundary; the interesting cases are semiconductors and plasmas, where it is not. The depletion region of a diode is exactly such a space-charge zone, and its width and the resulting junction capacitance follow directly from the charge density in it, which is why the same quantity underlies both device physics and the varactor tuning a radio.
It also sets the electric field through Gauss's law, which relates the divergence of the field to the local charge density. That relationship is what allows a field to be calculated from a distribution of charge rather than measured, and it is the reason this quantity appears in electrostatics problems far more often than any instrument ever reports it directly.