0.000000000089
F
88.542
pF
0.088542
nF
88.542
pF
1
×
0.000000000089
F
88.542
pF
0.088542
nF
88.542
pF
1
×
The Capacitance Calculator determines the capacitance of three common capacitor geometries: parallel plate, cylindrical, and spherical. Capacitance is a measure of a device's ability to store electric charge and energy. Defined as the ratio of charge to voltage, $$C = \frac{Q}{V}$$, capacitance depends solely on the geometry of the conductors and the properties of the dielectric material between them. For a parallel plate capacitor: $$C = \varepsilon_0 \kappa \frac{A}{d}$$. For a cylindrical capacitor: $$C = \frac{2\pi\varepsilon_0 \kappa L}{\ln(b/a)}$$. For a spherical capacitor: $$C = \frac{4\pi\varepsilon_0 \kappa ab}{b - a}$$. Capacitors are fundamental components in electronics, used for energy storage, filtering, timing circuits, power factor correction, and signal coupling. This calculator supports dielectric materials through the relative permittivity factor κ, which amplifies capacitance above the vacuum value.
Each capacitor geometry has a distinct formula derived from Gauss's Law and the relationship between electric field, potential, and charge:
The dielectric constant κ (relative permittivity) accounts for the insulating material: vacuum (κ = 1), air (κ ≈ 1.0006), paper (κ ≈ 3.5), glass (κ ≈ 5–10), ceramic (κ ≈ 20–15000). Inserting a dielectric increases capacitance by a factor of κ because the dielectric partially cancels the internal electric field, allowing more charge to be stored at the same voltage.
The capacitance result tells you how many coulombs of charge the capacitor stores per volt of applied voltage. Typical capacitor values range from picofarads (pF, 10⁻¹² F) in RF circuits to millifarads (mF) in power supplies. The three unit outputs (F, nF, pF) let you quickly read the value in the most convenient unit. The formula used output confirms which geometry equation was applied. Increasing the plate area or dielectric constant increases capacitance, while increasing the separation decreases it. For cylindrical and spherical capacitors, bringing the conductors closer together (making a closer to b) dramatically increases capacitance.
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A parallel plate capacitor with 100 cm² plates, 1 mm separation, and glass dielectric (κ = 7) has a capacitance of about 620 pF. Without the glass dielectric, it would be only 88.5 pF — the glass increases capacitance sevenfold.
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A 1-meter coaxial cable with polyethylene dielectric (κ = 2.3), 1 mm inner radius, and 4 mm outer radius has about 92 pF of capacitance. Standard RG-6 coaxial cable has approximately 68 pF/m, close to this calculation.
Capacitance (C) is the ability of a system to store electric charge per unit voltage: C = Q/V. The SI unit is the farad (F), where 1 farad = 1 coulomb per volt. Capacitance depends only on the geometry of the conductors and the dielectric material between them — not on the charge or voltage applied. One farad is an extremely large capacitance; practical capacitors range from picofarads to millifarads.
A dielectric is an insulating material placed between capacitor plates. It increases capacitance by a factor of κ (the relative permittivity or dielectric constant). This happens because the dielectric becomes polarized in the electric field, creating internal dipoles that partially cancel the field. This allows more charge to accumulate on the plates for the same voltage. Common dielectrics include air (κ ≈ 1), paper (κ ≈ 3.5), glass (κ ≈ 5–10), and high-κ ceramics (κ up to 15,000).
The maximum voltage is limited by the dielectric breakdown voltage — the electric field strength at which the insulating material conducts. For air, breakdown occurs at about 3 × 10⁶ V/m. The breakdown voltage of a parallel plate capacitor is approximately V_max = E_breakdown × d. Exceeding this voltage causes the dielectric to fail, often catastrophically. Rated voltage in datasheets includes a safety margin below the breakdown point.
In parallel: capacitances add directly (C_total = C₁ + C₂ + ...) because the voltage is the same across each. In series: reciprocals add (1/C_total = 1/C₁ + 1/C₂ + ...) because the charge is the same on each. Parallel combination always increases total capacitance; series combination always decreases it. This is opposite to how resistors combine.
A 1-farad parallel plate capacitor with 1 mm plate separation (in vacuum) would need plates with an area of about 113 million square meters — roughly the size of a small country. This is because ε₀ = 8.854 × 10⁻¹² F/m is extremely small. Modern supercapacitors achieve farad-level capacitance by using enormous effective surface areas (activated carbon) and nanometer-scale charge separation.
An isolated conducting sphere of radius a has capacitance C = 4πε₀a. This is the spherical capacitor formula with the outer radius b → ∞. The Earth (radius 6371 km) has a capacitance of about 710 μF. This concept is important in understanding lightning rods, Van de Graaff generators, and the self-capacitance of conductors in high-frequency circuits.
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