Calculate dielectric permittivity, capacitance, electric field, and energy storage for parallel plate and cylindrical capacitors. Material database with 30+ dielectrics.
The Permittivity Calculator computes capacitance, electric field strength, and energy storage for capacitors using various dielectric materials. Select from 30+ materials (vacuum, air, glass, ceramics, polymers, water) and enter your geometry to get complete electrical analysis. It is meant to connect the material choice directly to the electrical behavior you actually care about.
Permittivity (ε) measures a material's ability to store electrical energy in an electric field. Higher permittivity = more charge storage for the same geometry. The relative permittivity εᵣ (dielectric constant) compares a material to free space (ε₀ = 8.854 × 10⁻¹² F/m). Vacuum has εᵣ = 1, water ≈ 80, and high-k ceramics can exceed 10,000.
Enter the capacitor geometry (parallel plate or cylindrical), select a dielectric material from the database, and specify the applied voltage. The calculator shows capacitance, stored charge, electric field intensity, stored energy, and whether the field exceeds the material's dielectric breakdown strength.
Use this calculator when you need the actual capacitor behavior from a material and geometry instead of a generic dielectric label. It is useful for electronics, energy storage, and physics work where permittivity, field strength, and breakdown need to be checked together. That makes it easier to compare materials without losing sight of voltage limits.
Parallel plate: C = ε₀εᵣA/d. Cylindrical: C = 2πε₀εᵣL/ln(b/a). Charge: Q = CV. Electric field: E = V/d. Energy: U = ½CV². Permittivity: ε = ε₀εᵣ. ε₀ = 8.854×10⁻¹² F/m.
Result: C = 21.25 pF, Q = 21.25 nC, U = 10.63 μJ
Polyethylene (εᵣ = 2.4) parallel plate: C = 8.854e-12 × 2.4 × 100e-4 / 0.1e-3 = 21.25 pF. At 1000V: Q = 21.25 nC. E = 1000/0.0001 = 10 MV/m (below breakdown of 20 MV/m ✓). Energy = 0.5 × 21.25e-12 × 1000² = 10.63 μJ.
Permittivity connects three fundamental electromagnetic quantities: electric field (E), electric flux density (D), and polarization (P) via D = ε₀E + P = εE. When a dielectric is placed in an electric field, bound charges in the material polarize, creating an internal field that partially cancels the external field. Higher permittivity materials polarize more strongly.
The permittivity of free space ε₀ = 8.854 × 10⁻¹² F/m is one of the fundamental constants of physics, appearing in Coulomb's law, Maxwell's equations, and the speed of light (c = 1/√(ε₀μ₀)). All electromagnetic phenomena ultimately derive from ε₀ and μ₀.
Engineering materials span a vast range of permittivities. Low-εᵣ materials (air, Teflon, polyethylene at 1-2.4) serve as insulators and low-loss transmission line substrates. Medium-εᵣ materials (glass, alumina at 4-10) are used in printed circuit boards, capacitors, and insulators. High-εᵣ materials (titanates, ferroelectrics at 100-10,000) enable tiny yet high-capacitance MLCCs for electronics.
Material selection involves trade-offs: high-εᵣ ceramics offer great capacitance but often have high dielectric loss (tanδ), voltage dependence, and temperature sensitivity. Low-loss materials (PTFE, sapphire) are preferred for microwave and precision applications despite lower εᵣ.
The energy stored in a capacitor is U = ½CV² = ½εE²×Volume. This shows that energy density depends on both permittivity and the square of the electric field. High-energy-density capacitors need materials with both high εᵣ AND high dielectric strength — a challenging combination since high-εᵣ materials often have lower breakdown fields. Film capacitors (polypropylene) can handle very high fields (200+ MV/m) despite moderate εᵣ (~2.2), making them competitive for pulsed power applications.
Permittivity (ε) is a material property that describes how much electric flux is generated per unit charge in that medium. Higher permittivity = more charge storage for the same voltage and geometry. It has units F/m (farads per meter). ε = ε₀ × εᵣ, where ε₀ is the permittivity of free space and εᵣ is the relative permittivity (dielectric constant).
The dielectric constant (relative permittivity) is the ratio of a material's permittivity to free space: εᵣ = ε/ε₀. It is dimensionless and always ≥ 1. Vacuum: 1. Air: 1.0006. Paper: 3.5. Glass: 4-10. Ceramics: 10-10,000. Water: 80. Barium titanate: 1,000-10,000.
When the electric field exceeds a material's dielectric strength, the insulator fails and conducts — this is dielectric breakdown. It can destroy capacitors and electronics. Air breaks down at ~3 MV/m (lightning!). Polymers: 10-30 MV/m. Glass: 10-40 MV/m. Always design with a safety margin (typically 50% of rated breakdown).
Water molecules are strongly polar (permanent dipole moment). In an electric field, they align to oppose the field, reducing the net field and allowing more charge storage. This makes water excellent for energy storage but poor for most electronics applications (it's also conductive due to dissolved ions).
High-k: materials with high εᵣ (>10) used to increase capacitance in smaller components. Examples: HfO₂ (εᵣ ≈ 25) in modern transistor gates, barium titanate (≈1000) in MLCCs. Low-k: materials with low εᵣ (<3) used as insulation in ICs to reduce parasitic capacitance and signal delay. Examples: SiO₂ (3.9), fluorinated polymers (<2.5).
Most dielectrics see εᵣ decrease at higher temperatures as molecular motion disrupts alignment. Ferroelectric materials (BaTiO₃) show sharp peaks near the Curie temperature. Water's εᵣ drops from 80 at 20°C to 55 at 100°C. Temperature coefficients matter for precision capacitor design.