Volume Charge Density Converter
Convert volume charge density, the electric charge contained in a unit of volume, between coulomb per cubic meter, coulomb per cubic centimeter, coulomb per cubic 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.
Volume charge density is charge per volume (C/m³). It is not linear charge density (C/m), not surface charge density (C/m²) and not total charge (C).
Volume Charge Density Formula
Volume charge density is charge divided by volume: ρ = Q ÷ V, in C/m³. Every unit is a fixed multiple of C/m³. Result = value × (source factor ÷ target factor). Volume scales with the cube of length, so 1 cm³ = 10⁻⁶ m³ and 1 C/cm³ = 1,000,000 C/m³. Exact building blocks: 1 in³ = 1.6387064 × 10⁻⁵ m³ and 1 abcoulomb = 10 C.
What Is Volume Charge Density?
Volume charge density, usually written ρ (rho), is the amount of electric charge contained in a unit of volume. It describes charge spread through a three-dimensional region: the space charge in a vacuum tube or an ion beam, the net charge in a plasma or an electrolyte, the depletion region of a semiconductor junction or the charge inside a thundercloud. Its SI unit is the coulomb per cubic meter (C/m³).
If a region of 0.5 m³ holds a net charge of 1 mC, its volume charge density is 1 mC ÷ 0.5 m³ = 2 mC/m³. The total charge in a region is the density times the volume, Q = ρ × V. Gauss’s law links ρ to the electric field: the divergence of the field equals ρ ÷ ε₀.
The units here pair a charge unit (the coulomb or the abcoulomb of the CGS electromagnetic system) with a volume unit (cubic meter, cubic centimeter or cubic inch). Volume scales with the cube of length, so the numbers change quickly between units: 1 C/cm³ is a million times 1 C/m³, and 1 C/in³ is about 61,024 times 1 C/m³.
Do not confuse it with other quantities. Linear charge density is per length (Linear Charge Density Converter), surface charge density is per area (Surface Charge Density Converter) and total charge is in coulombs (Charge Converter). Volume charge density is also not the charge concentration of chemistry, which counts particles or moles per volume.
Supported Units
This converter supports the following 6 volume charge density units. The last column gives the value of each unit in the base unit, C/m³.
| Unit | Symbol | Value in C/m³ |
|---|---|---|
| Coulomb per cubic meter | C/m³ | 1 |
| Coulomb per cubic centimeter | C/cm³ | 1,000,000 |
| Coulomb per cubic inch | C/in³ | 61,023.74409 |
| Abcoulomb per cubic meter | abC/m³ | 10 |
| Abcoulomb per cubic centimeter | abC/cm³ | 10,000,000 |
| Abcoulomb per cubic inch | abC/in³ | 610,237.4409 |
How to Use the Volume Charge Density Converter
- Type the volume 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/m³): 1 C/cm³ = 1,000,000 C/m³ and 1 C/m³ = 1 C/m³.
- Divide the source size by the target size to get the conversion factor: 1,000,000 ÷ 1 = 1,000,000, so 1 C/cm³ = 1,000,000 C/m³.
- Multiply by your value: 0.0003 C/cm³ × 1,000,000 = 300 C/m³.
Charge density can be positive or negative, so a minus sign is accepted. Zero is also valid.
Common Volume Charge Density Conversions
- Per cubic centimeter to per cubic meter: 0.0003 C/cm³ equals 300 C/m³.
- Per cubic inch to per cubic meter: 2 C/in³ equals 122,047.4882 C/m³.
- CGS to SI: 5 abC/cm³ equals 50,000,000 C/m³.
- Cubic inch to cubic centimeter: 1 C/in³ equals 0.06102374409 C/cm³.
- Same charge, different volume: 1 abC/m³ equals 1e-6 abC/cm³.
- Small value: 0.00002 C/m³ equals 2e-11 C/cm³.
C/m³ to Other Volume Charge Density Units
Quick reference for frequently used values
| C/m³ | C/cm³ | C/in³ | abC/m³ |
|---|---|---|---|
| 0.001 | 1e-9 | 1.6387064e-8 | 0.0001 |
| 0.01 | 1e-8 | 1.6387064e-7 | 0.001 |
| 0.1 | 1e-7 | 1.6387064e-6 | 0.01 |
| 1 | 1e-6 | 1.6387064e-5 | 0.1 |
| 5 | 5e-6 | 8.193532e-5 | 0.5 |
| 10 | 1e-5 | 0.00016387064 | 1 |
| 100 | 0.0001 | 0.0016387064 | 10 |
| 1,000 | 0.001 | 0.016387064 | 100 |
Where and Why This Conversion Is Used
- Semiconductor physics: space charge in a p–n junction depletion region sets the built-in field.
- Vacuum electronics and beams: space charge limits the current in electron guns and ion sources.
- Plasma and electrolytes: net charge per volume in a plasma or an ionic solution.
- Atmospheric electricity: charge inside clouds and charged aerosols.
- Electrostatics teaching: Gauss’s law and the Poisson equation are written in terms of ρ.
Limitations
- The value describes a uniform distribution. It gives the total charge only when the volume is known.
- Only per-volume units are offered here. Prefixed versions such as µC/m³ are not in the supported list, so enter the value in C/m³ using scientific notation, for example 2e-6.
Important Differences Between Related Electrical Measurements
- Volume charge density, C/m³ is charge per volume. Total charge, C is the density multiplied by the volume: 2 mC/m³ in 0.5 m³ is 1 mC.
- Volume vs surface vs linear density: C/m³, C/m² and C/m spread charge through a volume, over a surface and along a line. They have different dimensions and cannot be converted into each other without a geometry.
- Volume charge density vs charge concentration: the first is net electric charge per volume. A concentration counts particles or moles per volume and says nothing about the sign or net charge.
- Volume charge density vs electric field: the density is the source. By Gauss’s law the field it produces, in V/m, depends on how the charge is arranged.
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.