Calculate capacitance for parallel plate, cylindrical, and spherical capacitors. Dielectric materials, stored charge, energy, and electric field.
Capacitance is the ability of a system to store electric charge per unit voltage. The simplest and most common geometry is the parallel plate capacitor, where C = κε₀A/d — capacitance is proportional to plate area and dielectric constant, and inversely proportional to plate separation.
Dielectric materials between the plates increase capacitance by a factor equal to the dielectric constant (κ). Vacuum has κ = 1, while ceramic materials like barium titanate can have κ in the thousands, enabling tiny but high-value capacitors for electronics.
This calculator handles three capacitor geometries: parallel plate (most common), cylindrical (coaxial cables), and spherical (theoretical and some sensors). It computes capacitance in multiple units, stored charge and energy, and the electric field between the plates. A built-in dielectric material database makes it easy to compare materials for capacitor design. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Capacitor design requires balancing geometry, dielectric material, voltage rating, and physical size. Calculating capacitance for different geometries involves different formulas with different unit conventions, making manual calculation error-prone.
This calculator handles all three standard geometries with automatic unit conversion, dielectric material lookup, and derived quantities (charge, energy, electric field). It is valuable for electronics designers, physics students, and engineers selecting or designing capacitors for specific applications.
Parallel plate: C = κε₀A/d. Cylindrical: C = 2πκε₀/ln(b/a) per unit length. Spherical: C = 4πκε₀ab/(b−a). Q = CV, E = ½CV², Electric field = V/d.
Result: 88.5 pF
A parallel plate capacitor with 0.01 m² plates separated by 1 mm of air has C = (1 × 8.854×10⁻¹² × 0.01) / 0.001 = 88.5 pF. At 12V, it stores 1.06 nC of charge and 6.37 nJ of energy.
The parallel plate geometry is the foundation of most practical capacitors. The idealized formula C = κε₀A/d assumes infinite plates with uniform field between them. In reality, fringing fields at the edges increase the effective capacitance slightly, and the field is not perfectly uniform near the edges.
Modern multi-layer ceramic capacitors (MLCCs) use this geometry with hundreds of interleaved electrode layers and ceramic dielectric layers only a few micrometers thick. A single 0402-size MLCC (1mm × 0.5mm) can achieve 10 µF by stacking 400+ layers of high-κ ceramic.
Cylindrical capacitors appear in coaxial cables, where the capacitance per unit length determines signal propagation characteristics. A typical RG-6 coaxial cable has about 67 pF/m capacitance, which affects bandwidth and impedance.
Spherical capacitors are less common in practice but important in theoretical physics. The Earth itself acts as a spherical capacitor with C ≈ 710 µF, and the concept is used in Van de Graaff generators and some specialized sensors.
Capacitors store energy in the electric field between their plates. The energy density is ½κε₀E², where E is the electric field strength. This means energy storage increases with both dielectric constant and field strength. Supercapacitors achieve extremely high energy density by using porous carbon electrodes with nanometer-scale separation and ionic electrolytes, achieving effective surface areas of 1000+ m² per gram.
Capacitance is the ratio of charge stored to voltage applied: C = Q/V. It depends on the physical geometry and dielectric material, not on voltage or charge.
A dielectric material polarizes in the electric field, effectively reducing the field strength for a given charge. This allows more charge to be stored at the same voltage, increasing capacitance by a factor of κ.
ε₀ (epsilon naught) is the permittivity of free space, equal to 8.854 × 10⁻¹² F/m. It relates electric field strength to charge distribution in a vacuum.
Closer plates create a stronger electric field for the same voltage, allowing more charge to accumulate on each plate. However, the dielectric breakdown voltage also decreases with distance.
The dielectric breakdown strength limits the maximum voltage. Air breaks down at about 3 kV/mm, while solid dielectrics can withstand 10-40 kV/mm depending on the material.
Ceramic capacitors use materials with κ of 1000-14000 and extremely thin layers (micrometers). Multi-layer ceramic capacitors (MLCCs) stack hundreds of layers to multiply the capacitance further.